# Write an iterative O(Log y) function for pow(x, y)

• Difficulty Level : Medium
• Last Updated : 15 Jul, 2022

Given an integer x and a positive number y, write a function that computes xy under following conditions.
a) Time complexity of the function should be O(Log y)
b) Extra Space is O(1)

Examples: ```Input: x = 3, y = 5
Output: 243

Input: x = 2, y = 5
Output: 32
```

## We strongly recommend that you click here and practice it, before moving on to the solution.

We have discussed recursive O(Log y) solution for power. The recursive solutions are generally not preferred as they require space on call stack and they involve function call overhead.

Following is implementation to compute xy.

## C++

 `// Iterative C program to implement pow(x, n)``#include ``using` `namespace` `std;`` ` `/* Iterative Function to calculate (x^y) in O(logy) */``int` `power(``int` `x, unsigned ``int` `y)``{``    ``int` `res = 1; ``// Initialize result`` ` `    ``while` `(y > 0) {``        ``// If y is odd, multiply x with result``        ``if` `(y & 1)``            ``res = res * x;`` ` `        ``// y must be even now``        ``y = y >> 1; ``// y = y/2``        ``x = x * x; ``// Change x to x^2``    ``}``    ``return` `res;``}`` ` `// Driver program to test above functions``int` `main()``{``    ``int` `x = 3;``    ``unsigned ``int` `y = 5;`` ` `    ``cout<<``"Power is "``<

## C

 `// Iterative C++ program to implement pow(x, n)``#include `` ` `/* Iterative Function to calculate (x^y) in O(logy) */``int` `power(``int` `x, unsigned ``int` `y)``{``    ``int` `res = 1; ``// Initialize result`` ` `    ``while` `(y > 0) {``        ``// If y is odd, multiply x with result``        ``if` `(y & 1)``            ``res = res * x;`` ` `        ``// y must be even now``        ``y = y >> 1; ``// y = y/2``        ``x = x * x; ``// Change x to x^2``    ``}``    ``return` `res;``}`` ` `// Driver program to test above functions``int` `main()``{``    ``int` `x = 3;``    ``unsigned ``int` `y = 5;`` ` `    ``printf``(``"Power is %d"``, power(x, y));`` ` `    ``return` `0;``}`

## Java

 `// Iterative Java program``// to implement pow(x, n)``import` `java.io.*;`` ` `class` `GFG ``{``     ` `/* Iterative Function to ``calculate (x^y) in O(logy) */``static` `int` `power(``int` `x, ``int` `y)``{``    ``// Initialize result``    ``int` `res = ``1``; `` ` `    ``while` `(y > ``0``) ``    ``{``        ``// If y is odd, ``        ``// multiply``        ``// x with result``        ``if` `((y & ``1``) == ``1``)``            ``res = res * x;`` ` `        ``// y must be even now``        ``y = y >> ``1``; ``// y = y/2``        ``x = x * x; ``// Change x to x^2``    ``}``    ``return` `res;``}`` ` `// Driver Code``public` `static` `void` `main (String[] args) ``{``    ``int` `x = ``3``;``    ``int` `y = ``5``;`` ` `    ``System.out.println(``"Power is "` `+ ``                        ``power(x, y));``}``}`` ` `// This code is contributed``// by aj_36`

## Python3

 `# Iterative Python3 program``# to implement pow(x, n)`` ` `# Iterative Function to``# calculate (x^y) in O(logy)``def` `power(x, y):`` ` `    ``# Initialize result``    ``res ``=` `1``     ` `    ``while` `(y > ``0``):``         ` `        ``# If y is odd, multiply``        ``# x with result``        ``if` `((y & ``1``) ``=``=` `1``) :``            ``res ``=` `res ``*` `x`` ` `        ``# y must be even ``        ``# now y = y/2``        ``y ``=` `y >> ``1``         ` `        ``# Change x to x^2``        ``x ``=` `x ``*` `x``     ` `    ``return` `res`` ` ` ` `# Driver Code``x ``=` `3``y ``=` `5`` ` `print``(``"Power is "``,``       ``power(x, y))`` ` `# This code is contributed``# by ihritik`

## C#

 `// Iterative C# program``// to implement pow(x, n)``using` `System;`` ` `class` `GFG``{``     ` `/* Iterative Function to ``calculate (x^y) in O(logy) */``static` `int` `power(``int` `x, ``int` `y)``{``    ``int` `res = 1; ``// Initialize result`` ` `    ``while` `(y > 0) ``    ``{``        ``// If y is odd, multiply``        ``// x with result``        ``if` `((y & 1) == 1)``            ``res = res * x;`` ` `        ``// y must be even now``        ``y = y >> 1; ``// y = y/2``        ``x = x * x; ``// Change x to x^2``    ``}``    ``return` `res;``}`` ` `// Driver Code``static` `public` `void` `Main ()``{``int` `x = 3;``int` `y = 5;`` ` `Console.WriteLine(``"Power is "``+ ``                   ``power(x, y));``}``}`` ` `// This code is contributed``// by aj_36`

## PHP

 ``` ` `// Iterative Function to ``// calculate (x^y) in O(logy)`` ` `function` `power(``\$x``, ``\$y``)``{``     ` `    ``// Initialize result``    ``\$res` `= 1;     `` ` `    ``while` `(``\$y` `> 0)``    ``{``         ` `        ``// If y is odd, multiply``        ``// x with result``        ``if` `(``\$y` `& 1)``            ``\$res` `= ``\$res` `* ``\$x``;`` ` `        ``// y must be even now``         ` `        ``// y = y/2``        ``\$y` `= ``\$y` `>> 1; ``         ` `        ``// Change x to x^2``        ``\$x` `= ``\$x` `* ``\$x``; ``    ``}``    ``return` `\$res``;``}`` ` `    ``// Driver Code``    ``\$x` `= 3;``    ``\$y` `= 5;`` ` `    ``echo` `"Power is "``, power(``\$x``, ``\$y``);`` ` `// This code is contributed by ajit``?>`

## Javascript

 ``

Output:

`Power is 243`

Time Complexity: O(log y), since in loop each time the value of y decreases by half it’s current value.

Auxiliary Space: O(1), since no extra space has been taken.