Introduction to Backtracking, recursion and sets

theory/backtracking/findingSubsets.cpp

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+#include <iostream>
+
+void findSubsets(char *input, char *output, int i, int j) {
+
+    //base case
+    if(input[i] == '\0') {
+        output[j] = '\0';
+        if(output[0]=='\0')
+            std::cout << "NULL";
+        std::cout << output << std::endl;
+        return;
+    }
+
+    //rec case
+    //include the ith letter
+    output[j] = input[i];
+    findSubsets(input, output, i+1, j+1);
+
+    //exclude the ith letter
+    output[j] = '\0';
+    findSubsets(input,output,i+1,j);
+
+}
+
+
+
+
+int main(){
+
+    char s[100], output[100];
+
+    std::cin >> s;
+    findSubsets(s,output,0,0);
+
+}
+
+
+

theory/backtracking/permutations.cpp

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+#include <iostream>
+#include <cstring>
+#include <string>
+
+void swap(char *a, char *b) {
+    char tmp = *a;
+    *a=*b;
+    *b=tmp;
+}
+
+/*
+
+    Given a string s, find all permutations of the string
+    
+
+*/
+
+void permutationsString(char *n1, int l, int r) {
+
+    int i;
+    if(l == r)
+        std::cout << n1 << std::endl;
+
+    for(i = l; i <= r; ++i) {
+        swap((n1+l), (n1+i));
+        permutationsString(n1, l+1, r);
+        swap((n1+l),(n1+i));
+    }
+
+}
+
+int main(){
+
+    char str[100];
+    std::cin >> str;
+    int n = strlen(str);
+
+    permutationsString(str, 0 , n-1);
+
+
+}
+
+
+

theory/inclusion_and_exclusion/inclusion_exclusion.md

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+# Principles of Inclusion and Exclusion
+
+-> Set Theory
+
+Set is a form to store elements that doesn't repeat
+Generally sets're sorted
+
+'''
+{AuB} = A + B - {A^B} -> union of the sets
+
+-> Generalised function
+
+'''
+Discovering the pattern of even and odd sets
+Let's see if we've 3 sets
+
+|AuBuC| ->  A + B + C
+          - |AB| - |AC| - |BC|
+          + |ABC|
+
+Now let's see for 4 sets
+
+|AuBuCuD| ->  A + B + C + D
+             - |AB| - |AC| - |BC|
+             + |ABC| + |ABD| + |BCD| + |ACD|
+             - |ABCD|

theory/recursion/factorial.cpp

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+#include <iostream>
+
+
+int factorial(int n) {
+
+    if (n == 1)
+        return 1;
+
+    return n*factorial(n-1);
+
+}
+
+
+int main(){
+
+    std::cout << factorial(5) << std::endl;
+
+
+}

theory/recursion/fibonnaci.cpp

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+#include <iostream>
+
+int fib(int n) {
+
+    if(n == 0 or n == 1)
+        return n;
+
+    return fib(n-1) + fib(n-2);
+
+}
+
+
+int main(){
+
+    std::cout << fib(5) << std::endl;
+
+}