Extended Euclidean Algorithm in PHP (#2988)

* Extended Euclidean Algorithm in PHP

* Update Extended_Euclidean_Algorithm.php

* Update Extended_Euclidean_Algorithm.php

Extended_Euclidean_Algorithm/Extended_Euclidean_Algorithm.php

@@ -0,0 +1,45 @@
+<?php 
+
+/* Extended Euclidean Algorithm 
+  ==============================
+  GCD of two numbers is the largest number that divides both of them.  
+    GCD(a,b) = ax + by
+  If we can find the value of  x and y then we can easily find the 
+  value of GCD(a,b) by replacing (x,y) with their respective values.
+*/
+
+//Function to find GCD
+//This function returns an array having elements gcd, x and y
+function gcd($a, $b) 
+{  
+    // Base Case 
+    if ($a == 0)
+        return array($b, 0, 1);
+
+    // To store results of recursive call 
+    $arr = gcd($b % $a, $a);
+    // Update x and y using results of recursive call 
+    $gcd = $arr[0];
+    $x = $arr[1];
+    $y = $arr[2];
+    return array($gcd, (int)($y - ($b / $a) * $x), $x);
+}
+
+// Driver Code 
+$a = readline("Enter number 1 : ");
+$b = readline("Enter number 2 : ");
+$arr = gcd($a, $b);
+echo "\nGCD of ", $a, " and ", $b, " is ", $arr[0];
+echo "\nx = ", $arr[1];
+echo "\ny = ", $arr[2];
+
+
+/*
+Sample input/output: 
+Enter number 1 : 100                                                                                                          
+Enter number 2 : 20                                                                                                                                                                                                                                         
+GCD of 100 and 20 is 20                                                                                                       
+x = 0                                                                                                                         
+y = 1   
+*/ 
+?>