Added Karatsuba_Algorithm.php

Karatsuba_Algorithm/Karatsuba_Algorithm.php

@@ -0,0 +1,50 @@
+<?php
+/*
+The Karatsuba Algorithm implements faster multiplication, 
+than the traditional approach.
+*/
+function karatsuba($num1,$num2){
+
+    // for single digit number multiply directly
+    if ($num1 < 10 || $num2 < 10) {
+        return $num1 * $num2;
+    }
+
+    $num1Str = strval($num1);
+    $num2Str = strval($num2);
+
+    $n = min(strlen($num1Str),strlen($num2Str));
+    $half = round($n / 2);
+
+    // divide num1 into two halves
+    $num1_H = intval(substr($num1Str,0, strlen($num1Str) - $half));
+    $num1_L = intval(substr($num1Str,strlen($num1Str) - $half, strlen($num1Str)));
+
+    // divide num2 into two halves
+    $num2_H = intval(substr($num2Str,0, strlen($num2Str) - $half));
+    $num2_L = intval(substr($num2Str,strlen($num2Str) - $half, strlen($num2Str)));
+
+    // using the KaratSuba Definition
+    $s1 = karatSuba($num1_L, $num2_L);
+    $s2 = karatSuba($num1_L + $num1_H, $num2_L + $num2_H);
+    $s3 = karatSuba($num1_H, $num2_H);
+
+    $s4 = $s2 - $s3 -$s1;
+
+    // karatsuba formula for finding product
+    $result = $s3 * pow(10, 2 * $half) + $s4 * pow(10, $half) + $s1;
+
+    return $result;
+}
+
+$num1 = 23984;
+$num2 = 183672;
+echo "\nInputs are: ".$num1." ".$num2;
+$result = karatSuba($num1,$num2);
+echo "\nThe result is: ".$result;
+
+// Input :
+// 23984 183672
+// Output: 
+// 4405189248
+?>