Create Euclidean algorithm.cpp

algorithms/CPlusPlus/Maths/Euclidean algorithm.cpp

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+/*The Euclidean Algorithm is a technique for quickly finding the GCD of two integers.
+GCD of two numbers is the largest number that divides both of them. A simple way to find GCD is to factorize both numbers and multiply common prime factors.
+
+Basic Euclidean Algorithm for GCD: 
+If we subtract a smaller number from a larger one (we reduce a larger number), GCD doesn’t change. So if we keep subtracting repeatedly the larger of two, we end up with GCD.
+Now instead of subtraction, if we divide the smaller number, the algorithm stops when we find the remainder 0.
+If A = 0 then GCD(A,B)=B, since the GCD(0,B)=B, and we can stop.  
+If B = 0 then GCD(A,B)=A, since the GCD(A,0)=A, and we can stop.  
+Write A in quotient remainder form (A = B⋅Q + R)
+Find GCD(B,R) using the Euclidean Algorithm since GCD(A,B) = GCD(B,R)
+
+Below is a recursive function to evaluate gcd using Euclid’s algorithm: */
+
+#include <bits/stdc++.h>
+using namespace std;
+ 
+// Function to return gcd of a and b
+int gcd(int a, int b)
+{
+    if (a == 0)
+        return b;
+    return gcd(b % a, a);
+}
+ 
+// Driver Code
+int main()
+{
+    int a,b;
+  cout<<"Enter two numbers : ";
+  cin>>a>>b>>endl;
+   
+      // Function call
+    cout << "GCD(" << a << ", " << b << ") = " << gcd(a, b)
+         << endl;
+   =
+    return 0;
+}
+
+
+
+/*
+Sample input-output
+GCD(10, 15) = 5
+GCD(35, 10) = 5
+GCD(31, 2) = 1
+*/
+
+
+//Time Complexity: O(Log min(a, b))
+//Auxiliary Space: O(Log (min(a,b))