Create HCF_using_Euclidean_algorithm.cpp

This program computes the HCF of given two numbers using Euclidean algorithm which takes logarithmic time complexity.

Author: Barun-Ojha

CPP/Basics/HCF_using_Euclidean_algorithm.cpp

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+//C++ program to compute HCF/GCD of two numbers using Euclidean algorithm
+//This algorithm finds HCF of two numbers in logarithmic time complexity
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// Function to compute HCF/GCD
+
+int Compute_HCF(int a, int b){
+    // Loop as long as both the numbers are greater than zero
+    while(a>0 && b>0){
+        // If a is greater than b then modularise a with b
+        if(a>b){
+            a = a%b;
+        }
+        // Otherwise modularise b with a
+        else{
+            b = b%a;
+        }
+    }
+    // After the termination of loop, the non zero number will be the HCF/GCD
+    if(a==0) return b;
+    return a;
+}
+
+
+int main(){
+    // Input two numbers
+    int a,b;
+    cin >> a >> b;
+    // Call Compute_HCF function to evaluate HCF
+    cout << Compute_HCF(a,b) ;
+}
+
+/*
+Time complexity = O(log(min(a,b)))
+Space complexity = O(1)
+*/