Create time_complexity_Examples.cpp

others/time_complexity_Examples.cpp

@@ -0,0 +1,66 @@
+#include <iostream>
+using namespace std;
+
+/*
+Time Complexity
+
+O(1):
+Runs in constant time.
+The algorithm runs in a fixed number of steps regardless of input size.
+Examples: accessing an array element, simple operations.
+
+O(log n):
+Number of steps depends on how many times we divide n by 2.
+Example: Binary Search.
+
+O(sqrt(n)):
+The loop runs until i * i <= n.
+Example: checking divisors or prime numbers.
+
+O(n):
+The algorithm iterates over all elements once.
+
+O(n log n):
+Used in efficient sorting algorithms like Merge Sort and Quick Sort.
+
+O(n^2):
+Occurs in nested loops (comparing all pairs).
+
+O(n^3):
+Triple nested loops.
+
+Polynomial Time:
+O(n^k), where k is constant.
+
+Exponential Time:
+O(2^n): subsets, brute force recursion.
+O(n!): permutations.
+
+Note:
+1 second ≈ 10^8 operations
+
+O(1)       -> ∞
+O(log n)   -> ∞
+O(n)       -> 1e7
+O(n log n) -> 1e6
+O(n^2)     -> 2000
+O(n^3)     -> 200
+O(2^n)     -> 20
+O(n!)      -> 10
+*/
+
+// Example: O(n^2)
+void printPairs(int arr[], int n) {
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+            cout << arr[i] << " " << arr[j] << endl;
+        }
+    }
+}
+
+int main() {
+    int arr[] = {1, 2, 3};
+    int n = 3;
+    printPairs(arr, n);
+    return 0;
+}