diff --git "a/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/05-\350\256\276\345\244\207\347\256\241\347\220\206/index.html" "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/05-\350\256\276\345\244\207\347\256\241\347\220\206/index.html" index 682a9227..928b2e25 100644 --- "a/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/05-\350\256\276\345\244\207\347\256\241\347\220\206/index.html" +++ "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/05-\350\256\276\345\244\207\347\256\241\347\220\206/index.html" @@ -528,6 +528,15 @@ + + +
  • + + + 输入输出程序接口,设备驱动程序接口 + + +
    • @@ -1191,6 +1200,61 @@

    I/O控制方式

  • 总结

    • I/O软件层次结构

    + +

    输入输出程序接口,设备驱动程序接口

    + diff --git "a/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-20.png" "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-20.png" new file mode 100644 index 00000000..a3c08eae Binary files /dev/null and "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-20.png" differ diff --git "a/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-21.png" "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-21.png" new file mode 100644 index 00000000..d5939217 Binary files /dev/null and "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-21.png" differ diff --git "a/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-22.png" "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-22.png" new file mode 100644 index 00000000..9c74f784 Binary files /dev/null and "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-22.png" differ diff --git "a/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-23.png" "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-23.png" new file mode 100644 index 00000000..e061b664 Binary files /dev/null and "b/Notebook/\346\223\215\344\275\234\347\263\273\347\273\237/img/image-23.png" differ diff --git "a/Notebook/\346\225\260\345\255\246\345\210\206\346\236\220/06-\344\270\215\345\256\232\347\247\257\345\210\206/index.html" "b/Notebook/\346\225\260\345\255\246\345\210\206\346\236\220/06-\344\270\215\345\256\232\347\247\257\345\210\206/index.html" index 236f55dc..c67a8a05 100644 --- "a/Notebook/\346\225\260\345\255\246\345\210\206\346\236\220/06-\344\270\215\345\256\232\347\247\257\345\210\206/index.html" +++ "b/Notebook/\346\225\260\345\255\246\345\210\206\346\236\220/06-\344\270\215\345\256\232\347\247\257\345\210\206/index.html" @@ -606,6 +606,17 @@ + + @@ -616,6 +627,172 @@ + + + + @@ -955,9 +1132,87 @@

    不定积分

    +

    不定积分的概念和运算法则

    +

    不定积分,微分的逆运算

    +

    定义 6.1.1

    + +

    定义 6.1.2

    + +

    不定积分的线性性质

    +

    定理 6.1.1

    + +

    换元积分法和分部积分法

    +

    换元积分法

    +

    第一类换元积分法

    + +

    第二类换元积分法

    + +

    分部积分法

    + +

    基本积分表

    +

    \(\begin{aligned} + & \int x^\alpha \mathrm{d} x = + \begin{cases} + \frac{1}{\alpha+1} x^{\alpha+1}+C, & \alpha \neq -1, \\ + \ln |x|+C, & \alpha=-1 ; + \end{cases} + & \int \ln x \mathrm{~d} x = x(\ln x-1)+C ; \\ + & \int a^x \mathrm{~d} x = \frac{a^x}{\ln a}+C, \text{ 特别地 } \int \mathrm{e}^x \mathrm{~d} x = \mathrm{e}^x+C ; + & \int \sin x \mathrm{~d} x = -\cos x+C ; \\ + & \int \cos x \mathrm{~d} x = \sin x+C \text{;} + & \int \tan x \mathrm{~d} x = -\ln |\cos x|+C ;\\ + & \int \cot x \mathrm{~d} x = \ln |\sin x|+C \text{;} + & \int \sec x \mathrm{~d} x = \ln |\sec x+\tan x|+C ; \\ + & \int \csc x \mathrm{~d} x = \ln |\csc x-\cot x|+C ; + & \int \operatorname{sh} x \mathrm{~d} x = \operatorname{ch} x+C ; \\ + & \int \operatorname{ch} x \mathrm{~d} x = \operatorname{sh} x+C ; + & \int \frac{\mathrm{d} x}{\sqrt{a^2-x^2}} = \arcsin \frac{x}{a}+C ; \\ + & \int \frac{\mathrm{d} x}{\sqrt{x^2 \pm a^2}} = \ln \left|x+\sqrt{x^2 \pm a^2}\right|+C ; + & \int \frac{\mathrm{d} x}{x^2-a^2} = \frac{1}{2 a} \ln \left|\frac{x-a}{x+a}\right|+C ; \\ + & \int \frac{\mathrm{d} x}{x^2+a^2} = \frac{1}{a} \arctan \frac{x}{a}+C ; + & \int \sqrt{a^2-x^2} \mathrm{~d} x = \frac{1}{2} x \sqrt{a^2-x^2}+\frac{a^2}{2} \arcsin \frac{x}{a}+C ; \\ + & \int \sqrt{x^2 \pm a^2} \mathrm{~d} x = \frac{1}{2}\left(x \sqrt{x^2 \pm a^2} \pm a^2 \ln \left|x+\sqrt{x^2 \pm a^2}\right|\right)+C . +\end{aligned}\)

    +

    有理函数的不定积分及其应用

    diff --git "a/Notebook/\346\234\272\345\231\250\345\255\246\344\271\240/04-\345\244\232\345\217\230\351\207\217\347\272\277\346\200\247\345\233\236\345\275\222/index.html" "b/Notebook/\346\234\272\345\231\250\345\255\246\344\271\240/04-\345\244\232\345\217\230\351\207\217\347\272\277\346\200\247\345\233\236\345\275\222/index.html" index 1589e2ac..beee5035 100644 --- "a/Notebook/\346\234\272\345\231\250\345\255\246\344\271\240/04-\345\244\232\345\217\230\351\207\217\347\272\277\346\200\247\345\233\236\345\275\222/index.html" +++ "b/Notebook/\346\234\272\345\231\250\345\255\246\344\271\240/04-\345\244\232\345\217\230\351\207\217\347\272\277\346\200\247\345\233\236\345\275\222/index.html" @@ -745,6 +745,24 @@ + + +
  • + + + 特征缩放 + + + +
    • + +
  • + + + 学习率 + + +
    • @@ -971,11 +989,24 @@

    多维特征

    多变量梯度下降

    +

    特征缩放

    + +

    学习率

    + diff --git "a/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/01-\347\272\277\346\200\247\346\226\271\347\250\213\347\273\204/index.html" "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/01-\347\272\277\346\200\247\346\226\271\347\250\213\347\273\204/index.html" index e7c5a08e..0891bbc3 100644 --- "a/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/01-\347\272\277\346\200\247\346\226\271\347\250\213\347\273\204/index.html" +++ "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/01-\347\272\277\346\200\247\346\226\271\347\250\213\347\273\204/index.html" @@ -948,6 +948,27 @@ + + + + + + +
  • + + + + + n维度量线性空间 + + + + +
    • + + + + diff --git "a/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/02-\350\241\214\345\210\227\345\274\217/index.html" "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/02-\350\241\214\345\210\227\345\274\217/index.html" index c7c546ce..5f990ae2 100644 --- "a/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/02-\350\241\214\345\210\227\345\274\217/index.html" +++ "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/02-\350\241\214\345\210\227\345\274\217/index.html" @@ -18,7 +18,7 @@ - + @@ -970,6 +970,72 @@ + + +
  • + + + 2.5 Cramer 法则 + + + + + +
    • + +
  • + + + 2.6 行列式按 k 行展开 + + + + +
    • @@ -981,6 +1047,27 @@ + + + + + + +
  • + + + + + n维度量线性空间 + + + + +
    • + + + + @@ -1123,6 +1210,33 @@
    Vandermoode 行列式
    +

    2.5 Cramer 法则

    +

    定理 1

    + +

    定理 2

    + +

    2.6 行列式按 k 行展开

    +

    定义 1

    + +

    定理 1(Laplace定理)

    + diff --git "a/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/03-\347\272\277\346\200\247\347\251\272\351\227\264/index.html" "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/03-\347\272\277\346\200\247\347\251\272\351\227\264/index.html" new file mode 100644 index 00000000..9d388097 --- /dev/null +++ "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/03-\347\272\277\346\200\247\347\251\272\351\227\264/index.html" @@ -0,0 +1,1405 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + n维度量线性空间 - 𝓛𝓳𝔁'𝓟𝓪𝓰𝓮 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + + + + Skip to content + + +
    +
    + +
    + + + + +
    + + +
    + +
    + + + + + + + + + +
    +
    + + + +
    +
    +
    + + + + + + + + + +
    +
    +
    + + + + +
    +
    + + + + + + + +

    n维度量线性空间

    +
      +
    • 向量空间\(K^n\):
      • +
    • 数域\(K\),\(n\in N^*\),令\(K^n=\{(x_1,x_2,\cdots,x_n)|x_i\in K,i=1,2,\cdots,n\}\),称为\(n\)维向量空间
      • +
    • 在\(K^n\)中定义加法和数乘运算
        +
      • 加法:\((x_1,x_2,\cdots,x_n)+(y_1,y_2,\cdots,y_n)=(x_1+y_1,x_2+y_2,\cdots,x_n+y_n)\)
        • +
      • 数乘:\(k(x_1,x_2,\cdots,x_n)=(kx_1,kx_2,\cdots,kx_n)\)
        • +
      +
      • +
    • 运算法则
        +
      • 加法交换律:\(\alpha+\beta=\beta+\alpha\)
        • +
      • 加法结合律:\((\alpha+\beta)+\gamma=\alpha+(\beta+\gamma)\)
        • +
      • 加法单位元:\(\exists 0\in K^n,\forall \alpha\in K^n,\alpha+0=\alpha\)
        • +
      • 加法逆元:\(\forall \alpha\in K^n,\exists -\alpha\in K^n,\alpha+(-\alpha)=0\)
        • +
      • 乘法单位元:\(1\alpha=\alpha\)
        • +
      • 数乘结合律:\((kl)\alpha=k(l\alpha)\)
        • +
      • 数乘分配律:\(k(\alpha+\beta)=k\alpha+k\beta\)
        • +
      • 数乘分配律:\((k+l)\alpha=k\alpha+l\alpha\)
        • +
      +
      • +
    • +

      以上定义的有度量的线性空间实际上是基于数的,数的加法和数乘就是按通常所认为的定义的,但是实际上线性空间中的元素不一定是数,以下给出最基本的定义:

      +
        +
      • 映射:设\(X\)和\(Y\)是两个集合,如果存在一个规则\(f\),使得对于\(X\)中的每一个元素\(x\),都有唯一的元素\(y\)与之对应,则称\(f\)是从\(X\)到\(Y\)的映射,记作\(f:X\to Y\)
        • +
      • 单射:如果对于\(X\)中的每一个元素\(x\),都有唯一的元素\(y\)与之对应,则称\(f\)是从\(X\)到\(Y\)的单射
        • +
      • 满射:如果对于\(Y\)中的每一个元素\(y\),都有唯一的元素\(x\)与之对应,则称\(f\)是从\(X\)到\(Y\)的满射
        • +
      • 双射:如果\(f\)是单射和满射,则称\(f\)是从\(X\)到\(Y\)的双射
        • +
      • 定义 1 : 非空集合\(S\)上的一个代数运算是指\(S\times S\to S\)的一个代数运算
        • +
      +
      • +
    • +

      线性空间:设\(V\)是一个非空集合,\(K\)是一个数域,如果在\(V\)上有一个称为加法的运算\(\(V\times V\to V:(\alpha,\beta)\to \alpha+\beta\),\)K,V\(之间有一个称为数乘的运算:\)K\times V\to V:(k,\alpha)\to k\alpha$,并且满足以下八条运算法则:

      +
      • +
    • 加法交换律:\(\alpha+\beta=\beta+\alpha\)
      • +
    • 加法结合律:\((\alpha+\beta)+\gamma=\alpha+(\beta+\gamma)\)
      • +
    • 加法单位元:\(\exists \vec{0}\in V,\forall \alpha\in V,\alpha+\vec{0}=\alpha\)
      • +
    • 加法逆元:\(\forall \alpha\in V,\exists -\alpha\in V,s.t.\;\alpha+(-\alpha)=\vec{0}\)
      • +
    • 乘法单位元:\(1\alpha=\alpha\)
      • +
    • 数乘结合律:\((kl)\alpha=k(l\alpha)\)
      • +
    • 数乘分配律:\(k(\alpha+\beta)=k\alpha+k\beta\)
      • +
    • 数乘分配律:\((k+l)\alpha=k\alpha+l\alpha\) + 那么\(V\)称为数域\(K\)上的线性空间,简称线性空间(注意加法单位元取自于\(V\),乘法单位元取自于\(K\))
      • +
    +

    n 维向量空间

    +

    定义 1

    +
      +
    • 如上定义,线性空间是一个集合,在这个集合中有两种运算,一种是加法,一种是数乘,这两种运算满足八条运算法则,这个集合就是线性空间
      • +
    +
    ex:线性空间的例子
    +
      +
    • 几何空间\(R^3\):以\(O\)为起点的向量
      • +
    • \(K^n=\{(x_1,x_2,\cdots,x_n)|x_i\in K,i=1,2,\cdots,n\}\)
      • +
    • 非空集合\(X\)到实数集\(R\)上的所有实值函数的集合构成线性空间:
      • +
    • \(f,g\in X\to R\),定义加法和数乘运算如下:
        +
      • \((f+g)(x)=f(x)+g(x)\)
        • +
      • \((kf)(x)=kf(x)\)
        • +
      +
      • +
    • 且定义\(0\)元为\(0(x)=0\)
      • +
    • 乘法单位元为\(1(x)=1\)
        +
      • 那么\(X\)是数域\(R\)上的一个线性空间
        • +
      +
      • +
    +

    线性空间的性质

    +
      +
    • \(V\)是数域\(K\)上的线性空间,则:
      • +
    • 加法单位元唯一 +
      • +
    • 每个\(\alpha\in V\)的负元唯一
      • +
    • \(0\alpha=\vec{0},\forall \alpha\in V\)
      • +
    • \(k\vec{0}=\vec{0},\forall k\in K\)
      • +
    • 若\(k\alpha=\vec{0}\),则\(k=0\)或\(\alpha=\vec{0}\)
      • +
    • \((-1)\alpha=-\alpha\)
      • +
    +

    线性子空间

    +

    定义 1

    +
      +
    • 设\(V\)是数域\(K\)上的线性空间,\(U\subset V\),如果\(U\)对于\(V\)中定义的加法和数乘也构成线性空间,则称\(U\)是\(V\)的线性子空间,简称子空间
      • +
    • ex:过原点的平面是\(R^3\)的子空间,不过不过原点的平面不是\(R^3\)的子空间
      • +
    +

    定理 1

    +
      +
    • \(U\)是数域\(K\)上的线性空间\(V\)的子空间\(\iff U\)对于\(V\)中定义的加法和数乘封闭
      • +
    • 只需要证明对于加法和数乘封闭即可证明一个子空间是线性空间
      • +
    +

    线性组合

    +
      +
    • 记\(W=\{k_1\alpha_1+k_2\alpha_2+\cdots+k_n\alpha_s|k_i\in K,\alpha_i\in V,i=1,2,\cdots,s\}\),称\(W\)是向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\)的线性组合,则\(W\)是\(V\)的子空间,称为由向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\)生成的子空间,记作\(W=Span(\alpha_1,\alpha_2,\cdots,\alpha_s)\)或者\(<\alpha_1,\alpha_2,\cdots,\alpha_s>\)
      • +
    +

    线性表出

    +
      +
    • \(\beta\in W\iff\exists k_1,k_2,\cdots,k_s\in K,s.t.\;\beta=k_1\alpha_1+k_2\alpha_2+\cdots+k_n\alpha_s\)称\(\beta\)可以由向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\)线性表出
      • +
    +

    数域\(K\)上的\(n\)元线性方程组

    +
      +
    • 记\(\alpha_i=(a_{1i},a_{2i},\cdots,a_{ni})^T,i=1,2,\cdots,n,\beta=(b_1,b_2,\cdots,b_n)^T\),则线性方程组\(x_1\alpha_1+x_2\alpha_2+\cdots+x_n\alpha_n=\beta\)有解\(\iff \beta\)可以由向量组\(\alpha_1,\alpha_2,\cdots,\alpha_n\)线性表出\(\iff\beta\in Span(\alpha_1,\alpha_2,\cdots,\alpha_n)\)
      • +
    • 因此我们研究\(Span(\alpha)\)的结构
      • +
    +

    共线

    +
      +
    • 向量\(\alpha,\beta\)共线\(\iff\exists,k,l\in R.k,l\text{不全为}0,s.t.\;k\alpha+l\beta=\vec{0}\)
      • +
    • 向量\(\alpha,\beta\)不共线:\(k\alpha+l\beta=\vec{0}\iff k,l=0\)
      • +
    +

    定义 1

    +
      +
    • 线性相关:对于数域\(K\)上的线性空间\(V\)中的向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\),如果存在\(K\)中不全为0 的实数\(k_1,k_2,\cdots,k_s,s.t.\;k_1\alpha_1+\cdots+k_s\alpha_s=0\),那么称向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\)线性相关
      • +
    • 线性无关:如果\(k_1\alpha_1+\cdots+k_s\alpha_s=0\Rightarrow k_1=k_2=\cdots=k_s=0\),那么称向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\)线性无关
      • +
    +

    定理 2

    +
      +
    • 齐次线性方程组:\(x_1\alpha_1+x_2\alpha_2+\cdots+x_n\alpha_n=0\)有非零解\(\iff\alpha_1,\alpha_2,\cdots,\alpha_n\)线性相关
      • +
    • 只有零解\(\iff\alpha_1,\alpha_2,\cdots,\alpha_n\)线性无关
      • +
    +

    线性相关和线性无关的向量组

    +

    用\(\alpha\)表示向量组\(\alpha_1,\alpha_2,\cdots,\alpha_n\),一些明显的记号就不定义了,比如\(\alpha-\alpha_1\)就是\(\alpha\)去掉\(\alpha_1\)的向量组

    +
      +
    • \(\alpha_0\)线性相关\(\iff\alpha_0 = \vec{0}\)
      • +
    • 向量组的部分组如果线性相关,则整个向量组线性相关
      • +
    • 向量组线性无关,那么任一部分组都是线性无关的(上一点的逆否命题)
      • +
    • 含有零向量的向量组线性相关
      • +
    • 向量组线性相关\(\iff\exists\alpha_i\in\alpha,s.t.\;\alpha_i\in Span(\alpha-\alpha_i)\)
      • +
    +

    命题 1

    +
      +
    • 设\(\beta\in Span(\alpha)\),且表出方式唯一,则\(\alpha\)线性无关
      • +
    +

    命题 2

    +
      +
    • 若\(\alpha\)线性无关,但是\(\alpha,\beta\)线性相关,那么\(\beta\in Span(\alpha)\)
      • +
    +

    极大线性无关组,向量组的秩

    +
      +
    • +

      向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\)中的向量组\(\alpha_{i_1},\alpha_{i_2},\cdots,\alpha_{i_r}\)称为原向量组的 一个 极大线性无关组,如果\(\alpha_{i_1},\alpha_{i_2},\cdots,\alpha_{i_r}\)线性无关,但是从其余向量(如果有)中任取一个添进来得到的新的部分组都是线性相关的

      +
      • +
    • +

      \(span(\alpha_{i_1},\alpha_{i_2},\cdots,\alpha_{i_r})=span(\alpha_1,\alpha_2,\cdots,\alpha_s)\)换句话说,原向量组的极大线性无关组和原向量组生成的子空间是相等的

      +
      • +
    • 从而原向量组的任何一个极大线性无关组都是等价的
      • +
    • 线性表出是一个等价关系:满足反身性,对称性,传递性
      • +
    +

    命题 1

    +
      +
    • 设向量组\(\beta_1,\beta_2,\cdots,\beta_r\),可以由\(\alpha_1,\alpha_2,\cdots,\alpha_s\)线性表出并且有\(r>s\),则\(\beta_1,\beta_2,\cdots,\beta_r\)一定线性相关
      • +
    +

    推论 1

    +
      +
    • 设向量组\(\beta_1,\beta_2,\cdots,\beta_r\),可以由\(\alpha_1,\alpha_2,\cdots,\alpha_s\)线性表出,如果\(\beta_1,\beta_2,\cdots,\beta_r\)线性无关,则\(r\leq s\)(逆否命题)
      • +
    +

    推论 2

    +
      +
    • 等价的线性无关组所含向量个数相等
      • +
    +

    推论 3

    +
      +
    • 向量组的所有极大线性无关组所含的向量个数相等
      • +
    +

    定义 1

    +
      +
    • 向量组\(\alpha_1,\alpha_2,\cdots,\alpha_s\)的极大线性无关组所含向量个数称为向量组的秩,记作$rank(\alpha)=rank{\alpha_1,\cdots,\alpha_s} $,只有零向量的向量组的秩为0
      • +
    +

    命题 2

    +
      +
    • 向量组线性无关的充要条件是向量组的秩等于向量组的向量个数
      • +
    +

    命题 3

    +
      +
    • 如果向量组\(\alpha\)可以由向量组\(\beta\)线性表出\(\iff rank(\alpha)\leq rank(\beta)\)
      • +
    + + + + + + + + + + + + + +
    +
    + + + +
    + + + +
    + + + +
    +
    +
    +
    + + + + + + + + + + + + + + + + \ No newline at end of file diff --git "a/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/index.html" "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/index.html" index 920fea5b..1ecc4410 100644 --- "a/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/index.html" +++ "b/Notebook/\351\253\230\347\255\211\344\273\243\346\225\260/index.html" @@ -795,6 +795,27 @@ + + + + + + +
  • + + + + + n维度量线性空间 + + + + +
    • + + + + diff --git a/Tools/index.html b/Tools/index.html index 6840b019..8d5d9958 100644 --- a/Tools/index.html +++ b/Tools/index.html @@ -15,7 +15,7 @@ - + diff --git a/search/search_index.json b/search/search_index.json index f6878756..950ce59c 100644 --- a/search/search_index.json +++ b/search/search_index.json @@ -1 +1 @@ -{"config":{"lang":["en","zh"],"separator":"[\\s\\-]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"\ud835\udcdb\ud835\udcf3\ud835\udd01'\ud835\udcdf\ud835\udcea\ud835\udcf0\ud835\udcee","text":"\\[ \\int_{birth}^{death} study\\ dt = life \\] 
    #include <earth>     \nclass luojunxun {    \n    public:     \n        luojunxun(){    \n            std::cout << \"Hello, I'm luojunxun\" << std::endl;     \n            };    \n        ~luojunxun(){    \n            throw std::runtime_error(\"I'm not dead yet!\");     \n            };    \n\n    private:     \n        std::string name{\"luojunxun\"};     \n        Chat::email email{\"junxun-luo@outlook.com\"};     \n        Social::job{\"Student\"};     \n        Education::school University{\"Zhejiang University\"};     \n        Life::hobby hobby{\"coding+Math+Fitness\"};     \n};    \n
    "},{"location":"Notebook/","title":"\ud835\udc75\ud835\udc90\ud835\udc95\ud835\udc86\ud835\udc83\ud835\udc90\ud835\udc90\ud835\udc8c","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/","title":"\u738b\u9053\u64cd\u4f5c\u7cfb\u7edf\u7b14\u8bb0","text":"

    \u89c6\u9891\u5730\u5740

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/05-%E8%AE%BE%E5%A4%87%E7%AE%A1%E7%90%86/","title":"\u8bbe\u5907\u7ba1\u7406","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/05-%E8%AE%BE%E5%A4%87%E7%AE%A1%E7%90%86/#io","title":"I/O \u8bbe\u5907\u7684\u57fa\u672c\u6982\u5ff5\u548c\u5206\u7c7b","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/05-%E8%AE%BE%E5%A4%87%E7%AE%A1%E7%90%86/#io_1","title":"I/O\u63a7\u5236\u5668","text":"

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/05-%E8%AE%BE%E5%A4%87%E7%AE%A1%E7%90%86/#io_2","title":"I/O\u63a7\u5236\u65b9\u5f0f","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/05-%E8%AE%BE%E5%A4%87%E7%AE%A1%E7%90%86/#io_3","title":"I/O\u8f6f\u4ef6\u5c42\u6b21\u7ed3\u6784","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/","title":"\u64cd\u4f5c\u7cfb\u7edf\u6982\u8ff0","text":"

    1.\u662f\u7cfb\u7edf\u8d44\u6e90\u7684\u7ba1\u7406\u8005 

    \u5904\u7406\u673a\u7ba1\u7406:\u662f\u8fdb\u7a0b\u7ba1\u7406\u5417?\n

    2.\u63d0\u4f9b\u63a5\u53e3\u548c\u73af\u5883 

    \u6bd4\u5982GUI,\u8054\u673a\u547d\u4ee4\u63a5\u53e3(terminal),\u6279\u5904\u7406\u547d\u4ee4\u63a5\u53e3(.bat \u6587\u4ef6,.sh \u6587\u4ef6\u7b49\u7b49)\n\u7a0b\u5e8f\u63a5\u53e3\u7b49\u7b49(\u7531\u64cd\u4f5c\u7cfb\u7edf\u63d0\u4f9b,\u4f9b\u7a0b\u5e8f\u5458\u4f7f\u7528\u7b49\u7b49)\n

    3.\u662f\u7cfb\u7edf\u8f6f\u4ef6

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_2","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u56db\u5927\u7279\u5f81","text":"
    \u5e76\u53d1:\u5b8f\u89c2\u4e0a\u540c\u65f6\u53d1\u751f, \u5fae\u89c2\u4e0a\u4ea4\u66ff\u53d1\u751f\n\u5e76\u884c:\u5fae\u89c2\u4e0a\u540c\u65f6\u53d1\u751f\n

    \u8d85\u8fc7 4 \u4e2a\u5c31\u9700\u8981\u5e76\u53d1\u6027

    \u5171\u4eab\u65b9\u5f0f\u5bf9\u5e94\u7684\u4e5f\u6709\u4e92\u65a5\u5171\u4eab\u65b9\u5f0f\u548c\u540c\u65f6\u5171\u4eab\u65b9\u5f0f(\u5fae\u89c2\u4e0a\u53ef\u80fd\u662f\u4ea4\u66ff\u5171\u4eab\u4e5f\u53ef\u80fd\u662f\u540c\u65f6\u5171\u4eab)

    \u6bd4\u5982\u4e00\u5757\u786c\u76d8\u5206\u6210\u51e0\u4e2a\u76d8(D,E)\n\u65f6\u5206\u590d\u7528\u6280\u672f:\u5355\u6838 cpu \u7cfb\u7edf\u540c\u65f6\u8fd0\u884c\u51e0\u4e2a\u5f15\u7528\u7a0b\u5e8f\n

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_3","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_4","title":"\u64cd\u4f5c\u7cfb\u7edf\u53d1\u5c55","text":"
    \u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u65f6\u671f OS \u624d\u51fa\u73b0\n\u5206\u65f6\u64cd\u4f5c\u7cfb\u7edf:\u4ea4\u4e92\u529f\u80fd\u51fa\u73b0\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_5","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_6","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fd0\u884c\u673a\u5236","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_7","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_8","title":"\u4e2d\u65ad\u548c\u5f02\u5e38","text":"

    \u64cd\u4f5c\u7cfb\u7edf\u593a\u56decpu\u4f7f\u7528\u6743\u7684\u552f\u4e00\u65b9\u5f0f\u5c31\u662f\u4e2d\u65ad

    \u5185\u4e2d\u65ad:\u6bd4\u5982\u5e94\u7528\u7a0b\u5e8f\u4f01\u56fe\u4f7f\u7528\u7279\u6743\u6307\u4ee4,\u6216\u8005\u6570\u7ec4\u8d8a\u754c\u9700\u8981\u5904\u7406(\u8f6c\u5230 OS \u5904\u7406\u5f02\u5e38),\n    \u6216\u8005\u9677\u5165\u6307\u4ee4(\u5e94\u7528\u7a0b\u5e8f\u5e0c\u671b OS \u4e3a\u4ed6\u63d0\u4f9b\u67d0\u4e9b\u64cd\u4f5c),\u9677\u5165\u6307\u4ee4\u4e0d\u662f\u7279\u6743\u6307\u4ee4\n\u5916\u4e2d\u65ad:\u65f6\u949f\u4e2d\u65ad(\u5b9e\u73b0\u5e76\u53d1),I/O\u4e2d\u65ad\u8bf7\u6c42\u7b49\u7b49\n

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_9","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_10","title":"\u7cfb\u7edf\u8c03\u7528","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_11","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u4f53\u7cfb\u7ed3\u6784","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/#_12","title":"\u865a\u62df\u673a","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/","title":"\u5904\u7406\u673a\u7ba1\u7406(\u8fdb\u7a0b\u7ba1\u7406)","text":"
    \u5f53\u8fdb\u7a0b\u88ab\u521b\u5efa,\u64cd\u4f5c\u7cfb\u7edf\u4f1a\u4e3a\u8be5\u8fdb\u7a0b\u5206\u914d\u4e00\u4e2a\u552f\u4e00\u7684\u6807\u8bc6:PID(Process ID)\n

    \u64cd\u4f5c\u7cfb\u7edf\u8bb0\u5f55\u7684\u6240\u6709\u4fe1\u606f\u90fd\u5b58\u50a8\u5728\u4e00\u4e2a\u6570\u636e\u7ed3\u6784PCB(Process control block)\u4e2d,\u5373\u8fdb\u7a0b\u63a7\u5236\u5757

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_2","title":"\u8fdb\u7a0b\u7684\u7ec4\u6210","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_3","title":"\u8fdb\u7a0b\u7684\u7279\u6027","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_4","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_5","title":"\u8fdb\u7a0b\u7684\u72b6\u6001\u548c\u8f6c\u5316","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_6","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_7","title":"\u8fdb\u7a0b\u63a7\u5236","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_8","title":"\u521b\u5efa\u539f\u8bed","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_9","title":"\u64a4\u9500\u539f\u8bed","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_10","title":"\u963b\u585e\u539f\u8bed","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_11","title":"\u5207\u6362\u539f\u8bed","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_12","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_13","title":"\u8fdb\u7a0b\u901a\u4fe1","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_14","title":"\u5171\u4eab\u5b58\u50a8","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_15","title":"\u6d88\u606f\u901a\u4fe1","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_16","title":"\u7ba1\u9053\u901a\u4fe1","text":"
    \u7ba1\u9053\u53ea\u80fd\u5b9e\u884c\u534a\u53cc\u5de5\u901a\u4fe1,\u5982\u679c\u8981\u5b9e\u73b0\u5168\u53cc\u5de5\u901a\u4fe1,\u90a3\u4e48\u5c31\u8981\u5411\u64cd\u4f5c\u7cfb\u7edf\u7533\u8bf7\u4e24\u4e2a\u7ba1\u9053\n\u6bcf\u4e2a\u8fdb\u7a0b\u4e92\u65a5\u7684\u8bbf\u95ee\u7ba1\u9053(\u64cd\u4f5c\u7cfb\u7edf\u5b9e\u73b0)\n\u7ba1\u9053\u5199\u6ee1\u7684\u65f6\u5019,\u5199\u8fdb\u7a0b\u88ab\u963b\u585e\n\u7ba1\u9053\u4e3a\u7a7a\u7684\u65f6\u5019,\u8bfb\u8fdb\u7a0b\u88ab\u963b\u585e\n\u7ba1\u9053\u4e2d\u7684\u6570\u636e\u4e00\u65e6\u88ab\u8bfb\u53d6\u5c31\u4f1a\u6d88\u5931,\u6240\u4ee5\u591a\u4e2a\u8fdb\u7a0b\u8bfb\u53d6\u7684\u65f6\u5019\u53ef\u80fd\u4f1a\u51fa\u73b0\u95ee\u9898,(\u6807\u51c6\u7b54\u6848\u662f\u53ef\u4ee5\u6709\u591a\u4e2a\u5199\u8fdb\u7a0b\u4f46\u662f\u53ea\u80fd\u6709\u4e00\u4e2a\u8bfb\u8fdb\u7a0b,\u4f46\u662f\u5b9e\u9645\u4e0a\u901a\u8fc7\u64cd\u4f5c\u7cfb\u7edf\u7684\u8c03\u5ea6\u53ef\u4ee5\u5b9e\u73b0\u591a\u4e2a\u8bfb\u8fdb\u7a0b<linux>)\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_17","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_18","title":"\u7ebf\u7a0b\u591a\u7ebf\u7a0b\u6a21\u578b","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_19","title":"\u7ebf\u7a0b\u5f15\u5165\u5e26\u6765\u7684\u53d8\u5316","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_20","title":"\u7ebf\u7a0b\u7684\u5c5e\u6027","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_21","title":"\u591a\u7ebf\u7a0b\u6a21\u578b","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_22","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_23","title":"\u7ebf\u7a0b\u7684\u72b6\u6001\u4e0e\u8f6c\u6362","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_24","title":"\u5904\u7406\u673a\u8c03\u5ea6","text":"

    \u5f53\u6709\u4e00\u5806\u4efb\u52a1\u8981\u5904\u7406\uff0c\u4f46\u7531\u4e8e\u8d44\u6e90\u6709\u9650\uff0c\u8fd9\u4e9b\u4e8b\u60c5\u6ca1\u6cd5\u540c\u65f6\u5904\u7406\u3002\u8fd9\u5c31\u9700\u8981\u786e\u5b9a\u67d0\u79cd\u89c4\u5219\u6765\u51b3\u5b9a\u5904\u7406 \u8fd9\u4e9b\u4efb\u52a1\u7684\u987a\u5e8f\uff0c\u8fd9\u5c31\u662f\u201c\u8c03\u5ea6\u201d\u7814\u7a76\u7684\u95ee\u9898\u3002

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_25","title":"\u4e03\u72b6\u6001\u6a21\u578b","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_26","title":"\u8c03\u5ea6\u7684\u8054\u7cfb\u5bf9\u6bd4","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_27","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_28","title":"\u8fdb\u7a0b\u8c03\u5ea6","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_29","title":"\u8fdb\u7a0b\u8c03\u5ea6\u7684\u65f6\u673a","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_30","title":"\u8fdb\u7a0b\u8c03\u5ea6\u7684\u65b9\u5f0f","text":"

    \u5b9e\u73b0\u7b80\u5355,\u7cfb\u7edf\u5f00\u9500\u5c0f\u4f46\u662f\u65e0\u6cd5\u5904\u7406\u7d27\u6025\u4efb\u52a1,\u9002\u7528\u4e8e\u65e9\u671f\u7684\u6279\u5904\u7406\u7cfb\u7edf

    \u53ef\u4ee5\u4f18\u5148\u5904\u7406\u7d27\u6025\u4efb\u52a1,\u8ba9\u8fdb\u7a0b\u6309\u65f6\u95f4\u7247\u8f6e\u6d41\u6267\u884c,\u9002\u5408\u5206\u65f6\u64cd\u4f5c\u7cfb\u7edf,\u5b9e\u65f6\u64cd\u4f5c\u7cfb\u7edf

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_31","title":"\u8fdb\u7a0b\u8c03\u5ea6\u548c\u8fdb\u7a0b\u5207\u6362","text":"
    \u72ed\u4e49\u5c31\u662f\u53ef\u4ee5\u4e0d\u5207\u6362\u8fdb\u7a0b\uff0c\u53ef\u4ee5\u7ee7\u7eed\u9009\u62e9\u521a\u624d\u7684\uff1b\u5e7f\u4e49\u7684\u5c31\u662f:\u4e0d\u884c\uff0c\u4f60\u5fc5\u987b\u5207\u6362\u53e6\u4e00\u4e2a\u8fdb\u7a0b\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_32","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_33","title":"\u95f2\u901b\u8fdb\u7a0b","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_34","title":"\u8bc4\u4ef7\u8c03\u5ea6\u7b97\u6cd5\u7684\u6307\u6807","text":"
    cpu\u5229\u7528\u7387:cpu \u4f7f\u7528\u65f6\u95f4/\u8fd0\u884c\u603b\u65f6\u95f4\n\u7cfb\u7edf\u541e\u5410\u91cf:\u5355\u4f4d\u65f6\u95f4\u5185\u5b8c\u6210\u7684\u4f5c\u4e1a\u91cf\n\u5468\u8f6c\u65f6\u95f4:\u4f5c\u4e1a\u63d0\u4ea4\u7ed9\u7cfb\u7edf\u5230\u4f5c\u4e1a\u88ab\u5b8c\u6210\u7684\u65f6\u95f4,\u7531\u6b64\u53ef\u4ee5\u63d0\u51fa\u5e73\u5747\u5468\u8f6c\u65f6\u95f4\n\u5e26\u6743\u5468\u8f6c\u65f6\u95f4:\u4f5c\u4e1a\u5468\u8f6c\u65f6\u95f4/\u4f5c\u4e1a\u5b9e\u9645\u8fd0\u884c\u7684\u65f6\u95f4=(\u4f5c\u4e1a\u5b8c\u6210\u65f6\u95f4-\u4f5c\u4e1a\u63d0\u4ea4\u65f6\u95f4)/\u4f5c\u4e1a\u5b9e\u9645\u8fd0\u884c\u65f6\u95f4\n    \u53ef\u4ee5\u770b\u51fa\u5e26\u6743\u5468\u8f6c\u65f6\u95f4\u80af\u5b9a\u662f\u5927\u4e8e\u7b49\u4e8e 1 \u7684,\u540c\u65f6\u5e26\u6743\u5468\u8f6c\u65f6\u95f4\u8d8a\u5c0f\u8d8a\u597d\n    \u540c\u7406\u6709\u5e73\u5747\u5e26\u5168\u5468\u8f6c\u65f6\u95f4\n\u7b49\u5f85\u65f6\u95f4:\u4f5c\u4e1a/\u8fdb\u7a0b\u5904\u4e8e\u5904\u7406\u673a\u7b49\u5f85\u72b6\u6001\u65f6\u95f4\u7684\u548c\n\u54cd\u5e94\u65f6\u95f4:\u7528\u6237\u63d0\u4ea4\u8bf7\u6c42\u5230\u9996\u6b21\u88ab\u54cd\u5e94\u7684\u65f6\u95f4\n
    \u8fd9\u91cc\u6ce8\u610f\u963b\u585e\u6001\u4e0d\u8ba1\u5165\u7b49\u5f85\u65f6\u95f4(\u7b49\u5f85I/O\u8bbe\u5907)\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_35","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_36","title":"\u51e0\u79cd\u8c03\u5ea6\u7b97\u6cd5","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_37","title":"\u65f6\u95f4\u7247\u8f6e\u8f6c\u8c03\u5ea6\u7b97\u6cd5","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_38","title":"\u4f18\u5148\u7ea7\u8c03\u5ea6\u7b97\u6cd5","text":"
    \u975e\u62a2\u5360\u6027\u7b97\u6cd5\u53ea\u9700\u8003\u8651\u8fdb\u7a0b\u4e3b\u52a8\u653e\u5f03\u5904\u7406\u673a\u7684\u60c5\u51b5\n\u62a2\u5360\u6027\u7b97\u6cd5\u5728\u6bcf\u6b21\u5c31\u7eea\u961f\u5217\u66f4\u65b0\u7684\u65f6\u5019\u4e5f\u9700\u8981\u68c0\u6d4b\u662f\u5426\u9700\u8981\u91cd\u65b0\u8c03\u5ea6\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_39","title":"\u591a\u7ea7\u53cd\u9988\u961f\u5217\u8c03\u5ea6\u7b97\u6cd5","text":"

    (UNIX \u5c31\u662f\u4f7f\u7528\u591a\u7ea7\u53cd\u9988\u961f\u5217\u8c03\u5ea6\u7b97\u6cd5)

    \u5206\u6790\u8fd9\u91cc\u6bcf\u4e2a\u961f\u5217\u9009\u62e9\u7684\u7b97\u6cd5\u7684\u539f\u56e0(\u8fd9\u53ea\u662f\u4e2a\u4f8b\u5b50,\u5e76\u4e0d\u662f\u771f\u662f\u8fd9\u6837)

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_40","title":"\u8fdb\u7a0b\u540c\u6b65\u8fdb\u7a0b\u4e92\u65a5","text":"
    \u4e00\u6b21\u4ec5\u5141\u8bb8\u4e00\u4e2a\u8fdb\u7a0b\u4f7f\u7528\u7684\u8d44\u6e90\u79f0\u4e3a\u4e34\u754c\u8d44\u6e90\n
    while(ture){\n    entry section;//\u8fdb\u5165\u533a<\u68c0\u67e5\u662f\u5426\u80fd\u8fdb\u5165>\n    critical section; //\u4e34\u754c\u533a<\u8bbf\u95ee\u4e34\u754c\u8d44\u6e90\u7684\u4ee3\u7801,\u53c8\u79f0\u4e3a\u4e34\u754c\u6bb5>\n    exit section; //\u9000\u51fa\u533a<\u5c06\u6b63\u5728\u8bbf\u95ee\u7684\u6807\u5fd7\u6e05\u9664>\n    remainder section; //\u5269\u4f59\u533a\n}\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_41","title":"\u8fdb\u7a0b\u4e92\u65a5\u7684\u8f6f\u4ef6\u5b9e\u73b0\u65b9\u6cd5","text":"

    \u8bbe\u7f6e\u4e00\u4e2a\u516c\u7528\u7684\u6574\u578b\u53d8\u91cf turn,\u6307\u5411\u5141\u8bb8\u8fdb\u5165\u4e34\u754c\u533a\u7684\u7f16\u53f7 \u53ef\u4ee5\u5b9e\u73b0\u6bcf\u6b21\u53ea\u5141\u8bb8\u4e00\u4e2a\u8fdb\u7a0b\u8fdb\u5165\u4e34\u754c\u533a,\u4f46\u662f\u4e24\u4e2a\u7a0b\u5e8f\u6bd4\u5982\u4ea4\u66ff\u8fdb\u5165\u4e34\u754c\u533a,\u5982\u679c\u67d0\u4e2a\u7a0b\u5e8f\u4e0d\u6253\u7b97\u8fdb\u5165\u4e34\u754c\u533a,\u90a3\u4e48\u53e6\u4e00\u4e2a\u4e5f\u5c31\u4e0d\u80fd\u518d\u8fdb\u5165\u4e34\u754c\u533a,\u8fdd\u80cc\u4e86<\u7a7a\u95f2\u8ba9\u8fdb>\u7684\u539f\u5219

    \u8bbe\u7f6e\u5e03\u5c14\u578b\u6570\u7ec4 flag[2] \u6807\u8bb0\u53cc\u65b9\u8fdb\u5165\u7684\u610f\u613f,\u8fdb\u5165\u4e34\u754c\u533a\u4e4b\u524d\u5148\u68c0\u67e5\u5bf9\u65b9\u662f\u5426\u60f3\u8fdb\u5165,\u5982\u679c\u662f\u5c31\u5faa\u73af\u68c0\u67e5\u5e76\u7b49\u5f85,\u4e0d\u662f\u5219\u7f6e\u81ea\u5df1\u7684 flag \u4e3a true,\u7136\u540e\u8bbf\u95ee\u4e34\u754c\u533a,\u9000\u51fa\u7684\u65f6\u5019\u518d\u7f6e\u81ea\u5df1\u7684 flag \u4e3a false

    \u8fd9\u79cd\u505a\u6cd5\u4e0d\u9700\u8981\u8fdb\u7a0b\u4ea4\u66ff\u8fdb\u5165,\u53ef\u4ee5\u8fde\u7eed\u4f7f\u7528,\u4f46\u662f\u4e24\u4e2a\u8fdb\u7a0b\u53ef\u80fd\u540c\u65f6\u8bbf\u95ee\u4e34\u754c\u533a,\u539f\u56e0\u5728\u4e8e\u68c0\u67e5\u5bf9\u65b9\u6807\u5fd7\u540e\u5230\u5207\u6362\u81ea\u5df1\u6807\u5fd7\u4e2d\u53ef\u80fd\u53d1\u751f\u8fdb\u7a0b\u5207\u6362,\u5bfc\u81f4\u53cc\u65b9\u90fd\u68c0\u67e5\u901a\u8fc7,\u8fdd\u80cc<\u5fd9\u7740\u7b49\u5f85>\u539f\u5219

    \u539f\u56e0\u5728\u4e8e\u68c0\u67e5\u548c\u8bbe\u7f6e\u4e0d\u662f\u4e00\u6c14\u5475\u6210\u7684

    \u5148\u8bbe\u7f6e\u81ea\u5df1\u7684\u6807\u5fd7\u518d\u68c0\u67e5\u5bf9\u65b9 \u95ee\u9898\u5728\u4e8e\u5982\u679c\u5728\u8bbe\u7f6e\u81ea\u5df1\u6807\u5fd7\u548c\u68c0\u67e5\u5bf9\u65b9\u7684\u65f6\u5019\u53d1\u751f\u4e86\u8fdb\u7a0b\u5207\u6362,\u90a3\u4e48\u4e24\u4e2a\u7a0b\u5e8f\u90fd\u65e0\u6cd5\u8fdb\u5165\u4e34\u754c\u533a,\u8fdd\u80cc\u4e86<\u7a7a\u95f2\u8ba9\u8fdb>\u7684\u539f\u5219, \u6b64\u5916\u4e24\u4e2a\u8fdb\u7a0b\u957f\u671f\u5f97\u4e0d\u5230\u8bbf\u95ee\u5bfc\u81f4\u9965\u997f,\u8fdd\u80cc\u4e86<\u6709\u9650\u7b49\u5f85>\u539f\u5219

    \u7ed3\u5408\u7b97\u6cd5 1,3.\u5229\u7528 flag \u89e3\u51b3\u4e92\u65a5\u95ee\u9898,turn \u89e3\u51b3\u9965\u997f\u95ee\u9898.

    \u8fdb\u5165\u4e4b\u524d\u5c06\u81ea\u5df1\u7684 flag \u7f6e true \u7136\u540e turn \u8bbe\u7f6e\u4e3a\u5bf9\u65b9,\u5982\u679c turn \u662f\u5bf9\u65b9\u4e14\u5bf9\u65b9\u60f3\u8fdb\u5c31\u7b49\u5f85,\u5426\u5219\u8fdb\u5165,\u5b8c\u6210\u540e\u7f6e flag \u4e3a false \u552f\u4e00\u7f3a\u70b9\u662f\u6ca1\u6709\u9075\u5faa<\u8ba9\u6743\u7b49\u5f85>

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_42","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_43","title":"\u8fdb\u7a0b\u4e92\u65a5\u7684\u786c\u4ef6\u5b9e\u73b0\u65b9\u6cd5","text":"

    \u4e2d\u65ad\u5c4f\u853d\u65b9\u6cd5

    TestAndSet \u6307\u4ee4

    Swap\u6307\u4ee4

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_44","title":"\u4e92\u65a5\u9501","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_45","title":"\u4fe1\u53f7\u91cf\u673a\u5236","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_46","title":"\u7ba1\u7a0b","text":"

    \u5b9e\u9645\u4e0a\u5c31\u662f\u628a\u5bf9\u8ba1\u7b97\u673a\u7684\u67d0\u79cd\u8d44\u6e90\u7684\u63cf\u8ff0,\u8c03\u7528\u7b49\u7b49\u5199\u6210\u4e86\u4e00\u4e2a\u7c7b,\u5176\u4ed6\u8fdb\u7a0b\u60f3\u8981\u5bf9\u8fd9\u79cd\u8d44\u6e90\u8fdb\u884c\u4f7f\u7528\u53ea\u80fd\u901a\u8fc7\u8fd9\u4e2a\u7c7b

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_47","title":"\u6b7b\u9501","text":"

    \u8868\u793a\u8fdb\u7a0b\u7ade\u4e89\u8d44\u6e90\u9677\u5165\u7684\u4e00\u79cd\u50f5\u5c40(\u7b49\u5f85\u5bf9\u65b9\u624b\u4e2d\u7684\u8d44\u6e90),\u4f7f\u5f97\u5404\u4e2a\u7a0b\u5e8f\u90fd\u88ab\u963b\u585e

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_48","title":"\u6b7b\u9501\u4ea7\u751f\u7684\u5fc5\u8981\u6761\u4ef6","text":"
    1.\u4e92\u65a5\u6761\u4ef6:\u5bf9\u4e92\u65a5\u8d44\u6e90\u7684\u4e89\u593a\u624d\u4f1a\u5bfc\u81f4\u6b7b\u9501\n2.\u4e0d\u5265\u593a:\u8fdb\u7a0b\u6240\u83b7\u7684\u8d44\u6e90\u6ca1\u6709\u4f7f\u7528\u5b8c\u4e4b\u524d\u4e0d\u80fd\u88ab\u5176\u4ed6\u8fdb\u7a0b\u5265\u593a,\n    \u53ea\u80fd\u8be5\u8fdb\u7a0b\u81ea\u5df1\u4e3b\u52a8\u91ca\u653e\n3.\u8bf7\u6c42\u548c\u4fdd\u6301\u6761\u4ef6:\u8fdb\u7a0b\u5df2\u7ecf\u62e5\u6709\u4e86\u4e00\u4e2a\u8d44\u6e90,\u540c\u65f6\u8fd8\u5728\u8bf7\u6c42\u5176\u4ed6\u8d44\u6e90,\n    \u800c\u8bf7\u6c42\u7684\u8d44\u6e90\u6b63\u5728\u88ab\u5176\u4ed6\u8fdb\u7a0b\u5360\u7528,\u6b64\u65f6\u8bf7\u6c42\u88ab\u963b\u585e\u4f46\u662f\u81ea\u5df1\u5df2\u6709\u7684\u8d44\u6e90\u4e5f\u4e0d\u91ca\u653e\n4.\u5faa\u73af\u7b49\u5f85\u6761\u4ef6:\u5b58\u5728\u4e00\u4e2a\u8d44\u6e90\u7684\u5faa\u73af\u7b49\u5f85\u94fe,\u6bcf\u4e2a\u8fdb\u7a0b\u5df2\u7ecf\u83b7\u5f97\u7684\u8d44\u6e90\u5728\u88ab\u4e0b\u4e00\u4e2a\u8fdb\u7a0b\u8bf7\u6c42\n

    \u53d1\u751f\u5faa\u73af\u4e0d\u4e00\u5b9a\u6b7b\u9501,\u4f46\u662f\u6b7b\u9501\u4e00\u5b9a\u6709\u5faa\u73af\u7b49\u5f85

    \u5bf9\u4e0d\u53ef\u5265\u593a\u8d44\u6e90\u7684\u4e0d\u5408\u7406\u5206\u914d\u5c31\u6709\u53ef\u80fd\u5bfc\u81f4\u6b7b\u9501

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_49","title":"\u5904\u7406\u7b56\u7565","text":"

    1. \u9884\u9632\u6b7b\u9501\u3002\u7834\u574f\u6b7b\u9501\u4ea7\u751f\u7684\u56db\u4e2a\u5fc5\u8981\u6761\u4ef6\u4e2d\u7684\u4e00\u4e2a\u6216\u51e0\u4e2a\u3002

    2. \u907f\u514d\u6b7b\u9501\u3002\u7528\u67d0\u79cd\u65b9\u6cd5\u9632\u6b62\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u4ece\u800c\u907f\u514d\u6b7b\u9501\uff08\u94f6\u884c\u5bb6\u7b97\u6cd5\uff09

    3. \u6b7b\u9501\u7684\u68c0\u6d4b\u548c\u89e3\u9664\u3002\u5141\u8bb8\u6b7b\u9501\u7684\u53d1\u751f\uff0c\u4e0d\u8fc7\u64cd\u4f5c\u7cfb\u7edf\u4f1a\u8d1f\u8d23\u68c0\u6d4b\u51fa\u6b7b\u9501\u7684\u53d1\u751f\uff0c\u7136\u540e\u91c7\u53d6\u67d0\u79cd\u63aa \u65bd\u89e3\u9664\u6b7b\u9501\u3002

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_50","title":"\u6b7b\u9501\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_51","title":"\u6b7b\u9501\u5904\u7406","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_52","title":"\u5b89\u5168\u5e8f\u5217","text":"

    \u5c31\u662f\u6307\u5982\u679c\u7cfb\u7edf\u6309\u7167\u8fd9\u79cd\u5e8f\u5217\u5206\u914d\u8d44\u6e90\uff0c\u5219\u6bcf\u4e2a\u8fdb\u7a0b\u90fd\u80fd\u987a\u5229\u5b8c\u6210\u3002

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_53","title":"\u5b89\u5168\u72b6\u6001","text":"

    \u53ea\u8981\u80fd\u627e\u51fa\u4e00\u4e2a\u5b89\u5168\u5e8f\u5217\uff0c\u7cfb\u7edf\u5c31\u662f\u5b89\u5168\u72b6\u6001\u3002\u5f53\u7136\uff0c\u5b89\u5168\u5e8f\u5217\u53ef\u80fd\u6709\u591a\u4e2a\u3002 

    \u5982\u679c\u5206\u914d\u4e86\u8d44\u6e90\u4e4b\u540e\uff0c\u7cfb\u7edf\u4e2d\u627e\u4e0d\u51fa\u4efb\u4f55\u4e00\u4e2a\u5b89\u5168\u5e8f\u5217\uff0c\u7cfb\u7edf\u5c31\u8fdb\u5165\u4e86\u4e0d\u5b89\u5168\u72b6\u6001\u3002\n\u8fd9\u5c31\u610f\u5473\u7740\u4e4b\u540e \u53ef\u80fd\u6240\u6709\u8fdb\u7a0b\u90fd\u65e0\u6cd5\u987a\u5229\u7684\u6267\u884c\u4e0b\u53bb\u3002\u5f53\u7136\uff0c\u5982\u679c\u6709\u8fdb\u7a0b\u63d0\u524d\u5f52\u8fd8\u4e86\u4e00\u4e9b\u8d44\u6e90\uff0c\n\u90a3\u7cfb\u7edf\u4e5f\u6709\u53ef\u80fd\u91cd\u65b0 \u56de\u5230\u5b89\u5168\u72b6\u6001\uff0c\u4e0d\u8fc7\u6211\u4eec\u5728\u5206\u914d\u8d44\u6e90\u4e4b\u524d\u603b\u662f\u8981\u8003\u8651\u5230\u6700\u574f\u7684\u60c5\u51b5\u3002\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_54","title":"\u548c\u6b7b\u9501\u7684\u5173\u7cfb","text":"
    \u5982\u679c\u7cfb\u7edf\u5904\u4e8e\u5b89\u5168\u72b6\u6001\uff0c\u5c31\u4e00\u5b9a\u4e0d\u4f1a\u53d1\u751f\u6b7b\u9501\u3002\n\u5982\u679c\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u5c31\u53ef\u80fd\u53d1\u751f\u6b7b\u9501\n\u5904\u4e8e\u4e0d \u5b89\u5168\u72b6\u6001\u672a\u5fc5\u5c31\u662f\u53d1\u751f\u4e86\u6b7b\u9501\uff0c\u4f46\u53d1\u751f\u6b7b\u9501\u65f6\u4e00\u5b9a\u662f\u5728\u4e0d\u5b89\u5168\u72b6\u6001\uff09\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_55","title":"\u94f6\u884c\u5bb6\u7b97\u6cd5","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/2-%E8%BF%9B%E7%A8%8B%E4%B8%8E%E7%BA%BF%E7%A8%8B/#_56","title":"\u6b7b\u9501\u89e3\u9664","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/","title":"\u5185\u5b58\u7ba1\u7406","text":"

    \u5185\u5b58\u53ef\u4ee5\u5b58\u50a8\u6570\u636e,\u7a0b\u5e8f\u6267\u884c\u4e4b\u524d\u9700\u8981\u653e\u8fdb\u5185\u5b58\u4e2d--\u7f13\u548c cpu \u548c\u786c\u76d8\u4e4b\u95f4\u901f\u5ea6\u7684\u77db\u76fe

    \u6309\u5b57\u8282\u7f16\u5740\u90a3\u4e48\u6bcf\u4e2a\u5b58\u50a8\u5355\u5143\u7684\u5927\u5c0f\u5c31\u662f 1b,\u4e5f\u5c31\u662f 8 \u4e2a \u4e8c\u8fdb\u5236\u4f4d\n\n\u6309\u5b57\u7f16\u5740,\u6bcf\u4e2a\u5b58\u50a8\u5355\u4f4d\u5c31\u662f\u4e00\u4e2a\u5b57\u7684\u5927\u5c0f(\u5982\u679c\u8ba1\u7b97\u673a\u5b57\u957f\u662f16 \u4f4d,\u90a3\u5c31\u662f 16 \u4e2a\u4e8c\u8fdb\u5236\u4f4d )\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_2","title":"\u5355\u4f4d","text":"

    \\(1GB=2^{10}MB=1024MB=2^{20}KB={1024}^2KB=2^{30}B\\)

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_3","title":"\u5185\u5b58\u7ba1\u7406\u7684\u6982\u5ff5","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_4","title":"\u5185\u5b58\u7a7a\u95f4\u7684\u6269\u5145","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_5","title":"\u8986\u76d6\u6280\u672f","text":"
    \u8986\u76d6\u6280\u672f\u7684\u601d\u60f3:\u5c06\u7a0b\u5e8f\u5206\u6210\u591a\u4e2a\u6bb5,\u5e38\u7528\u7684\u90e8\u5206\u5e38\u9a7b\u5185\u5b58,\u4e0d\u5e38\u7528\u7684\u90e8\u5206\u9700\u8981\u7684\u65f6\u5019\u8c03\u5165\u5185\u5b58\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_6","title":"\u4ea4\u6362\u6280\u672f","text":"
    \u5185\u5b58\u7a7a\u95f4\u7d27\u5f20\u7684\u65f6\u5019,\u628a\u5185\u5b58\u4e2d\u67d0\u4e9b\u8fdb\u7a0b\u6682\u65f6\u8c03\u51fa\u5916\u5b58,\u628a\u5916\u5b58\u4e2d\u67d0\u4e9b\u5177\u5907\u8fd0\u884c\u6761\u4ef6\u7684\u8fdb\u7a0b\u6362\u5165\u5185\u5b58\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_7","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_8","title":"\u5185\u5b58\u5206\u914d","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_9","title":"\u8fde\u7eed\u5206\u914d","text":"
    \u4e3a\u7528\u6237\u5206\u914d\u7684\u662f\u8fde\u7eed\u7a7a\u95f4\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_10","title":"\u5355\u4e00\u8fde\u7eed\u5206\u914d:","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_11","title":"\u56fa\u5b9a\u5206\u533a\u5206\u914d","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_12","title":"\u52a8\u6001\u5206\u533a\u5206\u914d","text":"

    \u8bb0\u5f55\u5185\u5b58\u4f7f\u7528\u60c5\u51b5

    \u5982\u4f55\u9009\u62e9\u5206\u533a\u5206\u914d

    \u5206\u914d\u548c\u56de\u6536

    \u5185\u90e8\u788e\u7247:\u5206\u914d\u7ed9\u67d0\u4e2a\u8fdb\u7a0b\u7684\u5185\u5b58\u4e2d,\u67d0\u4e9b\u90e8\u5206\u6ca1\u6709\u88ab\u8fdb\u7a0b\u4f7f\u7528\n\u5916\u90e8\u788e\u7247:\u5185\u5b58\u4e2d\u7684\u67d0\u4e9b\u7a7a\u95f2\u5206\u533a\u7531\u4e8e\u592a\u5c0f\u800c\u96be\u4ee5\u5229\u7528\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_13","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_14","title":"\u52a8\u6001\u5206\u533a\u5206\u914d\u7b97\u6cd5","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_15","title":"\u9996\u6b21\u9002\u5e94\u7b97\u6cd5","text":"
    \u6bcf\u6b21\u90fd\u4ece\u4f4e\u5730\u5740\u5f00\u59cb\u67e5\u627e,\u76f4\u5230\u627e\u5230\u6ee1\u8db3\u5927\u5c0f\u7684\u7a7a\u95f2\u5206\u533a\n

    \u5b9e\u73b0\u65b9\u6cd5:\u7a7a\u95f2\u5206\u533a\u5757\u6309\u7167\u8d77\u59cb\u5730\u5740\u4ece\u4f4e\u5230\u9ad8\u6392\u5217,\u6bcf\u6b21\u67e5\u627e\u65f6\u6309\u987a\u5e8f\u67e5\u627e,\u76f4\u5230\u7a7a\u95f2\u5206\u533a\u5927\u5c0f\u8db3\u591f

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_16","title":"\u6700\u4f73\u9002\u5e94\u7b97\u6cd5","text":"
    \u5c3d\u91cf\u5148\u5206\u914d\u5927\u5c0f\u5c0f\u7684\u7a7a\u95f2\u5206\u533a\n

    \u5b9e\u73b0\u65b9\u6cd5:\u7a7a\u95f2\u5206\u533a\u6309\u5927\u5c0f\u9012\u589e\u6392\u5217,\u67e5\u627e\u65f6\u6309\u987a\u5e8f\u67e5\u627e,\u76f4\u5230\u8fdb\u7a0b\u53ef\u4ee5\u88ab\u653e\u5165\u7a7a\u95f2\u5206\u533a

    \u7f3a\u70b9:\u4f1a\u7559\u4e0b\u8d8a\u6765\u8d8a\u591a\u7684\u5916\u90e8\u788e\u7247,\u96be\u4ee5\u5229\u7528

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_17","title":"\u6700\u574f\u9002\u5e94\u7b97\u6cd5","text":"
    \u5c3d\u91cf\u5148\u5206\u914d\u5927\u5c0f\u5927\u7684\u7a7a\u95f2\u5206\u533a(\u4e3a\u4e86\u5f25\u8865\u6700\u4f73\u9002\u5e94\u7b97\u6cd5\u7684\u7f3a\u70b9)\n

    \u7f3a\u70b9:\u5982\u679c\u6709\u5927\u8fdb\u7a0b\u5230\u8fbe\u53ef\u80fd\u4f1a\u65e0\u6cd5\u5206\u914d

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_18","title":"\u4e34\u8fd1\u9002\u5e94\u7b97\u6cd5","text":"
    \u9996\u6b21\u9002\u5e94\u7b97\u6cd5\u6bcf\u6b21\u90fd\u4ece\u94fe\u5934\u5f00\u59cb\u67e5\u627e\u7684\u3002\u8fd9\u53ef\u80fd\u4f1a\u5bfc\u81f4\u4f4e\u5730\u5740\u90e8\u5206\u51fa\u73b0\u5f88\u591a\u5c0f\u7684\u7a7a\u95f2 \u5206\u533a\uff0c\n\u800c\u6bcf\u6b21\u5206\u914d\u67e5\u627e\u65f6\uff0c\u90fd\u8981\u7ecf\u8fc7\u8fd9\u4e9b\u5206\u533a\uff0c\u56e0\u6b64\u4e5f\u589e\u52a0\u4e86\u67e5\u627e\u7684\u5f00\u9500\u3002\n\u5982\u679c\u6bcf\u6b21\u90fd\u4ece\u4e0a\u6b21\u67e5\u627e\u7ed3\u675f\u7684\u4f4d\u7f6e\u5f00\u59cb\u68c0\u7d22\uff0c\u5c31\u80fd\u89e3\u51b3\u4e0a\u8ff0\u95ee\u9898\u3002\n

    \u5b9e\u73b0\u65b9\u6cd5:\u7a7a\u95f2\u5206\u533a\u6309\u5730\u5740\u9012\u589e\u6392\u6210\u5faa\u73af\u94fe\u8868

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_19","title":"\u603b\u7ed3","text":"

    \u6700\u540e\u8fd8\u662f\u9996\u6b21\u9002\u5e94\u6700\u597d\u7528

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_20","title":"\u5206\u9875\u5b58\u50a8\u7ba1\u7406","text":"
    \u5c06\u5185\u5b58\u7a7a\u95f4\u5206\u6210\u4e00\u4e2a\u4e2a\u5927\u5c0f\u76f8\u7b49\u7684\u5206\u533a,\u6bcf\u4e2a\u5206\u533a\u5c31\u662f\u4e00\u4e2a\u9875\u6846(\u9875\u5e27)\n    \u6bcf\u4e00\u4e2a\u9875\u6846\u6709\u4e00\u4e2a\u7f16\u53f7\u79f0\u4e3a\u9875\u6846\u53f7,\u4ece 0 \u5f00\u59cb\n\u5c06\u8fdb\u7a0b\u7684\u903b\u8f91\u5730\u5740\u7a7a\u95f4\u4e5f\u5206\u6210\u4e00\u4e2a\u4e2a\u5927\u5c0f\u76f8\u7b49\u7684\u90e8\u5206,\u6bcf\u4e2a\u90e8\u5206\u79f0\u4e3a\u4e00\u4e2a\u9875,\u6216\u8005\u9875\u9762\n    \u6bcf\u4e2a\u9875\u4e5f\u6709\u4e00\u4e2a\u7f16\u53f7,\u79f0\u4e3a\u9875\u53f7,\u4ece 0 \u5f00\u59cb\n

    \u64cd\u4f5c\u7cfb\u7edf\u4ee5\u9875\u6846\u4e3a\u5355\u4f4d\u5206\u914d\u5185\u5b58,\u8fdb\u7a0b\u7684\u6bcf\u4e2a\u9875\u653e\u8fdb\u4e00\u4e2a\u9875\u6846\u4e2d,\u4e5f\u5c31\u662f\u8bf4,\u8fdb\u7a0b\u7684\u9875\u9762\u548c\u5185\u5b58\u7684\u9875\u6846\u4e00\u4e00\u5bf9\u5e94(\u9875\u8868\u5b9e\u73b0)

    \u9875\u8868:

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_21","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_22","title":"\u5177\u6709\u5feb\u8868\u7684\u5730\u5740\u53d8\u6362\u673a\u6784","text":"

    \u5feb\u8868\uff0c\u53c8\u79f0\u8054\u60f3\u5bc4\u5b58\u5668\uff08TLB\uff0ctranslation lookaside buffer \uff09\uff0c\u662f\u4e00\u79cd\u8bbf\u95ee\u901f\u5ea6\u6bd4\u5185\u5b58\u5feb\u5f88\u591a\u7684\u9ad8\u901f\u7f13\u5b58\uff08TLB\u4e0d\u662f\u5185\u5b58\uff01\uff09\uff0c \u7528\u6765\u5b58\u653e\u6700\u8fd1\u8bbf\u95ee\u7684\u9875\u8868\u9879\u7684\u526f\u672c\uff0c\u53ef\u4ee5\u52a0\u901f\u5730\u5740\u53d8\u6362\u7684\u901f\u5ea6\u3002 \u4e0e\u6b64\u5bf9\u5e94\uff0c\u5185\u5b58\u4e2d\u7684\u9875\u8868\u5e38\u79f0\u6162\u8868\u3002

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_23","title":"\u5feb\u8868\u80fd\u63d0\u9ad8\u6548\u7387\u7684\u539f\u56e0","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_24","title":"\u603b\u7ed3","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_25","title":"\u9875\u5f0f\u7ba1\u7406","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_26","title":"\u6bb5\u9875\u5f0f\u7ba1\u7406","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_27","title":"\u865a\u62df\u5185\u5b58","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_28","title":"\u5c40\u90e8\u6027\u539f\u7406","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_29","title":"\u8bf7\u6c42\u5206\u9875\u7ba1\u7406\u65b9\u5f0f","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_30","title":"\u9875\u8868\u53d8\u5316","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_31","title":"\u7f3a\u9875\u4e2d\u65ad","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_32","title":"\u6700\u4f73\u7f6e\u6362\u7b97\u6cd5","text":"

    \u6700\u4f73\u7f6e\u6362\u7b97\u6cd5(OPT,Optimal):\u6bcf\u6b21\u9009\u62e9\u6dd8\u6c70\u7684\u9875\u9762\u5c06\u662f\u4ee5\u540e\u6c38\u4e0d\u4f7f\u7528\uff0c\u6216\u8005\u5728\u6700\u957f\u65f6\u95f4\u5185\u4e0d\u518d\u88ab \u8bbf\u95ee\u7684\u9875\u9762\uff0c\u8fd9\u6837\u53ef\u4ee5\u4fdd\u8bc1\u6700\u4f4e\u7684\u7f3a\u9875\u7387\u3002

    \u5148\u8fdb\u5148\u51fa\u7f6e\u6362\u7b97\u6cd5(FIFO):\u6bcf\u6b21\u9009\u62e9\u7684\u6dd8\u6c70\u9875\u9762\u662f\u6700\u65e9\u8fdb\u5165\u5185\u5b58\u7684\u9875\u9762

    \u6700\u8fd1\u6700\u4e45\u672a\u4f7f\u7528\u7f6e\u6362\u7b97\u6cd5(LRU,least recently used):\u6bcf\u6b21\u6dd8\u6c70\u7684\u9875\u9762\u662f\u6700\u8fd1\u6700\u4e45\u672a\u4f7f\u7528\u7684\u9875\u9762

    \u65f6\u949f\u7f6e\u6362\u7b97\u6cd5\u662f\u4e00\u79cd\u6027\u80fd\u548c\u5f00\u9500\u8f83\u5747\u8861\u7684\u7b97\u6cd5\uff0c\u53c8\u79f0CLOCK\u7b97\u6cd5\uff0c\u6216\u6700\u8fd1\u672a\u7528\u7b97\u6cd5(NRU,Not Recently Used)

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_33","title":"\u9875\u9762\u5206\u914d\u7b56\u7565","text":"

    \u9a7b\u7559\u96c6:\u8bf7\u6c42\u5206\u9875\u7ba1\u7406\u4e2d\u7ed9\u8fdb\u7a0b\u5206\u914d\u7684\u7269\u7406\u5757\u7684\u96c6\u5408

    \u5de5\u4f5c\u96c6:\u67d0\u6bb5\u65f6\u95f4\u5185,\u8fdb\u7a0b\u5b9e\u9645\u8bbf\u95ee\u7684\u9875\u9762\u7684\u96c6\u5408

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/3-%E5%86%85%E5%AD%98%E7%AE%A1%E7%90%86/#_34","title":"\u5185\u5b58\u6620\u5c04\u6587\u4ef6","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/","title":"\u6587\u4ef6\u7ba1\u7406","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_2","title":"\u6587\u4ef6\u7684\u5c5e\u6027","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_3","title":"\u6587\u4ef6\u7684\u903b\u8f91\u7ed3\u6784","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_4","title":"\u6587\u4ef6\u76ee\u5f55","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_5","title":"\u6587\u4ef6\u7684\u7269\u7406\u7ed3\u6784","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_6","title":"\u903b\u8f91\u7ed3\u6784&\u7269\u7406\u7ed3\u6784","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_7","title":"\u6587\u4ef6\u5b58\u50a8\u7a7a\u95f4\u7ba1\u7406","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_8","title":"\u6587\u4ef6\u7684\u57fa\u7840\u64cd\u4f5c","text":"
    \u901a\u8fc7\u76ee\u5f55\u5757\u64cd\u4f5c\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_9","title":"\u6587\u4ef6\u5171\u4eab","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_10","title":"\u6587\u4ef6\u4fdd\u62a4","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_11","title":"\u6587\u4ef6\u7cfb\u7edf\u7684\u7ed3\u6784\u5c42\u6b21","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_12","title":"\u6587\u4ef6\u7cfb\u7edf\u7684\u5168\u5c40\u7ed3\u6784","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/4-%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86/#_13","title":"\u865a\u62df\u6587\u4ef6\u7cfb\u7edf&\u6587\u4ef6\u7cfb\u7edf\u6302\u8f7d","text":""},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/note-chapter1/","title":"Note chapter1","text":"

    \u63d0\u9ad8\u5355\u673a\u8d44\u6e90\u5229\u7528\u7387\u7684\u5173\u952e\u6280\u672f\u662f\u591a\u9053\u7a0b\u5e8f\u8bbe\u8ba1\u6280\u672f,\u865a\u62df\u6280\u672f\u548c\u4ea4\u6362\u6280\u672f\u4ee5\u591a\u9053\u7a0b\u5e8f\u8bbe\u8ba1\u6280\u672f\u4e3a\u524d\u63d0

    \u5f15\u5165\u591a\u9053\u7a0b\u5e8f\u8bbe\u8ba1\u6280\u672f\u540e,\u7a0b\u5e8f\u7684\u6267\u884c\u5c31\u5931\u53bb\u4e86\u5c01\u95ed\u6027\u548c\u987a\u5e8f\u6027

    \u8981\u6c42\u5feb\u901f\u54cd\u5e94\u7528\u6237\u662f\u5206\u65f6\u64cd\u4f5c\u7cfb\u7edf\u51fa\u73b0\u7684\u91cd\u8981\u539f\u56e0

    \u73b0\u4ee3\u64cd\u4f5c\u7cfb\u7edf\u90fd\u662f\u591a\u4efb\u52a1\u7684,\u5141\u8bb8\u7528\u6237\u5c06\u628a\u7a0b\u5e8f\u5206\u6210\u591a\u4e2a\u72ec\u7acb\u7684\u4efb\u52a1,\u5728\u5b8f\u89c2\u4e0a\u5e76\u884c\u6267\u884c,\u5fae\u89c2\u4e0a\u5e76\u53d1,\u5982\u679c\u662f\u591a\u5904\u7406\u5668\u7cfb\u7edf,\u5219\u662f\u771f\u6b63\u7684\u5e76\u884c\u6267\u884c

    \u901a\u7528\u64cd\u4f5c\u7cfb\u7edf:\u5177\u6709\u591a\u79cd\u7c7b\u578b\u64cd\u4f5c\u7279\u5f81\u7684\u64cd\u4f5c\u7cfb\u7edf\u3002\u53ef\u4ee5\u540c\u65f6\u517c\u6709\u591a\u9053\u6279\u5904\u7406\u3001\u5206\u65f6\u3001\u5b9e\u65f6\u5904\u7406\u7684\u529f\u80fd\uff0c\u6216\u5176\u4e2d\u4e24\u79cd\u4ee5\u4e0a\u7684\u529f\u80fd\u3002

    \u901a\u7528\u64cd\u4f5c\u7cfb\u7edf\u4f7f\u7528\u65f6\u95f4\u7247\u8f6e\u8f6c\u8c03\u5ea6\u7b97\u6cd5,\u7528\u6237\u7a0b\u5e8f\u4e0d\u9700\u8981\u5411\u7cfb\u7edf\u9884\u5b9a\u8fd0\u884c\u65f6\u95f4,\u7cfb\u7edf\u4f1a\u81ea\u52a8\u5206\u914d\u65f6\u95f4\u7247 \n\u64cd\u4f5c\u7cfb\u7edf\u6267\u884c\u7a0b\u5e8f\u65f6,\u5fc5\u987b\u4ece\u8d77\u59cb\u5730\u5740\u5f00\u59cb\u6267\u884c\n

    \u8ba1\u7b97\u673a\u901a\u8fc7\u786c\u4ef6\u5b9e\u73b0\u7528\u6237\u6001\u5230\u6838\u5fc3\u6001\u7684\u8f6c\u6362,\u4ece\u6838\u5fc3\u6001\u5230\u7528\u6237\u6001\u7684\u8f6c\u6362\u662f\u7531\u64cd\u4f5c\u7cfb\u7edf\u5b8c\u6210\u7684

    \u9519\u8bef\u7684\u89c2\u70b9\u6709:\u7528\u6237\u6001\u5230\u6838\u5fc3\u6001\u662f\u7531:\n    1.\u6838\u5fc3\u6001\u7a0b\u5e8f\u5b8c\u6210:\u4e0d\u53ef\u80fd,\u56e0\u4e3a\u8f6c\u6362\u4e4b\u524d\u5728\u7528\u6237\u6001\n    2.\u7528\u6237\u7a0b\u5e8f:\u4e0d\u53ef\u80fd,\u8fd9\u6837\u7528\u6237\u80fd\u64cd\u4f5c\u7279\u6743\u6307\u4ee4\n    3.\u4e2d\u65ad\u5904\u7406\u7a0b\u5e8f:\u4e0d\u53ef\u80fd,\u8fd9\u4e00\u822c\u662f\u5728\u64cd\u4f5c\u7cfb\u7edf\u5185\u6838\u6001\u6267\u884c\u7684\n

    \u7cfb\u7edf\u8c03\u7528\u7684\u6267\u884c\u4e00\u5b9a\u5728\u5185\u6838\u6001,\u4f46\u662f\u7cfb\u7edf\u8c03\u7528\u7684\u8c03\u7528\u8005\u53ef\u4ee5\u662f\u7528\u6237\u6001\u7a0b\u5e8f

    \u5904\u4e8e\u6838\u5fc3\u6001\u7684 CPU \u53ef\u4ee5\u6267\u884c\u6307\u4ee4\u7cfb\u7edf\u4e2d\u7684\u6240\u6709\u6307\u4ee4

    \u8bbf\u7ba1\u6307\u4ee4:\u4e5f\u79f0\u9677\u5165\u6307\u4ee4,\u662f\u5e94\u7528\u7a0b\u5e8f\u8bf7\u6c42\u64cd\u4f5c\u7cfb\u7edf\u4ecb\u5165\u7684\u65f6\u5019\u6267\u884c\u7684\u6307\u4ee4

    \u5e93\u51fd\u6570\u662f\u5c01\u88c5\u5728\u5e93\u6587\u4ef6\u4e2d\u7684\u53ef\u590d\u7528\u4ee3\u7801\u5feb,\u8fd0\u884c\u5728\u7528\u6237\u6001,\u7cfb\u7edf\u8c03\u7528\u662f\u9762\u5411\u786c\u4ef6\u7684,\u8fd0\u884c\u5728\u5185\u6838\u6001,\u662f\u64cd\u4f5c\u7cfb\u7edf\u4e3a\u7528\u6237\u63d0\u4f9b\u7684\u63a5\u53e3

    \u5e93\u51fd\u6570\u65b9\u4fbf\u8c03\u8bd5,\u65b9\u4fbf\u5207\u6362,\u5f00\u9500\u5f88\u5c0f\n\u7cfb\u7edf\u8c03\u7528\u5f88\u9ebb\u70e6,\u8fd0\u884c\u5728\u6838\u5fc3\u6001,\u9700\u8981\u5207\u6362,\u5f00\u9500\u5f88\u5927\n

    \u7a0b\u5e8f\u8ba1\u6570\u5668PC(Program Counter)

    \u7a0b\u5e8f\u72b6\u6001\u5b57\u5bc4\u5b58\u5668PSW(Program Status Word)

    \u901a\u7528\u5bc4\u5b58\u5668

    \u5904\u7406\u5916\u90e8\u4e2d\u65ad\u7684\u65f6\u5019,\u7a0b\u5e8f\u8ba1\u6570\u5668 PC \u7531\u4e2d\u65ad\u6307\u4ee4\u4fdd\u5b58,\u901a\u7528\u5bc4\u5b58\u5668\u7684\u6570\u636e\u7531\u64cd\u4f5c\u7cfb\u7edf\u4fdd\u5b58,\u5757\u8868,cache\u4e2d\u7684\u5185\u5bb9\u7531\u786c\u4ef6\u673a\u6784\u4fdd\u5b58

    \u5fae\u5185\u6838:

    \u57fa\u672c\u6982\u5ff5:\u5c06\u64cd\u4f5c\u7cfb\u7edf\u5206\u4e3a\u4e24\u5927\u90e8\u5206:\u5fae\u5185\u6838\u548c\u591a\u4e2a\u670d\u52a1\u5668,\u5fae\u5185\u6838\u53ea\u63d0\u4f9b\u6700\u57fa\u672c\u7684\u529f\u80fd,\u5176\u4ed6\u529f\u80fd\u7531\u670d\u52a1\u5668\u63d0\u4f9b\n        \u5fae\u5185\u6838\u901a\u5e38\u5305\u62ec:\n                1.\u4e0e\u786c\u4ef6\u7d27\u5bc6\u76f8\u8fde\u7684\u90e8\u5206\n                2.\u4e00\u4e9b\u57fa\u672c\u529f\u80fd\n                3.\u5ba2\u6237\u548c\u670d\u52a1\u5668\u4e4b\u95f4\u7684\u901a\u4fe1\n        \u5fae\u5185\u6838\u7684\u57fa\u672c\u529f\u80fd:\n                1.\u8fdb\u7a0b(\u7ebf\u7a0b)\u7ba1\u7406,\n                2.\u4f4e\u7ea7\u5b58\u50a8\u5668\u7ba1\u7406:\u6bd4\u5982\u5982\u4f55\u5b9e\u73b0\u5c06\u903b\u8f91\u5730\u5740\u8f6c\u5316\u4e3a\u7269\u7406\u5730\u5740\u7684\u673a\u5236\u5c31\u5e94\u8be5\u5728\u5fae\u5185\u6838\u4e2d\u5b9e\u73b0\n                    \u4f46\u662f\u5982\u5982\u4f55\u5206\u914d\u7269\u7406\u5185\u5b58,\u5b9e\u73b0\u56de\u6536\u7b49\u7b49,\u5219\u5e94\u8be5\u5728\u670d\u52a1\u5668\u4e2d\u5b9e\u73b0\n                3.\u4e2d\u65ad\u548c\u9677\u5165\u5904\u7406:\u8bc6\u522b\u4e2d\u65ad\u548c\u9677\u5165\u540e,\u5c06\u63a7\u5236\u6743\u4ea4\u7ed9\u76f8\u5e94\u7684\u670d\u52a1\u5668\n        \u5fae\u5185\u6838\u7684\u7279\u70b9:\n            \u5b9e\u73b0\u4e86\u9ad8\u53ef\u9760\u6027,\u9ad8\u7075\u6d3b\u6027,\u9ad8\u53ef\u6269\u5c55\u6027\n            \u53ef\u79fb\u690d\u6027\n            \u5206\u5e03\u5f0f\u8ba1\u7b97\n            \u4e3b\u8981\u7f3a\u70b9\u662f\u662f\u9700\u8981\u9891\u7e41\u7684\u5728\u6838\u5fc3\u6001\u548c\u7528\u6237\u6001\u4e4b\u95f4\u5207\u6362,\u5bfc\u81f4\u6027\u80fd\u4e0b\u964d\n

    ROM(\u53ea\u8bfb\u5b58\u50a8\u5668),SRAM(\u9759\u6001\u968f\u673a\u5b58\u53d6\u5668),DRAM(\u52a8\u6001\u968f\u673a\u5b58\u53d6\u5668)

    \u4e2d\u65ad\u5411\u91cf\u8868

    \u5c42\u6b21\u7ed3\u6784\u6700\u5927\u7684\u4e0d\u8db3\u662f\u8bbe\u8ba1\u56f0\u96be:\u9700\u8981\u5bf9\u6bcf\u4e00\u5c42\u8fdb\u884c\u7cbe\u5fc3\u7684\u5212\u5206\u548c\u8bbe\u8ba1,\u4fdd\u8bc1\u63a5\u53e3\u7684\u4e00\u81f4\u6027\u548c\u5b8c\u5907\u6027

    \u6a21\u5757\u5316\u64cd\u4f5c\u7cfb\u7edf\u7531\u4e8e\u5404\u4e2a\u6a21\u5757\u76f8\u4e92\u8c03\u7528,\u4e00\u65e6\u67d0\u4e2a\u6a21\u5757\u51fa\u73b0\u95ee\u9898\u53ef\u80fd\u5bfc\u81f4\u6574\u4e2a\u7cfb\u7edf\u5d29\u6e83

    \u64cd\u4f5c\u7cfb\u7edf\u7684\u5f15\u5bfc\u7a0b\u5e8f\u4f4d\u4e8e\u78c1\u76d8\u6d3b\u52a8\u5206\u533a\u7684\u5f15\u5bfc\u6247\u533a\u4e2d,\u5f15\u5bfc\u7a0b\u5e8f\u5206\u4e3a\u4e24\u79cd,\u4e00\u79cd\u662f\u4f4d\u4e8e ROM \u4e2d\u7684\u81ea\u4e3e\u7a0b\u5e8f(BIOS \u7684\u7ec4\u6210\u90e8\u5206),\u7528\u4e8e\u542f\u52a8\u5177\u4f53\u7684\u8bbe\u5907;\u53e6\u4e00\u79cd\u662f\u4f4d\u4e8e\u88c5\u6709\u64cd\u4f5c\u7cfb\u7edf\u7684\u6d3b\u52a8\u5206\u533a\u7684\u5f15\u5bfc\u6247\u533a\u4e2d\u7684\u5f15\u5bfc\u7a0b\u5e8f (\u79f0\u4e3a\u542f\u52a8\u7ba1\u7406\u5668),\u7528\u4e8e\u5f15\u5bfc\u64cd\u4f5c\u7cfb\u7edf.<\u8ba1\u7b97\u673a\u7684\u5f15\u5bfc\u7a0b\u5e8f\u4f4d\u4e8e\u786c\u76d8\u4e2d>

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/note-chapter1/#_1","title":"\u8ba1\u7b97\u673a\u542f\u52a8\u8fc7\u7a0b:","text":"
    \u6fc0\u6d3b CPU (\u8bfb\u53d6 ROM \u4e2d\u7684 boot \u7a0b\u5e8f,\u5c06\u6307\u4ee4\u5bc4\u5b58\u5668\u8bbe\u7f6e\u4e3a BIOS \u7684\u7b2c\u4e00\u6761\u6307\u4ee4,\u4e5f\u5c31\u662f\u5f00\u59cb\u6267\u884c BIOS \u7684\u6307\u4ee4) \n-> \u786c\u4ef6\u81ea\u68c0: BIOS \u6784\u5efa\u4e2d\u65ad\u5411\u91cf\u8868,\u68c0\u67e5\u786c\u4ef6\n-> \u52a0\u8f7d\u5e26\u6709\u64cd\u4f5c\u7cfb\u7edf\u7684\u786c\u76d8:\u8bfb\u53d6 Boot Sequence ,\u5c06\u63a7\u5236\u6743\u4ea4\u7ed9\u542f\u52a8\u987a\u5e8f\u5728\u7b2c\u4e00\u4f4d\u7684\u5b58\u50a8\u8bbe\u5907\n    (\u6216\u8005\u548c\u7528\u6237\u4ea4\u4e92,\u6bd4\u5982\u53cc\u7cfb\u7edf\u9009\u62e9\u8fdb\u5165 ubuntu \u8fd8\u662f Windows \u7684\u65f6\u5019\u51fa\u73b0\u7684\u754c\u9762)\n    \u7136\u540eCPU \u5c06\u5b58\u50a8\u8bbe\u5907\u5f15\u5bfc\u6247\u533a\u7684\u5185\u5bb9\u52a0\u8f7d\u5230\u5185\u5b58\u4e2d\n->\u52a0\u8f7d\u4e3b\u5f15\u5bfc\u8bb0\u5f55(MBR)<\u4f5c\u7528\u662f\u544a\u8bc9 CPU \u786c\u76d8\u7684\u54ea\u4e2a\u5206\u533a\u627e\u64cd\u4f5c\u7cfb\u7edf>:\u68c0\u67e5\u5b58\u50a8\u8bbe\u5907\u662f\u4e0d\u662f\u53ef\u5f15\u5bfc\u76d8,\u4e0d\u662f\u5c31\u5230\u4e0b\u4e00\u4e2a\u5b58\u50a8\u8bbe\u5907\n->\u626b\u63cf\u786c\u76d8\u5206\u533a\u8868,\u52a0\u8f7d\u786c\u76d8\u6d3b\u52a8\u5206\u533a:\u5c06\u63a7\u5236\u6743\u4ea4\u7ed9\u6d3b\u52a8\u5206\u533a(\u64cd\u4f5c\u7cfb\u7edf\u5728\u8fd9\u91cc)\n->\u52a0\u8f7d\u5206\u533a\u5f15\u5bfc\u8bb0\u5f55(PBR):\u8fd9\u662f\u6d3b\u52a8\u5206\u533a\u7684\u7b2c\u4e00\u4e2a\u6247\u533a,\u5bfb\u627e\u5e76\u6fc0\u6d3b\u6839\u76ee\u5f55\u4e0b\u7528\u4e8e\u5f15\u5bfc\u64cd\u4f5c\u7cfb\u7edf\u7684\u7a0b\u5e8f(\u542f\u52a8\u7ba1\u7406\u5668)\n->\u52a0\u8f7d\u542f\u52a8\u7ba1\u7406\u5668\n->\u52a0\u8f7d\u64cd\u4f5c\u7cfb\u7edf:\u5c06\u64cd\u4f5c\u7cfb\u7edf\u7684\u521d\u59cb\u5316\u7a0b\u5e8f\u52a0\u8f7d\u5230\u5185\u5b58\u4e2d\u5f00\u59cb\u6267\u884c\n
    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/note-chapter2/","title":"Note chapter2","text":"

    \u7ebf\u7a0b\u662f CPU \u8c03\u5ea6\u7684\u57fa\u672c\u5355\u4f4d,\u53ef\u4ee5\u72ec\u7acb\u7684\u6267\u884c\u7a0b\u5e8f(\u5e76\u4e0d\u662f\u4e00\u5b9a\u8981\u8bf4\u8fdb\u7a0b)

    \u7ebf\u7a0b\u6ca1\u6709\u81ea\u5df1\u72ec\u7acb\u7684\u5730\u5740\u7a7a\u95f4,\u5b83\u5171\u4eab\u5176\u8fdb\u7a0b\u6240\u5c5e\u7684\u5730\u5740\u7a7a\u95f4

    \u4e00\u4e2a\u8fdb\u7a0b\u53ef\u4ee5\u987a\u5e8f\u7684\u6267\u884c\u4e00\u4e2a\u6216\u8005\u591a\u4e2a\u7a0b\u5e8f,\u4f46\u662f\u4e0d\u80fd\u540c\u65f6\u6267\u884c\u591a\u4e2a\u7a0b\u5e8f

    \u4e00\u4e2a\u7a0b\u5e8f\u7684\u4e00\u6b21\u6267\u884c\u6709\u53ef\u80fd\u4ea7\u751f\u591a\u4e2a\u8fdb\u7a0b,\u6bd4\u5982\u957f\u6309\u53cc\u51fb\u52a0\u70b9\u8d5e( )

    \u7a0b\u5e8f\u5c01\u95ed\u6027\u662f\u6307\u8fdb\u7a0b\u6267\u884c\u7684\u7ed3\u679c\u53ea\u53d6\u51b3\u4e8e\u8fdb\u7a0b\u672c\u8eab,\u4e0d\u53d7\u5916\u754c\u7684\u5f71\u54cd,\u4e5f\u5c31\u662f\u8bf4\u4e0d\u7ba1\u8fdb\u7a0b\u662f\u4e0d\u505c\u987f\u6267\u884c\u8fd8\u662f\u8d70\u8d70\u505c\u505c,\u7ed3\u679c\u90fd\u662f\u4e00\u6837\u7684,\u5e76\u53d1\u4ee5\u540e\u8fdb\u7a0b\u7684\u6267\u884c\u7ed3\u679c\u4f1a\u4e0d\u540c

    \u6bd4\u5982\u5e76\u53d1\u8fdb\u7a0b\u5171\u4eab\u53d8\u91cf\u7684\u65f6\u5019,\u5404\u4e2a\u8fdb\u7a0b\u6267\u884c\u7684\u5148\u540e\u987a\u5e8f\u4e0d\u540c\u53d8\u91cf\u7684\u6700\u7ec8\u7ed3\u679c\u4e5f\u6709\u53ef\u80fd\u4e0d\u540c\n

    \u901f\u5ea6\u6700\u5feb\u7684\u8fdb\u7a0b\u901a\u4fe1\u65b9\u5f0f\u662f\u5171\u4eab\u5185\u5b58,\u6d88\u606f\u4f20\u9012\u9700\u8981\u62f7\u8d1d\u6570\u636e,\u4f20\u9012,\u6392\u961f\u7b49\u7b49,\u7ba1\u9053\u901a\u4fe1\u540c\u7406

    \u5355\u5904\u7406\u5668\u7cfb\u7edf\u5b9e\u73b0\u5e76\u53d1\u6280\u672f\u540e,\u540c\u4e00\u65f6\u95f4\u6bb5\u5185\u5404\u4e2a\u8fdb\u7a0b\u5e76\u53d1\u8fd0\u884c,cpu \u548c I/O \u8bbe\u5907\u5e76\u884c\u5de5\u4f5c

    \u7ebf\u7a0b\u7684\u4f18\u70b9\u6709\u63d0\u9ad8\u7cfb\u7edf\u5e76\u53d1\u6027,\u8282\u7ea6\u7cfb\u7edf\u8d44\u6e90,\u4fbf\u4e8e\u8fdb\u7a0b\u95f4\u901a\u4fe1\u7b49\u7b49,\u4f46\u662f\u7ebf\u7a0b\u4f1a\u964d\u4f4e\u8fdb\u7a0b\u7684\u5b89\u5168\u6027,\u56e0\u4e3a\u4e00\u65e6\u4e00\u4e2a\u7ebf\u7a0b\u51fa\u73b0\u95ee\u9898,\u6574\u4e2a\u8fdb\u7a0b\u90fd\u6709\u53ef\u80fd\u51fa\u9519

    \u5185\u6838\u7ea7\u7ebf\u7a0b\u5728\u540c\u4e00\u8fdb\u7a0b\u4e0b\u5207\u6362\u7684\u65f6\u5019,\u7cfb\u7edf\u5f00\u9500\u5927,\u56e0\u4e3a\u8981\u8fdb\u884c\u6838\u5fc3\u6001\u7528\u6237\u6001\u7684\u8f6c\u5316,\u4f46\u662f\u7528\u6237\u7ea7\u7ebf\u7a0b\u5c31\u4e0d\u7528,\u56e0\u4e3a\u5728\u64cd\u4f5c\u7cfb\u7edf\u770b\u6765\u8fd9\u4e00\u76f4\u5c31\u662f\u4e00\u4e2a\u8fdb\u7a0b\u5728\u8fd0\u884c,\u56e0\u6b64\u7cfb\u7edf\u5f00\u9500\u5c0f\u7684\u591a

    \u540c\u65f6\u7528\u6237\u7ea7\u7ebf\u7a0b\u7684\u7f3a\u70b9\u5c31\u66b4\u9732\u51fa\u6765\u4e86,\u56e0\u4e3a\u5728\u64cd\u4f5c\u7cfb\u7edf\u770b\u6765\u5916\u90e8\u53ea\u6709\u4e00\u4e2a\u8fdb\u7a0b\u5728\u8fd0\u884c,\u56e0\u6b64\u53ea\u4f1a\u5206\u914d\u6700\u591a\u4e00\u4e2a cpu,\u6362\u53e5\u8bdd\u8bf4\u8fd9\u4e9b\u7ebf\u7a0b\u53ea\u80fd\u8f6e\u8f6c\u4f7f\u7528 cpu,\u800c\u4e14\u4e00\u65e6\u6709\u4e00\u4e2a\u51fa\u4e86\u95ee\u9898,\u6574\u4e2a\u8fdb\u7a0b\u90fd\u4f1a\u88ab\u963b\u585e

    \u8fdb\u7a0b\u5524\u9192\u7684\u6982\u5ff5\u662f\u8bf4,\u5f53\u8fdb\u7a0b\u9700\u8981\u7684\u8d44\u6e90(\u4e0d\u5305\u62ecCPU)\u53ef\u7528\u7684\u65f6\u5019,\u8fdb\u7a0b\u88ab\u5524\u9192.

    \u6240\u4ee5,\u65f6\u95f4\u7247\u7528\u5b8c\u4ee5\u540e\u4e0b\u4e00\u4e2a\u8fdb\u7a0b\u4e0a\u5904\u7406\u673a\u8fd0\u884c\u7684\u8fc7\u7a0b\u4e0d\u80fd\u8bf4\u662f\u5524\u9192,\u56e0\u4e3a\u4e8b\u5b9e\u4e0a\u8fd9\u4e2a\u8fdb\u7a0b\u7b49\u5f85\u7684\u7cfb\u7edf\u8d44\u6e90\u662f\u5904\u7406\u673a\n

    \u4e34\u754c\u8d44\u6e90\u53ea\u80fd\u540c\u65f6\u88ab\u4e00\u4e2a\u8fdb\u7a0b\u4f7f\u7528,\u5373\u4fbf\u662f\u7236\u5b50\u8fdb\u7a0b\u4e5f\u4e0d\u80fd\u540c\u65f6\u8bbf\u95ee,\u53e6\u5916\u7236\u5b50\u8fdb\u7a0b\u7684\u865a\u62df\u5730\u5740\u7a7a\u95f4\u4e0d\u662f\u5171\u4eab\u7684,\u7236\u8fdb\u7a0b\u53ea\u53ef\u4e0e\u5b50\u8fdb\u7a0b\u5171\u4eab\u4e00\u90e8\u5206\u8d44\u6e90

    \u8fdb\u7a0b\u4ece\u521b\u5efa\u6001\u5230\u5c31\u7eea\u6001\u662f\u7531\u9ad8\u7ea7\u8c03\u5ea6\u5b8c\u6210\u7684\uff0c\u9ad8\u7ea7\u8c03\u5ea6\uff08\u4f5c\u4e1a\u8c03\u5ea6\uff09\u7684\u4efb\u52a1\u662f\u4ece\u540e\u80cc\u961f\u5217\u4e2d\u9009\u62e9\u4e00\u4e2a\u6216\u8005\u4e00\u6279\u4f5c\u4e1a\uff0c\u521b\u5efaPCB\uff0c\u5206\u914d\u5185\u5b58\u7b49\u5176\u4ed6\u8d44\u6e90\uff0c\u5e76\u63d2\u5165\u5c31\u7eea\u961f\u5217

    \u8fdb\u963b\u585e\u6001\u5e94\u8be5\u662f\u4e2d\u7ea7\u8c03\u5ea6\uff0c\u4e0a\u5904\u7406\u673a\u8fd0\u884c\u548c\u56de\u5230\u5c31\u7eea\u6001\u90fd\u662f\u4f4e\u7ea7\u8c03\u5ea6

    \u5904\u4e8e\u4e34\u754c\u533a\u7684\u8fdb\u7a0b\u4e5f\u53ef\u4ee5\u88ab\u8c03\u5ea6\uff0c\u6216\u8005\u6709\u53ef\u80fd\u81ea\u5df1\u8bf7\u6c42I/O\u88ab\u963b\u585e

    FCFS\u5229\u4e8e\u957f\u4f5c\u4e1a\uff0c\u800cCPU\u578b\u7e41\u5fd9\u4f5c\u4e1a\u4e5f\u8981\u957f\u65f6\u95f4\u5360\u7528CPU\uff0c\u56e0\u6b64\u7c7b\u4f3c\u4e8e\u957f\u4f5c\u4e1a\uff0c\u4ece\u800cFCFS\u7b97\u6cd5\u4e5f\u5229\u4e8eCPU\u7e41\u5fd9\u578b\u4f5c\u4e1a

    \u5b9e\u65f6\u7cfb\u7edf\u666e\u904d\u91c7\u7528\u62a2\u5360\u5f0f\u7684\u4f18\u5148\u7ea7\u7b97\u6cd5\uff0c\u5916\u90e8\u76f4\u63a5\u8bbe\u7f6e\u9759\u6001\u4f18\u5148\u7ea7\uff0c\u4f7f\u5f97\u673a\u5668\u7acb\u523b\u505a\u51fa\u54cd\u5e94

    \u591a\u7ea7\u53cd\u9988\u961f\u5217\u9700\u8981\u8bbe\u7f6e\u5f88\u591a\u961f\u5217\uff0c\u5e76\u518d\u4e0d\u540c\u961f\u5217\u4e2d\u8f6c\u5316\uff0c\u7cfb\u7edf\u5f00\u9500\u8f83\u5927

    0\u65f6\u523b\u4e0a\u5904\u7406\u673a\u4e5f\u5c5e\u4e8e\u8fdb\u7a0b\u8c03\u5ea6\uff0c\u56e0\u6b64\u5982\u679c\u9898\u76ee\u95ee\u8c03\u5ea6\u6b21\u6570\u8bb0\u5f97\u52a0\u4e0a\u6700\u5f00\u59cb\u7684\u4e00\u6b21

    \u6b63\u5728\u8bbf\u95ee\u4e34\u754c\u8d44\u6e90\u7684\u8fdb\u7a0b\u7531\u4e8e\u8bf7\u6c42 I/O \u88ab\u963b\u585e\u65f6,\u8fd0\u6c14\u5176\u4ed6\u8fdb\u7a0b\u4e0a\u5904\u7406\u673a\u8fd0\u884c\u4f46\u662f\u4e0d\u5f97\u8fdb\u5165\u8be5\u8fdb\u7a0b\u6240\u9501\u5b9a\u7684\u4e34\u754c\u533a

    \u5171\u4eab\u6570\u636e\u548c\u4e34\u754c\u8d44\u6e90\u7684\u6700\u5927\u533a\u522b\u5c31\u662f\u662f\u5426\u5728\u540c\u4e00\u65f6\u95f4\u5185\u53ea\u5141\u8bb8\u4e00\u4e2a\u8fdb\u7a0b\u8bbf\u95ee,\u5982\u516c\u7528\u961f\u5217

    \u4e24\u4e2a\u8fdb\u7a0b\u9700\u8981\u534f\u540c\u5de5\u4f5c\u5c31\u662f\u6709\u540c\u6b65\u5173\u7cfb,\u6bd4\u5982\u5199\u548c\u8bfb\u6570\u636e

    \u7528 P,V \u64cd\u4f5c\u5b9e\u73b0\u8fdb\u7a0b\u540c\u6b65,\u4fe1\u53f7\u91cf\u7684\u521d\u503c\u5c31\u662f\u8d44\u6e90\u7684\u91cf\u5316

    \u7eaf\u4ee3\u7801:\u53c8\u79f0\u53ef\u91cd\u5165\u4ee3\u7801,\u5141\u8bb8\u591a\u4e2a\u8fdb\u7a0b\u540c\u65f6\u8bbf\u95ee

    \u6b7b\u9501\u7684\u60c5\u51b5

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/note-chapter2/#process1-px-ifyavailable-py-something-process2-py-ifxavailable-px-something","title":"
    process1{\n    P(X);\n    if(Y.available){\n        P(Y);\n        something;\n    }\n}\n\nprocess2{\n    P(Y);\n    if(X.available){\n        P(X);\n        something;\n    }\n}\n
    ","text":"

    \u53ef\u80fd\u51fa\u73b0\u8fdb\u7a0b\u5168\u90e8\u88ab\u963b\u585e\u7684\u60c5\u51b5(n \u4e2a ),\u4f46\u662f\u5982\u679c\u6ca1\u6709\u963b\u585e,\u5c31\u7eea\u961f\u5217\u6700\u591a\u6709 n-1 \u4e2a\u8fdb\u7a0b(\u603b\u5171 n \u4e2a)

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/note-%E6%A0%B8%E5%BF%83%E6%80%81%E6%8C%87%E4%BB%A4/","title":"Note \u6838\u5fc3\u6001\u6307\u4ee4","text":"

    \u5927\u591a\u6570\u64cd\u4f5c\u7cfb\u7edf\u7684\u5185\u6838\u5305\u62ec\u56db\u4e2a\u65b9\u9762:

    1.\u65f6\u949f\u7ba1\u7406\n2.\u4e2d\u65ad\u673a\u5236\n3.\u539f\u8bed\n4.\u7cfb\u7edf\u63a7\u5236\u7684\u6570\u636e\u7ed3\u6784\u548c\u5904\u7406\n

    \u5c4f\u853d\u4e2d\u65ad

    \u8bbe\u7f6e\u65f6\u949f\u7684\u503c

    \u505c\u673a\u6307\u4ee4

    "},{"location":"Notebook/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F/note-%E7%94%A8%E6%88%B7%E6%80%81%E6%8C%87%E4%BB%A4/","title":"Note \u7528\u6237\u6001\u6307\u4ee4","text":"

    \u4fee\u6539\u5185\u5b58\u5355\u5143\u7684\u503c,\u4f46\u662f\u8fdb\u7a0b\u53ea\u80fd\u8bbf\u95ee\u81ea\u5df1\u7684\u7528\u6237\u7a7a\u95f4

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/","title":"\u6570\u5b66\u5206\u6790","text":"

    RESOURCE

    \u6570\u5b66\u5206\u6790(\u9648\u7eaa\u4fee)\u53c2\u8003\u7b54\u6848

    \u5409\u7c73\u591a\u7ef4\u5947\u7b2c\u4e00\u5377

    \u5409\u7c73\u591a\u7ef4\u5947\u7b2c\u4e8c\u5377

    \u5409\u7c73\u591a\u7ef4\u5947\u7b2c\u4e09\u5377

    \u5409\u7c73\u591a\u7ef4\u5947\u603b\u5377

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/","title":"\u96c6\u5408\u4e0e\u6620\u5c04","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#111","title":"\u5b9a\u7406 1.1.1","text":"

    \u8bc1\u660e:\u5bf9\u89d2\u7ebf\u6cd5\u5219

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#112","title":"\u5b9a\u7406 1.1.2","text":"

    \u4f9d\u5b9a\u7406 1.1.1 \u53ea\u9700\u8bc1(0,1] \u95f4\u6709\u7406\u6570\u53ef\u5217,\u4efb\u610f\\(r\\in Q\\cap (0,1],\\exists p,q\\in N^+,s.t.\\;r=\\frac{p}{q}\\), \\(q=n\\)\u7684\u65e2\u7ea6\u5206\u6570\u6700\u591a\u6709\\(n-1\\) \u4e2a,\u4ece\u800c\u5f88\u5bb9\u6613\u6392\u6210\u4e00\u5217

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#_2","title":"\u6620\u5c04\u4e0e\u51fd\u6570","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#121","title":"\u5b9a\u4e49 1.2.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#122","title":"\u5b9a\u4e49 1.2.2","text":"

    note:\u53ea\u8981\\(f:A\\to B\\)\u662f\u5355\u5c04,\u90a3\u4e48\u5b58\u5728\u9006\u6620\u5c04\\(f^{-1}:f(A)\\to A\\),\u4e14\\(f^{-1}\\)\u4e00\u5b9a\u662f\u53cc\u5c04

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#123","title":"\u5b9a\u4e49 1.2.3","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#124-126","title":"\u5b9a\u4e49 1.2.4-1.2.6","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#121_1","title":"\u5b9a\u7406 1.2.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/01-%E9%9B%86%E5%90%88%E4%B8%8E%E6%98%A0%E5%B0%84/#122_1","title":"\u5b9a\u7406 1.2.2","text":"

    \u8bbe\\(a_1,a_2,\\cdots,a_n\\in R,\\)\u5219\u79f0\\(\\frac{a_1+a_2+\\cdots+a_n}{n}\\)\u4e3a\u7b97\u6570\u5e73\u5747\u6570,\u79f0\\(\\sqrt[n]{a_1a_2\\cdots a_n}\\)\u4e3a\u51e0\u4f55\u5e73\u5747\u6570, \u79f0\\(n/(\\frac{1}{a_1}+\\frac{1}{a_2}+\\cdots+\\frac{1}{a_n})\\)\u4e3a\u8c03\u548c\u5e73\u5747\u6570,\u5219\u6709 \\(\\(\\frac{a_1+a_2+\\cdots+a_n}{n}\\geq \\sqrt[n]{a_1a_2\\cdots a_n}\\geq n/(\\frac{1}{a_1}+\\frac{1}{a_2}+\\cdots+\\frac{1}{a_n})\\)\\)

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/","title":"\u6570\u5217\u6781\u9650","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#_2","title":"\u5b9e\u6570\u7cfb\u8fde\u7eed\u6027","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#211","title":"\u5b9a\u7406 2.1.1","text":"

    \u786e\u754c\u5b58\u5728\u539f\u7406-\u5b9e\u6570\u7cfb\u8fde\u7eed\u6027\u5b9a\u7406

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#212","title":"\u5b9a\u7406 2.1.2","text":"

    note:Dedekind\u5206\u5272\u539f\u7406

    \u5b9a\u4e49 1:\u8bbe\u4e24\u4e2a\u975e\u7a7a\u6709\u7406\u96c6\u5408\\(A,B\\)\u6ee1\u8db3\u5982\u4e0b\u6761\u4ef6:\\(Q=A\\cup B,\\forall a\\in A,b\\in B,a<b\\),\u5219\u79f0\\(A,B\\)\u4e3a\\(Q\\)\u7684\u4e00\u4e2a\u5207\u5272,\u8bb0\u4e3a\\(A/B\\)

    \u4ece\u903b\u8f91\u4e0a\u8bb2,\u4efb\u4f55\u4e00\u4e2a\u5207\u5272\u53ea\u6709\u4ee5\u4e0b\u56db\u79cd\u60c5\u51b5\n1.\u96c6\u5408 A \u6709\u6700\u5927\u6570 a,\u96c6\u5408 B \u65e0\u6700\u5c0f\u6570\n2.\u96c6\u5408 A \u65e0\u6700\u5927\u6570,\u96c6\u5408 B \u6709\u6700\u5c0f\u6570b\n3.\u96c6\u5408 A \u65e0\u6700\u5927\u6570,\u96c6\u5408 B \u65e0\u6700\u5c0f\u6570\n4.\u96c6\u5408 A \u6709\u6700\u5927\u6570a,\u96c6\u5408 B \u6709\u6700\u5c0f\u6570b\n\n\u5bf9\u4e8e\u60c5\u51b5 4 \u662f\u4e0d\u53ef\u80fd\u7684,\u5982\u679c\u4e0d\u7136(a+b)/2 \u662f\u4ecb\u4e8e a,b \u4e4b\u95f4\u7684\u6709\u7406\u6570,\u4e0e A/B \u662f\u6709\u7406\u6570\u7684\u5206\u5272\u77db\u76fe\n\u5bf9\u4e8e\u60c5\u51b5 1,2,\u4ed6\u4eec\u786e\u5b9a\u4e86\u4e24\u4e2a\u6709\u7406\u6570,\u5bf9\u4e8e\u60c5\u51b5 3,\u4ed6\u4eec\u6ca1\u6709\u786e\u5b9a\u6709\u7406\u6570,\u5f15\u8fdb\u65e0\u7406\u6570\u7684\u6982\u5ff5\n

    \u5b9a\u4e49 2:\u8bbe A/B \u662f\u6709\u7406\u6570\u96c6\u7684\u4e00\u4e2a\u5207\u5272,\u82e5 A \u6ca1\u6709\u6700\u5927\u6570,B \u6ca1\u6709\u6700\u5c0f\u6570,\u90a3\u4e48\u5c31\u79f0 A/B \u786e\u5b9a\u4e86\u4e00\u4e2a\u65e0\u7406\u6570 c,c \u5927\u4e8e A \u4e2d\u4efb\u4f55\u4e00\u4e2a\u6709\u7406\u6570,\u5c0f\u4e8e B \u4e2d\u4efb\u4f55\u4e00\u4e2a\u6709\u7406\u6570

    \u5b9a\u4e49 3:\u6709\u6709\u7406\u6570\u548c\u5b9a\u4e49 2 \u786e\u5b9a\u7684\u5168\u4f53\u65e0\u7406\u6570\u6784\u6210\u4e86\u5b9e\u6570\u96c6\\(R\\)

    Dedekind \u5207\u5272\u5b9a\u7406:\u8bbe A/B \u662f\u5b9e\u6570\u96c6\\(R\\) \u7684\u4e00\u4e2a\u5207\u5272,\u5219\u6216\u8005 A \u6709\u6700\u5927\u6570\u6216\u8005 B \u6709\u6700\u5c0f\u6570

    \u8fd9\u91cc\u662f\u5bf9 R \u5207\u5272,\u548c Q \u5207\u5272\u4e0d\u540c.\u8bc1\u660e\u53ef\u7528\u53cd\u8bc1\u6cd5,\u6ce8\u610f\u8fd9\u91cc\u7684\u6216\u8005\u662f\u6392\u4e2d\u7684\n\n\u7531 Dedekind \u5207\u5272\u5b9a\u7406\u53ef\u4ee5\u8bc1\u660e\u786e\u754c\u5b58\u5728\u5b9a\u7406: \u5bf9\u975e\u7a7a\u6709\u4e0a\u754c\u7684\u6570\u96c6 S,\u8bbe A \u662f S \u7684\u4e0a\u754c\u7ec4\u6210\u7684\u96c6\u5408,B \u662f A \u7684\u8865,\u90a3\u4e48\u6216\u8005 B \u6709\u6700\u5927\u6570,\u6216\u8005 A \u6709\u6700\u5c0f\u6570(\u786e\u754c\u5b58\u5728)\n\u8bc1\u660e B \u6ca1\u6709\u6700\u5927\u6570:\u5982\u679c\u6709b \u662f B \u7684\u6700\u5927\u6570,\u7531\u4e8e b \u4e0d\u662f S \u7684\u4e0a\u754c,\u4ece\u800c\u5b58\u5728 s\\in S, s>b,\u90a3\u4e48 s \u4e00\u5b9a\u5728 B \u4e2d,\u4e0e b \u662f B \u7684\u6700\u5927\u6570\u77db\u76fe\n
    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#_3","title":"\u6570\u5217\u6781\u9650","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#221","title":"\u5b9a\u4e49 2.2.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#_4","title":"\u5b9a\u4e49:\u65e0\u7a77\u5c0f\u91cf","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#221_1","title":"\u5b9a\u7406 2.2.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#222","title":"\u5b9a\u7406 2.2.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#223","title":"\u5b9a\u7406 2.2.3","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#_5","title":"\u63a8\u8bba","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#224","title":"\u5b9a\u7406 2.2.4","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#225","title":"\u5b9a\u7406 2.2.5","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#note","title":"note","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#_6","title":"\u65e0\u7a77\u5927\u91cf","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#231","title":"\u5b9a\u4e492.3.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#231_1","title":"\u5b9a\u7406 2.3.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#232","title":"\u5b9a\u7406 2.3.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#232_1","title":"\u5b9a\u4e49 2.3.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#233-stolz","title":"\u5b9a\u7406 2.3.3 (Stolz\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#_7","title":"\u6536\u655b\u51c6\u5219","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#241","title":"\u5b9a\u7406 2.4.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#_8","title":"\u91cd\u8981\u6781\u9650","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#241_1","title":"\u5b9a\u4e49 2.4.1(\u95ed\u533a\u95f4\u5957)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#242","title":"\u5b9a\u7406 2.4.2(\u95ed\u533a\u95f4\u5957\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#243","title":"\u5b9a\u7406 2.4.3","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#242_1","title":"\u5b9a\u4e49 2.4.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#244","title":"\u5b9a\u7406 2.4.4","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#245bolzano-weierstrass","title":"\u5b9a\u7406 2.4.5(Bolzano-Weierstrass\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#246","title":"\u5b9a\u7406 2.4.6","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#243_1","title":"\u5b9a\u4e49 2.4.3(\u57fa\u672c\u5217)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#247cauchy","title":"\u5b9a\u7406 2.4.7(Cauchy \u6536\u655b\u51c6\u5219)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/02-%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90/#248","title":"\u5b9a\u7406 2.4.8","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/","title":"\u51fd\u6570\u6781\u9650\u548c\u8fde\u7eed\u51fd\u6570","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#_2","title":"\u51fd\u6570\u6781\u9650","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#311","title":"\u5b9a\u4e49 3.1.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#311_1","title":"\u5b9a\u7406 3.1.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#312","title":"\u5b9a\u7406 3.1.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#313","title":"\u5b9a\u7406 3.1.3","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#314","title":"\u5b9a\u7406 3.1.4","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#315heine","title":"\u5b9a\u7406 3.1.5(Heine \u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#315","title":"\u5b9a\u7406 3.1.5\\('\\)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#312_1","title":"\u5b9a\u4e49 3.1.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#316","title":"\u5b9a\u7406 3.1.6","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#_3","title":"\u8fde\u7eed\u51fd\u6570","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#321","title":"\u5b9a\u4e49 3.2.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#322","title":"\u5b9a\u4e49 3.2.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#323","title":"\u5b9a\u4e49 3.2.3","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#324","title":"\u5b9a\u4e49 3.2.4","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#_4","title":"\u4e0d\u8fde\u7eed\u70b9","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#riemann","title":"Riemann \u51fd\u6570","text":"\\[R(x)=\\begin{cases} \\frac{1}{p}, & x=\\frac{q}{p}\\in Q \\\\ 0, & x\\notin Q \\end{cases}\\] "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#321_1","title":"\u5b9a\u7406 3.2.1(\u53cd\u51fd\u6570\u5b58\u5728\u6027\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#322_1","title":"\u5b9a\u7406 3.2.2(\u53cd\u51fd\u6570\u8fde\u7eed\u6027\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#323_1","title":"\u5b9a\u7406 3.2.3(\u590d\u5408\u51fd\u6570\u8fde\u7eed\u6027\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#324_1","title":"\u5b9a\u7406 3.2.4(\u521d\u7b49\u51fd\u6570\u7684\u8fde\u7eed\u6027)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#note","title":"note","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#_5","title":"\u65e0\u7a77\u5c0f\u91cf\u4e0e\u65e0\u7a77\u5927\u91cf\u7684\u9636","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#331","title":"\u5b9a\u4e49 3.3.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#332","title":"\u5b9a\u4e49 3.3.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#331_1","title":"\u5b9a\u7406 3.3.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#note_1","title":"note","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#_6","title":"\u95ed\u533a\u95f4\u4e0a\u7684\u8fde\u7eed\u51fd\u6570","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#341","title":"\u5b9a\u7406 3.4.1(\u6709\u754c\u6027\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#342","title":"\u5b9a\u7406 3.4.2(\u6700\u503c\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#343","title":"\u5b9a\u7406 3.4.3(\u96f6\u70b9\u5b58\u5728\u6027\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#344","title":"\u5b9a\u7406 3.4.4(\u4ecb\u503c\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#341_1","title":"\u5b9a\u4e49 3.4.1(\u4e00\u81f4\u8fde\u7eed\u6027)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#345","title":"\u5b9a\u7406 3.4.5","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#346cantor","title":"\u5b9a\u7406 3.4.6(Cantor \u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#347","title":"\u5b9a\u7406 3.4.7","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/03-%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0/#note_2","title":"note","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/","title":"\u5fae\u5206","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_2","title":"\u5fae\u5206\u548c\u5bfc\u6570","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#411","title":"\u5b9a\u4e49 4.1.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#412","title":"\u5b9a\u4e49 4.1.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#411_1","title":"\u5b9a\u7406 4.1.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#412_1","title":"\u5b9a\u7406 4.1.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_3","title":"\u5bfc\u6570\u7684\u610f\u4e49\u548c\u6027\u8d28","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_4","title":"\u5bfc\u6570\u56db\u5219\u8fd0\u7b97\u548c\u53cd\u51fd\u6570\u6c42\u5bfc\u6cd5\u5219","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#431-433","title":"\u5b9a\u7406 4.3.1-4.3.3","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#434","title":"\u5b9a\u7406 4.3.4(\u53cd\u51fd\u6570\u6c42\u5bfc\u6cd5\u5219)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_5","title":"\u590d\u5408\u51fd\u6570\u6c42\u5bfc\u6cd5\u5219\u53ca\u5176\u5e94\u7528","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#441","title":"\u5b9a\u7406 4.4.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_6","title":"\u4e00\u9636\u5fae\u5206\u5f62\u5f0f\u4e0d\u53d8\u6027","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_7","title":"\u53c2\u6570\u65b9\u7a0b\u6c42\u5bfc","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_8","title":"\u9ad8\u9636\u5bfc\u6570\u548c\u9ad8\u9636\u5fae\u5206","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#451","title":"\u5b9a\u4e49 4.5.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#451_1","title":"\u5b9a\u7406 4.5.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#452leibniz","title":"\u5b9a\u7406 4.5.2(Leibniz\u516c\u5f0f)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/04-%E5%BE%AE%E5%88%86/#_9","title":"\u9ad8\u9636\u5fae\u5206","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/","title":"\u5fae\u5206\u4e2d\u503c\u5b9a\u7406\u53ca\u5176\u5e94\u7528","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#_2","title":"\u5fae\u5206\u4e2d\u503c\u5b9a\u7406","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#511","title":"\u5b9a\u4e49 5.1.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#511fermat","title":"\u5b9a\u7406 5.1.1(Fermat \u5f15\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#512rolle","title":"\u5b9a\u7406 5.1.2(Rolle \u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#513lagrange","title":"\u5b9a\u7406 5.1.3(Lagrange \u4e2d\u503c\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#514","title":"\u5b9a\u7406 5.1.4","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#515","title":"\u5b9a\u7406 5.1.5(\u4e00\u9636\u5bfc\u6570\u548c\u5355\u8c03\u6027\u7684\u5173\u7cfb)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#512","title":"\u5b9a\u4e49 5.1.2","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#516","title":"\u5b9a\u7406 5.1.6(\u4e8c\u9636\u5bfc\u6570\u548c\u51f8\u6027\u7684\u5173\u7cfb)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#_3","title":"\u79f0\u66f2\u7ebf\u4e0a\u51f8\u548c\u4e0b\u51f8\u7684\u8f6c\u6298\u70b9\u4e3a\u62d0\u70b9","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#517","title":"\u5b9a\u7406 5.1.7","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#518jesen","title":"\u5b9a\u7406 5.1.8(Jesen \u4e0d\u7b49\u5f0f)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#519cauchy","title":"\u5b9a\u7406 5.1.9(Cauchy \u4e2d\u503c\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#lhospital","title":"L'Hospital \u6cd5\u5219","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#521lhospital","title":"\u5b9a\u7406 5.2.1(L'Hospital \u6cd5\u5219)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#_4","title":"\u53ef\u8f6c\u5316\u7684\u6781\u9650","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#taylor","title":"Taylor \u516c\u5f0f\u548c\u63d2\u503c\u591a\u9879\u5f0f","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#531-peano-taylor","title":"\u5b9a\u7406 5.3.1(\u5e26 Peano \u4f59\u9879\u7684 Taylor \u516c\u5f0f)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#532-lagrange-taylor","title":"\u5b9a\u7406 5.3.2(\u5e26 Lagrange \u4f59\u9879\u7684 Taylor \u516c\u5f0f)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#531","title":"\u5b9a\u4e49 5.3.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#533","title":"\u5b9a\u7406 5.3.3(\u63d2\u503c\u591a\u9879\u5f0f\u7684\u4f59\u9879\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#534","title":"\u5b9a\u7406 5.3.4","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#taylor_1","title":"\u51fd\u6570\u7684Taylor\u516c\u5f0f\u53ca\u5176\u5e94\u7528","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#maclaurin","title":"Maclaurin\u516c\u5f0f","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#541","title":"\u5b9a\u7406 5.4.1","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#taylor_2","title":"Taylor\u516c\u5f0f\u7684\u5e94\u7528","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#_5","title":"\u5e94\u7528\u4e3e\u4f8b","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#551","title":"\u5b9a\u7406 5.5.1(\u6781\u503c\u70b9\u5224\u5b9a\u5b9a\u7406)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#_6","title":"\u65b9\u7a0b\u8fd1\u4f3c\u89e3","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/05-%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%85%B6%E5%BA%94%E7%94%A8/#561","title":"\u5b9a\u7406 5.6.1(\u725b\u987f\u6cd5)","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90/06-%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86/","title":"\u4e0d\u5b9a\u79ef\u5206","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/","title":"\u6570\u5b66\u5efa\u6a21","text":"

    \u8c08\u4e4b\u5955

    RESOURCES

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/01-%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1%E6%A6%82%E8%AE%BA/","title":"\u6982\u8bba","text":"

    \u6ca1\u4ec0\u4e48\u597d\u8bf4\u7684\uff0c\u5c31\u662f\u6570\u5b66\u5efa\u6a21\u7684\u57fa\u7840\u77e5\u8bc6\uff0c\u8fd9\u91cc\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86\u3002

    RESOURCES

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/02-PageRank/","title":"PageRank","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/02-PageRank/#_1","title":"\u4e92\u8054\u7f51\u4e2d\u7684\u7f51\u9875\u901a\u8fc7\u8d85\u94fe\u63a5\u8fde\u63a5","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/02-PageRank/#_2","title":"\u7f51\u9875\u91cd\u8981\u5ea6","text":"

    \u4e00\u4e2a\u7f51\u9875\u91cd\u8981,\u662f\u56e0\u4e3a\u6709\u91cd\u8981\u7684\u7f51\u9875\u94fe\u63a5\u5230\u5b83

    \u5bf9\u6bcf\u4e00\u4e2a\u7f51\u9875,\u5b9a\u4e49\u4e00\u4e2a\u91cd\u8981\u5ea6,\u4f5c\u4e3a\u7f51\u9875\u6392\u5e8f\u7684\u89c4\u5219\n\u94fe\u63a5\u5230\u7f51\u9875\u7684\u7f51\u9875\u5bf9\u8fd9\u4e2a\u7f51\u9875\u7684\u91cd\u8981\u90fd\u90fd\u6709\u8d21\u732e,\u8d21\u732e\u7684\u5927\u5c0f\u548c\u81ea\u8eab\u7684\u91cd\u8981\u5ea6\u6709\u5173\n\n\u2022(\u4f20\u9012\u6027)\u91cd\u8981\u5ea6\u5927\u7684\u7f51\u9875\u94fe\u63a5\u5230\u7f51\u9875A\u65f6\u5bf9\u7f51\u9875A\u7684\u91cd\u8981\u5ea6\u7684\u8d21\u732e\u6bd4\u91cd\u8981\u5ea6\u5c0f\u7684\u7f51\u9875\u94fe\u63a5\u5230\u7f51\u9875A\u65f6\u5bf9\u7f51\u9875A\u7684\u91cd\u8981\u5ea6\u7684\u8d21\u732e\u5927\n\n    \u2022\u67d0\u7f51\u9875\u5bf9\u5176\u5b83\u7f51\u9875\u91cd\u8981\u5ea6\u7684\u8d21\u732e\u4e4b\u548c\u7b49\u4e8e\u5b83\u7684\u91cd\u8981\u5ea6\n\n\u2022(\u7b49\u6548\u6027)\u7f51\u9875\u5bf9\u5b83\u6240\u94fe\u63a5\u7684\u6bcf\u4e2a\u7f51\u9875\u7684\u91cd\u8981\u5ea6\u7684\u8d21\u732e\u76f8\u7b49\n\n    \u2022 \u67d0\u7f51\u9875\u5bf9\u5176\u5b83\u7f51\u9875\u7684\u91cd\u8981\u5ea6\u8d21\u732e\u4e0e\u5b83\u6240\u94fe\u63a5\u7684\u7f51\u9875\u6570\u91cf\u5448\u53cd\u6bd4\n\n\u2022(\u53e0\u52a0\u6027)\u94fe\u63a5\u5230\u7f51\u9875A\u7684\u7f51\u9875\u8d8a\u591a\uff0c\u7f51\u9875A\u8d8a\u91cd\u8981\n\n    \u2022 \u7f51\u9875A\u7684\u91cd\u8981\u5ea6\u662f\u6240\u6709\u94fe\u63a5\u5230A\u7684\u7f51\u9875\u5bf9\u7f51\u9875A\u7684\u91cd\u8981\u5ea6\u7684\u8d21\u732e\u4e4b\u548c\n\n\u2022(\u65e0\u5173\u6027)\u7f51\u9875\u94fe\u63a5\u5176\u5b83\u7f51\u9875\u7684\u591a\u5c11\uff0c\u4e0e\u5176\u672c\u8eab\u7684\u91cd\u8981\u5ea6\u65e0\u5173\n

    \u5b9e\u9645\u4e0a\u8fd9\u5c31\u662f\u4e00\u4e2a\u6709\u5411\u8d4b\u6743\u56fe

    \u5982\u4f55\u8ba1\u7b97\u5462\uff1f $$ x_j=\\frac{x_{j_1}}{q_{j_1}} + \\frac{x_{j_2}}{q_{j_2}} + \\cdots + \\frac{x_{j_k}}{q_{j_k}}=\\sum_{i=1}^{n}p_{i,j}x_i\\ X=\\begin{bmatrix} x_1 \\ x_2 \\ \\vdots \\ x_n \\end{bmatrix}\\ \\ p_{i,j}=\\begin{cases} \\frac{1}{q_j} & \\text{\u5982\u679c\u7f51\u9875j\u94fe\u63a5\u5230\u7f51\u9875i} \\ 0 & \\text{\u5176\u4ed6} \\end{cases} then:X=PX $$

    \u4e00\u5b9a\u6709\u975e\u96f6\u89e3\u5417\uff1f

    \u6ce8\u610f\u5230\\(P\\)\u7684\u6bcf\u4e00\u5217\u5143\u7d20\u4e4b\u548c\u4e3a1,\u6240\u4ee5 P \u662f\u5217\u968f\u673a\u77e9\u9635

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/02-PageRank/#_3","title":"\u968f\u673a\u77e9\u9635","text":"

    \u5404\u884c\uff08\u5217\uff09\u5143\u7d20\u4e4b\u548c\u5747\u4e3a1\u7684\u975e\u8d1f\u65b9\u9635\u79f0\u4e3a\u884c(\u5217)\u968f\u673a\u77e9\u9635(row(column) stochastic matrix)

    \u5404\u884c\u4e0e\u5404\u5217\u5143\u7d20\u4e4b\u548c\u5747\u4e3a1\u7684\u975e\u8d1f\u65b9\u9635\u79f0\u4e3a\u53cc\u968f\u673a\u77e9\u9635(doubly stochastic matrix)

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/02-PageRank/#1","title":"\u4efb\u610f\u968f\u673a\u77e9\u9635\u7684\u6a21\u6700\u5927\u7279\u5f81\u503c\u662f1","text":"

    \u8bbe\\(\\lambda\\)\u662f\u77e9\u9635\\(P\\)\u7684\u7279\u5f81\u503c,\u975e\u96f6\u5411\u91cf\\(X\\)\u662f\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf,\u8bbe\\(|x_s|=\\max |x_i|\\),\u5219

    \\[ \\lambda X=PX\\Rightarrow\\lambda x_s = \\sum_{i=1}^{n}p_{i,s}x_i\\Rightarrow \\lambda x_s = \\sum_{i=1}^{n}p_{i,s}x_i\\\\ then:|\\lambda|| x_s| = |\\sum_{i=1}^{n}p_{i,s}x_i|\\leq \\sum_{i=1}^{n}|p_{i,s}||x_i|\\leq |x_s|\\sum_{i=1}^{n}|p_{i,s}|=|x_s|\\\\ then:|\\lambda|\\leq 1 \\]"},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/02-PageRank/#_4","title":"\u94fe\u63a5\u77e9\u9635\u7684\u4fee\u6b63","text":"
    \u60ac\u6302\u7f51\u9875:\u6ca1\u6709\u94fe\u63a5\u51fa\u53bb\u7684\u7f51\u9875,\u4e5f\u5c31\u662f\u4e0d\u94fe\u63a5\u4efb\u4f55\u7f51\u9875\u7684\u7f51\u9875\n
    \u7f51\u9875\u56e2,\u76f8\u5f53\u4e8e\u4e00\u90e8\u5206\u7f51\u9875\u4e92\u76f8\u94fe\u63a5,\u4f46\u662f\u4e0d\u94fe\u63a5\u5230\u5916\u90e8\n\u6bd4\u5982\u6296\u97f3\u548c\u5feb\u624b\u76f8\u4e92\u94fe\u63a5,YouTube \u548c Facebook \u76f8\u4e92\u94fe\u63a5\n
    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/02-PageRank/#_5","title":"\u73b0\u5728\u53ef\u4ee5\u6c42\u89e3\u91cd\u8981\u5ea6","text":"

    \u89e3\u51b3\u552f\u4e00\u6027:\u5b8c\u5168\u6b63,\u5217\u968f\u673a\u77e9\u9635\u7684\u5c5e\u4e8e\u7279\u5f81\u503c 1 \u7684\u7279\u5f81\u5411\u91cf\u662f\u552f\u4e00\u7684

    \u5148\u8bc1\u660e\u5176\u7279\u5f81\u5411\u91cf\u7684\u5206\u91cf\u548c\u4e0d\u4e3a 0

    \u518d\u8bc1\u660e\u552f\u4e00\u6027,\u8fd9\u91cc\u5982\u679c v \u548c w \u662f\u4e00\u6837\u7684\u6309\u5b9a\u4e49 x \u5c31\u662f\u96f6\u5411\u91cf

    RESOURCES

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/03-NIM%E6%B8%B8%E6%88%8F/","title":"Nim \u6e38\u620f","text":"

    \u4e00\u5171\u6709 n \u5806\u786c\u5e01,\u6ca1\u5806\u6570\u91cf\u4e00\u5b9a,\u4e24\u4e2a\u4eba\u4f9d\u6b21\u53d6\u786c\u5e01,\u6bcf\u6b21\u4ece\u4e00\u5806\u4e2d\u53d6,\u6bcf\u6b21\u81f3\u5c11\u53d6\u4e00\u679a,\u53d6\u5230\u6700\u540e\u4e00\u679a\u786c\u5e01\u7684\u4eba\u83b7\u80dc

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/03-NIM%E6%B8%B8%E6%88%8F/#_1","title":"\u5206\u6790","text":"

    \u7528\u5411\u91cf(i,j,k)\u8868\u793a\u5806\u548c\u5806\u6570

    \u4e09\u4e2a\u5806\u7684\u60c5\u51b5:

    \u90a3\u4e48\u5982\u4f55\u5fc5\u80dc\u5462(\u53ef\u4ee5\u5417?)?

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/03-NIM%E6%B8%B8%E6%88%8F/#_2","title":"\u5b89\u5168\u72b6\u6001","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/03-NIM%E6%B8%B8%E6%88%8F/#_3","title":"\u5982\u4f55\u53d6\u80dc","text":"

    \u8ba9\u81ea\u5df1\u53d6\u5b8c\u4ee5\u540e\u53d8\u6210\u5b89\u5168\u72b6\u6001

    \u5c06\u6bcf\u4e00\u5806\u786c\u5e01\u7684\u6570\u91cf\u8f6c\u5316\u6210\u4e8c\u8fdb\u5236,\u7136\u540e\u5bf9\u6bcf\u4e00\u4f4d\u6c42\u548c\uff0c\u79f0\u5176\u5c3e\u6570\u4e3a\u4f4d\u548c

    \u53ea\u6709\u4e00\u5806\u786c\u5e01\u65f6\uff0c\u4f4d\u548c\u4e0d\u53ef\u80fd\u5168\u662f0\n\u6bcf\u6b21\u53d6\u786c\u5e01\u65f6\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u4f4d\u548c\u53d1\u751f\u53d8\u5316\n

    \u82e5\u6240\u6709\u4f4d\u548c\u90fd\u662f 0\uff0c\u5219\u72b6\u6001\u662f\u5b89\u5168\u7684\uff0c\u5426\u5219\u4e0d\u5b89\u5168

    python\u5b9e\u73b0

    \u5728\u7ebf\u8fd0\u884c

    RESOURCES

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/04-%E4%BC%AA%E5%B8%81%E8%BE%A8%E8%AF%86/","title":"\u4f2a\u5e01\u8fa8\u8bc6","text":"

    \u540e\u4e00\u6b21\u79f0\u91cf\u4f9d\u8d56\u4e8e\u4e4b\u524d\u7684\u79f0\u91cf\u7ed3\u679c\u7684\u65b9\u6848\u79f0\u4e3a\u81ea\u9002\u5e94\u7684,\u5426\u5219\u79f0\u4e3a\u975e\u81ea\u9002\u5e94\u7684

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/04-%E4%BC%AA%E5%B8%81%E8%BE%A8%E8%AF%86/#12","title":"12 \u4e2a\u786c\u5e01\u4e2d\u6709\u4e00\u4e2a\u5047\u5e01,\u4e0d\u77e5\u8f7b\u91cd,\u7528\u4e09\u6b21\u79f0\u91cf\u627e\u51fa\u8fd9\u4e2a\u5047\u5e01","text":"

    \u5bf9\u4efb\u610f\u6574\u6570\\(w>2\\):\u82e5\\(3\\leq n \\leq\\frac{3^w-3}{2}\\),\u5219\u5b58\u5728\u975e\u81ea\u9002\u5e94\u7684\u79f0\u91cf\u65b9\u6848,\u4f7f\u7528 w \u6b21\u79f0\u91cf\u53ef\u4ee5\u4ece n \u679a\u786c\u5e01\u4e2d\u786e\u5b9a\u4f2a\u5e01\u5e76\u5224\u5b9a\u8f7b\u91cd,\u4e0d\u7136\u5219\u4e0d\u5b58\u5728

    \u901a\u8fc7\u6784\u9020 Dyson \u96c6\u6765\u786e\u5b9a\u6bcf\u4e2a\u786c\u5e01\u5728\u6bcf\u6b21\u79f0\u91cf\u4e2d\u7684\u4f4d\u7f6e

    RESOURES

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/05-%E7%A7%98%E5%AF%86%E5%85%B1%E4%BA%AB/","title":"\u79d8\u5bc6\u5171\u4eab","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/05-%E7%A7%98%E5%AF%86%E5%85%B1%E4%BA%AB/#shamir","title":"Shamir\u95e8\u9650\u673a\u5236","text":"

    \u5f88\u7b80\u5355,\u5b9e\u9645\u4e0a\u5c31\u662f\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4

    \u5047\u8bbe\u6709\\(n\\)\u4e2a\u4eba,\u5e0c\u671b\\(t,(t<n)\\)\u4e2a\u4eba\u63d0\u4f9b\u4fe1\u606f\u7684\u65f6\u5019\u80fd\u5f97\u5230\u79d8\u5bc6,\u90a3\u5c31\u6784\u9020\u4e00\u4e2a\u6709\\(t\\)\u4e2a\u672a\u77e5\u6570\u7684\u591a\u9879\u5f0f, \u7136\u540e\u7ed9\u6bcf\u4e2a\u4eba\u4e00\u4e2a\u591a\u9879\u5f0f\u4e0a\u7684\u70b9,\u8fd9\u6837\u63d0\u4f9b\u4fe1\u606f\u7684\u4eba\u6570\u5927\u4e8et\u7684\u65f6\u5019,\u5c31\u53ef\u4ee5\u6c42\u89e3\u51fa\u591a\u9879\u5f0f,\u4ece\u800c\u5f97\u5230\u79d8\u5bc6.

    \\(K\\)\u662f\u79d8\u5bc6,\\(t\\)\u662f\u95e8\u9650,\\(n\\)\u662f\u4eba\u6570,\u90a3\u4e48\u9009\u53d6 \\(t-1\\)\u4e2a\u6570\\(a_1,a_2,\\cdots,a_{t-1}\\),\u6784\u9020\u591a\u9879\u5f0f

    \\[f(x)=K+a_1x+a_2x^2+\\cdots+a_{t-1}x^{t-1}\\]

    \u4fe1\u606f\u9009\u53d6\u4e3a\\((x_i,f(x_i))\\mod p\\),\u5176\u4e2d\\(p\\)\u662f\u7d20\u6570,\\(x_i\\)\u662f\u968f\u673a\u6570

    (\u6216\u8005\u522b\u7684\u4e5f\u884c,1,2,3,\u9009\u62e9\u968f\u673a\u6570\u4e3b\u8981\u662f\u4e3a\u4e86\u8ba9\u89c4\u5f8b\u4e0d\u90a3\u4e48\u660e\u663e,\u53d6\u6a21\u611f\u89c9\u662f\u4e3a\u4e86\u8ba9\u6570\u5b57\u5c0f\u4e00\u70b9,\u4e0d\u53d6\u4e5f\u662f\u53ef\u4ee5\u7684)\n

    \u8fd9\u6837\u628a\\(n\\)\u4e2a\u4e0d\u540c\u7684\u4fe1\u606f\u7ed9\u5230\\(n\\)\u4e2a\u4eba,\u7136\u540e\\(t\\)\u4e2a\u4eba\u63d0\u4f9b\u4fe1\u606f\u7684\u65f6\u5019,\u5c31\u53ef\u4ee5\u6c42\u89e3\u51fa\u591a\u9879\u5f0f,\u4ece\u800c\u5f97\u5230\u79d8\u5bc6.

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/05-%E7%A7%98%E5%AF%86%E5%85%B1%E4%BA%AB/#_2","title":"\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406","text":"

    \u7ed9\u4e00\u4e9b\u5b9a\u4e49:

    \u4e2d\u56fd\u5269\u4f59\u5b9a\u7406

    \\[ x = N_1N_1^{-1}a_1+\\cdots+N_kN_k^{-1}a_k \\] "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/05-%E7%A7%98%E5%AF%86%E5%85%B1%E4%BA%AB/#asmuth-bloom","title":"Asmuth-Bloom\u95e8\u9650\u673a\u5236","text":"

    \u53c2\u8003\u8fd9\u4e2a\u8bba\u6587

    \u592a\u590d\u6742\u4e86,\u5bf9\u7740\u770b\u5427

    RESOURCES

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/06-%E5%AE%89%E5%85%A8%E8%A7%82%E6%BC%94/","title":"\u5b89\u5168\u89c2\u6f14","text":""},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/06-%E5%AE%89%E5%85%A8%E8%A7%82%E6%BC%94/#_2","title":"\u4e0a\u754c\u4f30\u8ba1","text":"

    \u7b2c n \u4e2a\u4eba\u65e0\u6cd5\u9009\u5230\u5c0f\u4e8e\\(d_n\\)\u7684\u8ddd\u79bb:

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/06-%E5%AE%89%E5%85%A8%E8%A7%82%E6%BC%94/#_3","title":"\u4e0b\u754c\u4f30\u8ba1","text":"

    RESOURCES

    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/08-%E6%8B%9B%E8%81%98%E9%97%AE%E9%A2%98/","title":"\u62db\u8058\u95ee\u9898","text":"
    n\u4e2a\u6c42\u804c\u8005\u5e94\u8058.\u6309\u7167\u987a\u5e8f\u4f9d\u6b21\u9762\u8bd5,\u6bcf\u4e2a\u4eba\u9762\u8bd5\u7ed3\u675f\u540e\u9762\u8bd5\u5b98\u5fc5\u987b\u7acb\u9a6c\u51b3\u5b9a\u662f\u5426\u5f55\u7528\n\u4e00\u65e6\u5f55\u53d6\u4e00\u4e2a\u6c42\u804c\u8005,\u9762\u8bd5\u7acb\u9a6c\u7ed3\u675f\n\u73b0\u6c42\u4e00\u4e2a\u6700\u597d\u7684\u7b56\u7565.\u4f7f\u5f97\u5f55\u53d6\u6700\u597d\u7684\u6c42\u804c\u8005\u7684\u6982\u7387\u6700\u5927\n
    "},{"location":"Notebook/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1/08-%E6%8B%9B%E8%81%98%E9%97%AE%E9%A2%98/#-","title":"-","text":""},{"location":"Notebook/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/","title":"\u738b\u9053\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5","text":""},{"location":"Notebook/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/%E8%A1%A8/","title":"\u7ebf\u6027\u8868","text":"
    def\uff1a\u7ebf\u6027\u8868\u662f\u5177\u6709\u76f8\u540c\u6570\u636e\u7c7b\u578b\u7684n\u4e2a\u6570\u636e\u5143\u7d20\u7684\u6709\u9650\u5e8f\u5217\uff0cn\u4e3a\u8868\u957f\n
    "},{"location":"Notebook/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/%E8%A1%A8/#_2","title":"\u7ebf\u6027\u8868\u7684\u987a\u5e8f\u5b58\u50a8\u53c8\u53eb\u987a\u5e8f\u8868","text":"

    i def\uff1a\u7528\u4e00\u7ec4\u5730\u5740\u8fde\u7eed\u7684\u5b58\u50a8\u5355\u5143\u4f9d\u6b21\u5b58\u50a8\u7ebf\u6027\u8868\u4e2d\u7684\u6570\u636e\u5143\u7d20

    note:\u987a\u5e8f\u8868\u7684\u5143\u7d20\u5728\u903b\u8f91\u548c\u7269\u7406\u4e0a\u90fd\u662f\u76f8\u90bb\u7684(\u903b\u8f91\u987a\u5e8f\u548c\u5b58\u50a8\u7684\u7269\u7406\u987a\u5e8f\u76f8\u540c)

    "},{"location":"Notebook/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/%E8%A1%A8/#_3","title":"\u4f18\u70b9","text":"
    1.\u53ef\u8fdb\u884c\u968f\u673a\u8bbf\u95ee\uff0c\u53ef\u4ee5\u5728O(1)\u7684\u65f6\u95f4\u4e2d\u627e\u5230\u5143\u7d20\n2.\u5b58\u50a8\u5bc6\u5ea6\u9ad8,\u6bcf\u4e2a\u7ed3\u70b9\u53ea\u5b58\u50a8\u6570\u636e\u5143\u7d20(\u611f\u89c9\u662f\u4e0e\u94fe\u8868\u8fdb\u884c\u6bd4\u5bf9,\u94fe\u8868\u8fd8\u9700\u8981\u6307\u9488\u57df)\n
    "},{"location":"Notebook/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/%E8%A1%A8/#_4","title":"\u7f3a\u70b9","text":"

    1.\u5143\u7d20\u7684\u63d2\u5165\u548c\u5220\u9664\u9700\u8981\u79fb\u52a8\u5927\u91cf\u7684\u5143\u7d20,\u5e73\u5747O(n/2) 2.\u9700\u8981\u4e00\u6bb5\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4,\u4e0d\u591f\u7075\u6d3b

    note:\u987a\u5e8f\u8868\u4e00\u5b9a\u8981\u8fde\u7eed\u5b58\u50a8,\u4f46\u662f\u6570\u7ec4\u4e0d\u4e00\u5b9a

    \u53ef\u4ee5\u53d1\u73b0,\u6570\u7ec4\u5143\u7d20\u90fd\u88ab\u521d\u59cb\u5316\u4e3a 1,\u4f46\u662f\u5982\u679c index1-index2 \u4e24\u4e2a\u5730\u65b9\u7684\u5143\u7d20\u88ab\u4fee\u6539,\u90a3\u4e48\u4e2d\u95f4\u7684\u5143\u7d20\u4e5f\u4f1a\u88ab\u968f\u673a\u6539\u53d8

    "},{"location":"Notebook/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/%E8%A1%A8/#_5","title":"\u94fe\u8868:\u7ebf\u6027\u8868\u7684\u94fe\u5f0f\u8868\u793a","text":"

    \u5355\u94fe\u8868 

    //single node\nstruct Node{\n    Comparable value;\n    Node* next;\n}\n
    \u53cc\u94fe\u8868 
    // double node\nstruct Node{\n    Comparable value;\n    Node* prior,* next;\n}\n

    "},{"location":"Notebook/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%B8%8E%E7%AE%97%E6%B3%95/%E8%A1%A8/#_6","title":"\u987a\u5e8f\u8868\u548c\u94fe\u8868\u7684\u6bd4\u8f83:","text":"
    1.\u5b58\u53d6(\u8bfb\u5199\u65b9\u6cd5):\n    \u987a\u5e8f\u8868\u53ef\u4ee5\u987a\u5e8f\u5b58\u53d6\u4e5f\u53ef\u4ee5\u968f\u673a\u5b58\u53d6,\u94fe\u8868\u53ea\u80fd\u987a\u5e8f\u5b58\u53d6\n 2.\u903b\u8f91\u7ed3\u6784\u548c\u7269\u7406\u7ed3\u6784\n    \u987a\u5e8f\u8868\u7684\u903b\u8f91\u7ed3\u6784\u548c\u7269\u7406\u7ed3\u6784\u662f\u7edf\u4e00\u7684,\u94fe\u8868\u5219\u4e0d\u662f,\u903b\u8f91\u76f8\u90bb\u7684\u5143\u7d20\u7269\u7406\u4e0a\u4e0d\u4e00\u5b9a\u76f8\u90bb\n 3.\u67e5\u627e,\u63d2\u5165\u548c\u5220\u9664\n    \u6309\u503c\u67e5\u627e:\u5982\u679c\u5143\u7d20\u65e0\u5e8f\u4e24\u8005\u90fd\u662fO(n),\u6709\u5e8f\u987a\u5e8f\u8868\u53ef\u5230 O(logn)\n    \u6309\u5e8f\u67e5\u627e:\u987a\u5e8f\u8868O(1),\u94fe\u8868O(n)\n    \u63d2\u5165\u5220\u9664:\u987a\u5e8f\u8868\u9700\u8981\u79fb\u52a8\u5e73\u5747 \u4e00\u822c\u5143\u7d20,\u94fe\u8868\u53ea\u9700\u66f4\u6539\u6307\u9488\n 4.\u94fe\u8868\u66f4\u4e3a\u7075\u6d3b,\u4f46\u662f\u5b58\u50a8\u5bc6\u5ea6\u66f4\u4f4e(\u8fd8\u9700\u8981\u5b58\u50a8\u6307\u9488)\n
    "},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/","title":"\u673a\u5668\u5b66\u4e60","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/01-%E5%BC%95%E8%A8%80/","title":"\u5f15\u8a00(introduction)","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/01-%E5%BC%95%E8%A8%80/#_1","title":"\u4ec0\u4e48\u662f\u673a\u5668\u5b66\u4e60","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/01-%E5%BC%95%E8%A8%80/#_2","title":"\u7b97\u6cd5\u7c7b\u578b","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/01-%E5%BC%95%E8%A8%80/#note","title":"note","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/02-%E5%8D%95%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/","title":"\u5355\u53d8\u91cf\u7ebf\u6027\u56de\u5f52","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/02-%E5%8D%95%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/#_2","title":"\u6a21\u578b\u8868\u793a","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/02-%E5%8D%95%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/#_3","title":"\u4ee3\u4ef7\u51fd\u6570","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/02-%E5%8D%95%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/#_4","title":"\u68af\u5ea6\u4e0b\u964d","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/02-%E5%8D%95%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/#_5","title":"\u68af\u5ea6\u4e0b\u964d\u7684\u7ebf\u6027\u56de\u5f52","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/03-%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9B%9E%E9%A1%BE/","title":"\u7ebf\u6027\u4ee3\u6570\u56de\u987e","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/04-%E5%A4%9A%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/","title":"\u591a\u53d8\u91cf\u7ebf\u6027\u56de\u5f52","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/04-%E5%A4%9A%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/#_2","title":"\u591a\u7ef4\u7279\u5f81","text":""},{"location":"Notebook/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/04-%E5%A4%9A%E5%8F%98%E9%87%8F%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92/#_3","title":"\u591a\u53d8\u91cf\u68af\u5ea6\u4e0b\u964d","text":""},{"location":"Notebook/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%BB%84%E6%88%90%E5%8E%9F%E7%90%86/","title":"\u738b\u9053\u8ba1\u7b97\u673a\u7ec4\u6210","text":""},{"location":"Notebook/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%BB%84%E6%88%90%E5%8E%9F%E7%90%86/1-%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E6%A6%82%E8%BF%B0/","title":"\u8ba1\u7b97\u673a\u7cfb\u7edf\u6982\u8ff0","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/","title":"\u968f\u673a\u8fc7\u7a0b","text":"

    \u82cf\u4e2d\u6839

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/01-%E5%88%9D%E7%AD%89%E6%A6%82%E7%8E%87%E8%AE%BA/","title":"\u521d\u7b49\u6982\u7387\u8bba","text":"

    Bernoulli\u5206\u5e03,Poisson\u5206\u5e03,\u6b63\u6001\u5206\u5e03\u53ef\u52a0\u6027

    1.\\(X\\sim B(n,p),Y\\sim V(m,p)\\Rightarrow X+Y\\sim B(m+n,p)\\)

    2.\\(X\\sim P(\\lambda),Y\\sim P(\\mu)\\Rightarrow X+Y\\sim P(\\lambda+\\mu)\\)

    3.\\(X\\sim N(\\mu_1,\\sigma_1^2),Y\\sim N(\\mu_2,\\sigma_2^2)\\Rightarrow X+Y\\sim N(\\mu_1+\\mu_2,\\sigma_1^2+\\sigma_2^2)\\)

    \u5047\u8bbe\\((X,Y)\\sim N(\\mu_1,\\mu_2,\\sigma_1^2,\\sigma_2^2,\\rho)\\)

    1.\\(X\\sim N(\\mu_1,\\sigma_1^2),Y\\sim N(\\mu_2,\\sigma_2^2)\\)

    2.\u7ed9\u5b9a\\(X=x\\),\u5219\\(Y\\sim N(\\mu_2+\\rho\\frac{\\sigma_2}{\\sigma_1}(x-\\mu_1),\\sigma_2^2(1-\\rho^2))\\)

    3.X,Y\u72ec\u7acb\\(\\Leftrightarrow \\rho=0\\)

    4.\u7ed9\u5b9a\\(a,b\\in R,aX+bY\\sim N(\\mu,\\sigma^2)\\)

    \\(\\Rightarrow \\mu = a\\mu_1+b\\mu_2,\\sigma^2=a^2\\sigma_1^2+b^2\\sigma_2^2+2ab\\rho\\sigma_1\\sigma_2\\)

    k\u9636\u77e9

    \\(EX^k<\\infty\\Rightarrow EX^k\\)\u7684\\(X\\)\u7684\\(k\\)\u9636\u77e9

    \\(X\\sim P(\\lambda)\\) \\(\\Rightarrow\\) \\(EX=\\lambda,EX^2=\\lambda+\\lambda^2\\)

    \\(EX(X-1)\\cdots(X-k+1)=\\lambda^k\\)

    \u7531\u6b64\u53ef\u4ee5\u6c42\u51fa\\(P(\\lambda)\\)\u7684\u5404\u9636\u77e9

    \\(X\\sim N(0,\\sigma^2)\\) \\(\\Rightarrow\\) \\(m_{2k}=(zk-1)!!\\sigma^{2k},m_{2k-1}=0\\)

    \u77e9\u6bcd\u51fd\u6570 \\(iG_X(t)=Ee^{tX},|t|<|t_0|:Ee^{tX}<\\infty,|t|<t_0\\)

    \\(X\\sim P(\\lambda)\\) \\(\\Rightarrow\\) \\(G_X(t)=e^{\\lambda(e^t-1)}\\)

    \\(X\\sim N(0,\\sigma^2)\\) \\(\\Rightarrow\\) \\(G_X(t)=e^{\\frac{1}{2}\\sigma^2t^2}\\)

    Chebyshev\u4e0d\u7b49\u5f0f

    \\(P(|X-\\mu|\\geq \\varepsilon)\\leq \\frac{\\sigma^2}{\\varepsilon^2}\\)

    \u63a8\u5e7f\u4e3a:\\(f:R\\to R^+\\)\u4e3a\u975e\u8d1f\u5355\u8c03\u4e0d\u51cf\u51fd\u6570,\\(Ef(X)<\\infty\\),\u90a3\u4e48\\(P(X>\\epsilon)\\leq \\frac{Ef(X)}{f(\\epsilon)}\\))

    \u534f\u65b9\u5dee\u548c\u76f8\u5173\u7cfb\u6570

    \\(Cov(X,Y)=E(X-\\mu_X)(Y-\\mu_Y)\\)

    \\(\\rho(X,Y)=\\frac{Cov(X,Y)}{\\sigma_X\\sigma_Y}\\)=\\(\\frac{Cov(X,Y)}{\\sqrt{Var(X)Var(Y)}}\\)

    \\((X,Y)\\)\u7684\u6570\u5b57\u7279\u5f81\u5305\u62ec\u5747\u503c\u5411\u91cf\u548c\u534f\u65b9\u5dee\u77e9\u9635

    \\(\\mu=(EX,EY)\\),\\(\\Sigma=\\begin{pmatrix}Var(X)&Cov(X,Y)\\\\Cov(Y,X)&Var(Y)\\end{pmatrix}\\)

    \u7279\u5f81\u51fd\u6570

    \\(\\phi_X(t)=Ee^{itX}\\)=\\(\\int_{-\\infty}^{\\infty}e^{itx}dF_X(x),t\\in R\\)

    \u5bc6\u5ea6\u51fd\u6570\\(f_X(x)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}e^{-itx}\\phi_X(t)dt\\)

    \u5404\u79cd\u6536\u655b

    \u6781\u9650\u5b9a\u7406 1

    \\(\\{\\xi_n\\}\\)\u72ec\u7acb\u540c\u5206\u5e03,\\(P(\\xi_n=1)=p,P(\\xi_n=0)=1-p\\),\u4ee4\\(S_n=\\sum\\limits_{i=1}^n\\xi_i\\)\u90a3\u4e48:

    1.\\((Bernoulli):\\frac{S_n}{n}\\overset{p}\\to p\\)

    2.\\((De Moivre-Laplace):\\frac{S_n-np}{\\sqrt{np(1-p)}}\\overset{d}\\to N(0,1)\\)

    3.\\((Borel):\\frac{S_n}{n}\\to p,s.e.\\)

    Poisson\u6781\u9650\u5b9a\u7406

    \\(\\forall n,\\{\\xi_{n,k}\\}_{k=1}^n\\)\u72ec\u7acb\u540c\u5206\u5e03,\\(P(\\xi_{n,k}=1)=p_n,P(\\xi_{n,k}=0)=1-p_n,1\\leq k\\leq n\\), \u82e5:\\(n\\to\\infty\\)\u65f6,\\(p_n\\to\\infty,np_n\\to\\lambda\\in R^+\\),\u4ee4\\(S_n=\\sum\\limits_{k=1}^n\\xi_{n,k}\\),\u90a3\u4e48:

    \\[S_n\\overset{d}\\to \\mathcal{P}(\\lambda)\\]

    \\(\\{\\xi_n\\}\\)\u72ec\u7acb\u540c\u5206\u5e03,\u4ee4\\(S_n=\\sum\\limits_{i=1}^n\\xi_i\\)\u90a3\u4e48:

    1.\\((Khintchine):\\frac{S_n}{n}\\overset{p}\\to \\mu,a.e.\\) \\(\\iff\\) \\(E|\\xi_1|<\\infty,E\\xi=\\mu\\)

    2.\\((Feller-Levy):\\frac{S_n}{\\sqrt{n\\sigma^2}}\\overset{d}\\to N(0,1)\\) \\(\\iff\\) \\(E\\xi_n=0,Var\\xi_n=E\\xi_n^2=\\sigma^2\\)

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/","title":"\u968f\u673a\u8fc7\u7a0b\u7684\u57fa\u672c\u6982\u5ff5","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/#_2","title":"\u968f\u673a\u8fc7\u7a0b\u7684\u5b9a\u4e49","text":"

    \u6982\u7387\u7a7a\u95f4\\((\\Omega,\\mathcal{A},P)\\)\u4e0a\u7684\u968f\u673a\u8fc7\u7a0b\u662f\u4e00\u65cf\u968f\u673a\u53d8\u91cf\\(X(\\omega,t):\\Omega\\to\\epsilon,t\\in T\\)\uff0c\u5176\u4e2d\\(T\\)\u79f0\u4e3a\u65f6\u95f4\u53c2\u6570\u7a7a\u95f4,\\(\\epsilon\\) \u79f0\u4e3a\u72b6\u6001\u7a7a\u95f4

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/#_3","title":"\u5747\u503c\u51fd\u6570","text":"

    \u82e5\\(\\forall t \\in T,E|X(t)|<\\infty\\)\uff0c\u5219\u79f0\\(\\mu_X(t)=EX(t),t\\in T\\)\u4e3a\u968f\u673a\u8fc7\u7a0b\\(X(t)\\)\u7684\u5747\u503c\u51fd\u6570

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/#_4","title":"\u81ea\u534f\u65b9\u5dee\u51fd\u6570","text":"

    \u82e5\\(\\forall t\\in T,E|X(t)|<\\infty\\)\uff0c\u5219\u79f0\\(\\sigma_X^2(t)=Var(X(t)),t\\in T\\)\u4e3a\u968f\u673a\u8fc7\u7a0b\\(X(t)\\)\u7684\u65b9\u5dee\u51fd\u6570

    \\(r_X(s,t)=E(X(t)X(s)),s,t\\in T\\)\u4e3a X \u7684\u81ea\u76f8\u5173\u51fd\u6570

    \\(Cov(X(t),X(s))=E(X(t)X(s))-EX(t)EX(s)=r_X(s,t)-\\mu_X(s)\\mu_X(t)\\)\u4e3a\u81ea\u534f\u65b9\u5dee\u51fd\u6570

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/#_5","title":"\u4e92\u76f8\u5173\u51fd\u6570","text":"

    \\(r_{X,Y}(s,t)=E(Y(t)X(s)),s,t\\in T\\)\u4e3a\u968f\u673a\u8fc7\u7a0b\\(X(t)\\)\u548c\\(Y(t)\\)\u7684\u4e92\u76f8\u5173\u51fd\u6570

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/#_6","title":"\u5bbd\u5e73\u7a33\u8fc7\u7a0b(\u5f31\u5e73\u7a33\u8fc7\u7a0b)","text":"

    \u82e5\\(\\forall t\\in T,E(X(t))^2<\\infty\\)

    1. \\(\\mu_X(t)=\\mu,\\forall t\\in T\\)

    2. \\(r_X(s,t)=\\tau_X(s-t)\\;,\\forall s,t\\in T\\),\u5176\u4e2d\\(\\tau_X:R\\to R\\)

    \u5219\u79f0\u968f\u673a\u8fc7\u7a0b\\(X(t)\\)\u4e3a\u5bbd\u5e73\u7a33\u8fc7\u7a0b

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/#_7","title":"\u4e25\u5e73\u7a33\u8fc7\u7a0b","text":"

    \u82e5\\(\\forall k\\geq 1,t_1,t_2,\\cdots,t_k\\in T,t\\in T\\)

    \\[(X(t_1+t),X(t_2+t),\\cdots,X(t_k+t))\\overset{d}{=}(X(t_1),X(t_2),\\cdots,X(t_k))\\]

    \u5219\u79f0\u968f\u673a\u8fc7\u7a0b\\(X(t)\\)\u4e3a\u4e25\u5e73\u7a33\u8fc7\u7a0b

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/02-%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5/#_8","title":"\u72ec\u7acb\u589e\u91cf\u8fc7\u7a0b","text":"

    \u82e5\\(\\forall t_1<t_2<\\cdots<t_n\\),\u968f\u673a\u53d8\u91cf\\(X(t_1),X(t_2)-X(t_1),\\cdots,X(t_n)-X(t_{n-1})\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\u79f0\u968f\u673a\u8fc7\u7a0b\\(X(t)\\)\u4e3a\u72ec\u7acb\u589e\u91cf\u8fc7\u7a0b

    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/","title":"Poisson \u8fc7\u7a0b","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#poisson_1","title":"Poisson\u5206\u5e03","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#_1","title":"\u7279\u6027","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#1entlambda-t","title":"1.\\(E(N(t))=\\lambda t\\)","text":"
    \u8bc1\u660e\u5f88\u7b80\u5355\n
    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#2varntlambda-t","title":"2.\\(Var(N(t))=\\lambda t\\)","text":"
    \u8bc1\u660e\u4e5f\u5f88\u7b80\u5355\n
    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#3","title":"3.\u81ea\u76f8\u5173\u51fd\u6570","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#4","title":"4.\u81ea\u534f\u65b9\u5dee\u51fd\u6570","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#poisson_2","title":"Poisson\u6d41","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#_2","title":"\u65f6\u95f4\u95f4\u9694","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#poisson_3","title":"Poisson \u53ef\u52a0\u6027(\u6309\u6982\u5ff5\u53ef\u5206)","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#_3","title":"\u5230\u8fbe\u65f6\u523b\u7684\u6761\u4ef6\u5206\u5e03","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#_4","title":"\u6b21\u5e8f\u7edf\u8ba1\u91cf","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#poisson_4","title":"\u590d\u5408 Poisson \u8fc7\u7a0b","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#poisson_5","title":"\u975e\u9f50\u6b21 Poisson \u8fc7\u7a0b","text":"
    \u4e4b\u524d\u5b66\u4e60\u7684 Poisson \u8fc7\u7a0b\u53ea\u548c\u65f6\u95f4\u6bb5\u6709\u5173,\u6362\u53e5\u8bdd\u8bf4\u7cfb\u7edf\u5728\u5404\u4e2a\u65f6\u523b\u7684\u7e41\u5fd9\u7a0b\u5ea6\u662f\u4e00\u6837\u7684\n\u4f46\u662f\u6bd4\u5982\u98df\u5802\u5c31\u9910,\u5f88\u660e\u663e\u5403\u996d\u65f6\u95f4\u4eba\u66f4\u591a,\u8fd9\u5c31\u662f\u975e\u9f50\u6b21\u7684\u60c5\u51b5\n
    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/03-Poisson%E8%BF%87%E7%A8%8B/#poisson_6","title":"\u591a\u7ef4Poisson\u70b9\u8fc7\u7a0b","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/","title":"Markov Chain","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#markov-chain_1","title":"Markov Chain\u7684\u57fa\u672c\u6027\u8d28","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#_1","title":"\u5b9a\u4e49","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#markov-chain_2","title":"Markov-Chain\u7684\u5206\u5e03","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#m-","title":"m-\u6b65\u8f6c\u79fb\u6982\u7387","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#_2","title":"\u72b6\u6001\u7a7a\u95f4\u5206\u89e3","text":"
    \u7c7b\u4f3c\u7fa4\u4f5c\u7528\u7684\u8f68\u9053\n
    "},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#_3","title":"\u4e92\u901a\u7c7b","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#_4","title":"\u5468\u671f","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#41","title":"\u5b9a\u7406 4.1","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#_5","title":"\u72b6\u6001\u7a7a\u95f4\u5206\u89e3","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#42","title":"\u5b9a\u7406 4.2","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#43","title":"\u5b9a\u7406 4.3","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#44","title":"\u5b9a\u7406 4.4(\u72b6\u6001\u7a7a\u95f4\u7684\u5206\u89e3)","text":""},{"location":"Notebook/%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B/04-Markov%E8%BF%87%E7%A8%8B/#_6","title":"\u5e38\u8fd4\u6027\u4e0e\u77ac\u65f6\u6027","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/","title":"\u9ad8\u7b49\u4ee3\u6570","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/","title":"\u7ebf\u6027\u65b9\u7a0b\u7ec4","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#11","title":"1.1 \u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u77e9\u9635\u6d88\u5143\u6cd5","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#_2","title":"\u7814\u7a76\u95ee\u9898:","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#_3","title":"\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u521d\u7b49\u53d8\u6362","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#1","title":"\u5b9a\u4e49 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#_4","title":"\u77e9\u9635\u7684\u884c\u521d\u7b49\u53d8\u6362","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#1_1","title":"\u5b9a\u7406 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#12","title":"1.2 \u7ebf\u6027\u65b9\u7a0b\u7ec4\u89e3\u7684\u60c5\u51b5\u53ca\u5176\u5224\u522b\u51c6\u5219","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#1_2","title":"\u5b9a\u7406 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#13","title":"1.3 \u6570\u57df","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#1_3","title":"\u5b9a\u4e49 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/01-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84/#1_4","title":"\u547d\u9898 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/","title":"\u884c\u5217\u5f0f","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#21-n","title":"2.1 \\(n\\)\u5143\u6392\u5217","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#1","title":"\u5b9a\u7406 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#2","title":"\u5b9a\u7406 2","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#22","title":"2.2 \u884c\u5217\u5f0f\u7684\u5b9a\u4e49","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#1_1","title":"\u547d\u9898 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#23","title":"2.3 \u884c\u5217\u5f0f\u7684\u6027\u8d28","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#_2","title":"\u6027\u8d28","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#24","title":"2.4 \u884c\u5217\u5f0f\u6309\u884c(\u5217)\u5c55\u5f00","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#1_2","title":"\u5b9a\u4e49 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#1_3","title":"\u5b9a\u7406 1","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#2_1","title":"\u5b9a\u7406 2","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#3","title":"\u5b9a\u7406 3","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#4","title":"\u5b9a\u7406 4","text":""},{"location":"Notebook/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0/02-%E8%A1%8C%E5%88%97%E5%BC%8F/#vandermoode","title":"Vandermoode \u884c\u5217\u5f0f","text":""},{"location":"Tools/","title":"\u4e00\u4e9b\u5de5\u5177\u7684\u914d\u7f6e\u65b9\u6cd5","text":""},{"location":"Tools/edge/","title":"edge","text":""},{"location":"Tools/vscode/","title":"Vscode","text":"