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

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 <stdio.h>
  
/* 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;
  
        // n 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;
  
        // n 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
  
        # n 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;
  
        // n 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

<?php
// Iterative php program 
// to implement pow(x, n)>
  
// 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;
  
        // n 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
?>

Output:

Power is 243


This article is attributed to GeeksforGeeks.org

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