Merge pull request #33 from juan88/add-fast-exponentiation

Add fast exponentiation to math algorithms

DIRECTORY.md

@@ -12,6 +12,7 @@
 - [Check Prime](https://github.com/TheAlgorithms/PHP/blob/master/Maths/CheckPrime.php)
 - [Factorial](https://github.com/TheAlgorithms/PHP/blob/master/Maths/Factorial.php)
 - [Perfect Square](https://github.com/TheAlgorithms/PHP/blob/master/Maths/PerfectSquare.php)
+- [Fast Exponentiation](https://github.com/TheAlgorithms/PHP/blob/master/Maths/FastExponentiation.php)
 
 ## Searching
 

Maths/FastExponentiation.php

@@ -0,0 +1,24 @@
+<?php
+/**
+ * This functions computes an exponent by doing repeated squares
+ *
+ * @param Integer $base the base
+ * @param Integer $exponent the exponent (ie the number of times that the base is multiplied by itself)
+ * @return Integer
+ */
+function fastExponentiation(int $base, int $exponent)
+{
+    if ($exponent == 0) {
+		return 1;
+	}   
+
+	if ($exponent == 1) {
+		return $base;
+	}
+
+	if ($exponent % 2 == 0) {
+		return fastExponentiation($base*$base, $exponent/2);
+	} else {
+		return $base * fastExponentiation($base*$base, ($exponent-1)/2);
+	}
+}

tests/MathTest.php

@@ -11,6 +11,7 @@ require_once __DIR__ . '/../Maths/CheckPrime.php';
 require_once __DIR__ . '/../Maths/AbsoluteMax.php';
 require_once __DIR__ . '/../Maths/AbsoluteMin.php';
 require_once __DIR__ . '/../Maths/PerfectSquare.php';
+require_once __DIR__ . '/../Maths/FastExponentiation.php';
 
 class MathTest extends TestCase
 {
@@ -56,4 +57,13 @@ class MathTest extends TestCase
         assertFalse(is_perfect_square(2));
         assertTrue(is_perfect_square(225));
     }
+
+    public function testFastExponentiation()
+    {
+        assertEquals(fastExponentiation(10, 0), 1);
+        assertEquals(fastExponentiation(10, 1), 10);
+        assertEquals(fastExponentiation(10, 2), 100);
+        assertEquals(fastExponentiation(10, 3), 1000);
+        assertEquals(fastExponentiation(20, 5), 3200000);
+    }
 }