Create extended_euclid_algorithm.cpp (#759)

* Create extended_euclid_algorithm.cpp

* Fix wihitespaces and fix if else space issues

* Update extended_euclid_algorithm.cpp

* updating DIRECTORY.md

* Update extended_euclid_algorithm.cpp

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -96,6 +96,7 @@
 ## Math
   * [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binary_exponent.cpp)
   * [Eulers Totient Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/eulers_totient_function.cpp)
+  * [Extended Euclid Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/extended_euclid_algorithm.cpp)
   * [Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/factorial.cpp)
   * [Fast Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fast_power.cpp)
   * [Greatest Common Divisor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/greatest_common_divisor.cpp)

math/extended_euclid_algorithm.cpp

@@ -0,0 +1,28 @@
+#include <iostream>
+// Finding coefficients of a and b ie x and y in gcd(a, b) = a * x + b * y
+// d is gcd(a, b)
+// This is also used in finding Modular multiplicative inverse of a number.
+// (A * B)%M == 1 Here B is the MMI of A for given M,
+// so extendedEuclid (A, M) gives B.
+
+int d, x, y;
+void extendedEuclid(int A, int B) {
+    if (B == 0) {
+        d = A;
+        x = 1;
+        y = 0;
+    } else {
+        extendedEuclid(B, A%B);
+        int temp = x;
+        x = y;
+        y = temp - (A/B)*y;
+    }
+}
+
+int main() {
+    int a, b;
+    std::cin >> a >> b;
+    extendedEuclid(a, b);
+    std::cout << x << " " << y << std::endl;
+    return 0;
+}