Merge pull request rathoresrikant#274 from codetochangeMinds/master

Added Extended Eulid Gcd algorithm

Cryptography/extended_euclid_gcd.cpp

@@ -0,0 +1,53 @@
+// Extended Euclid Gcd is often useful in finding inverse of 
+// number mod n efficently. If gcd=1, then equation will turned to be
+// 1=x*a+y*b, no taking modulo with b we get x as inverse of 
+// a mod b
+#include <bits/stdc++.h>
+using namespace std;
+
+// (d,x,y) is tuple
+struct gcd_tuple{
+    int d;
+    int x;
+    int y;
+};
+
+// evaluate gcd using Extended-Euclid-Gcd
+// d=x*a+b*y
+// d is gcd of a and b
+// and is smallest number that can be expressed in this form.
+// extended_euclid_gcd(a,b){
+    // (d,x,y)=extended_euclid_gcd(b,a%b);
+    // a=b*q+r;
+    // return (d,y,x-y*q);
+// }
+struct gcd_tuple extended_euclid_gcd(int a,int b)
+{
+    struct gcd_tuple e_gcd;
+    if(b==0)
+    {
+        e_gcd.d=a;
+        e_gcd.x=1;
+        e_gcd.y=0;
+        return e_gcd;
+    }    
+
+    e_gcd=extended_euclid_gcd(b,a%b);
+    int q=a/b;
+    int x=e_gcd.x;
+    int y=e_gcd.y;
+    e_gcd.x=y;
+    e_gcd.y=x-y*q;
+
+    return e_gcd;
+}
+
+// output format is d=a*x+b*y
+int main(){
+
+    int a,b;
+    cin>>a>>b;
+    struct gcd_tuple e_gcd;
+    e_gcd=extended_euclid_gcd(a,b);
+    cout<<e_gcd.d<<"="<<a<<"*"<<e_gcd.x<<"+"<<b<<"*"<<e_gcd.y;
+}