Exercise_Unit_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.1 编写一个Python函数is_multiple(n, m)，用来接收两个整数值n和m，如果n是m的倍数，即存在整数i使得$n=mi$，那么函数返回True，否则返回False。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_multiple(n, m):\n",
    "    return not n % m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    result = is_multiple(25, 4)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_multiple(n, m):\n",
    "    return n % m == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    result = is_multiple(25, 5)\n",
    "    print(result)\n",
    "    result = is_multiple(25, 4)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.2 编写一个Python函数is_even(k)，用来接收一个整数k，如果k是偶数返回True，否则返回False。但是，函数中不能使用乘法、除法、或者取余操作。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_even(k):\n",
    "    return (k & 1 == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_even(k):\n",
    "    return (k & 1 == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    print(is_even(23))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def minmax(data):\n",
    "    min = data[0]\n",
    "    max = data[0]\n",
    "    for val in data:\n",
    "        if val < min:\n",
    "            min = val\n",
    "        if val > max:\n",
    "            max = val\n",
    "    return min, max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == '__main__':\n",
    "    result = minmax([1, 3, 3, 4, 5, 9, 5, 55, 99])\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def minmax(data):\n",
    "    small = big = data[0]    # assuming nonempty\n",
    "    for val in data:\n",
    "        if val in data:\n",
    "            if val < small:\n",
    "                small = val\n",
    "            if val >  big:\n",
    "                big = val\n",
    "    return small, big"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == '__main__':\n",
    "    result = minmax([1, 3, 3, 4, 5, 9, 5, 55, 99])\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_of_squares(n):\n",
    "    sum = 0\n",
    "    for val in range(1, n+1):\n",
    "        sum += val*val\n",
    "    return sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "if __name__ == '__main__':\n",
    "    result = sum_of_squares(1000)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_of_squares(n):\n",
    "    total = 0\n",
    "    for j in range(1, n+1):\n",
    "        total += j*j\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "if __name__ == '__main__':\n",
    "    result = sum_of_squares(1000)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_of_squares(n):\n",
    "    return sum([k*k for k in range(1, n+1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "if __name__ == '__main__':\n",
    "    result = sum_of_squares(1000)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "total = sum(j*j for j in range(1, n+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_of_squares(n):\n",
    "    sum = 0\n",
    "    for val in range(1, n+1, 2):\n",
    "        sum += val*val\n",
    "    return sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "if __name__ == '__main__':\n",
    "    result = sum_of_squares(1000)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_of_squares(n):\n",
    "    total = 0\n",
    "    for j in range(1, n+1, 2):\n",
    "        total += j*j\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == '__main__':\n",
    "    result = sum_of_squares(1000)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_of_squares(n):\n",
    "    return sum([k*k for k in range(1, n+1) if k % 2 == 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "if __name__ == '__main__':\n",
    "    result = sum_of_squares(1000)\n",
    "    print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "total = sum(j*j for j in range(1, n+1, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|负数索引|正数索引|\n",
    "|-|-|\n",
    "|-1|n-1|\n",
    "|-2|n-2|\n",
    "|k|n+k|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "n+k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = range(50, 90, 10)\n",
    "print(list(result))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "range(50, 91, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = range(8, -10, -2)\n",
    "print(list(result))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "range(8, -10, -2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = [2**k for k in range(0, 9)]\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "[2**k for k in range(9)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-1.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import randrange\n",
    "\n",
    "\n",
    "def choice(data):\n",
    "    index = randrange(len(data))\n",
    "    return data[index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == '__main__':\n",
    "    data = [k for k in range(100)]\n",
    "    for i in range(10):\n",
    "        result = choice(data)\n",
    "        print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参考答案"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def choice(data):\n",
    "    return data[randrange(len(data))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == '__main__':\n",
    "    data = [k for k in range(100)]\n",
    "    for i in range(10):\n",
    "        result = choice(data)\n",
    "        print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  }
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