Write a program to calculate pow(x,n)

Given two integers x and n, write a function to compute xn. We may assume that x and n are small and overflow doesn’t happen.

Examples :

Input : x = 2, n = 3
Output : 8

Input : x = 7, n = 2
Output : 49


Below solution divides the problem into subproblems of size y/2 and call the subproblems recursively.

C

#include<stdio.h>
  
/* Function to calculate x raised to the power y */
int power(int x, unsigned int y)
{
    if (y == 0)
        return 1;
    else if (y%2 == 0)
        return power(x, y/2)*power(x, y/2);
    else
        return x*power(x, y/2)*power(x, y/2);
}
  
/* Program to test function power */
int main()
{
    int x = 2;
    unsigned int y = 3;
  
    printf("%d", power(x, y));
    return 0;
}

Java

class GFG {
    /* Function to calculate x raised to the power y */
    static int power(int x, int y)
    {
        if (y == 0)
            return 1;
        else if (y % 2 == 0)
            return power(x, y / 2) * power(x, y / 2);
        else
            return x * power(x, y / 2) * power(x, y / 2);
    }
  
    /* Program to test function power */
    public static void main(String[] args)
    {
        int x = 2;
        int y = 3;
  
        System.out.printf("%d", power(x, y));
    }
}
  
// This code is contributed by Smitha Dinesh Semwal

Python3

# Python3 program to calculate pow(x,n)
  
# Function to calculate x
# raised to the power y 
def power(x, y):
  
    if (y == 0): return 1
    elif (int(y % 2) == 0):
        return (power(x, int(y / 2)) *
               power(x, int(y / 2)))
    else:
        return (x * power(x, int(y / 2)) *
                   power(x, int(y / 2)))
  
# Driver Code
x = 2; y = 3
print(power(x, y))
  
# This code is contributed by Smitha Dinesh Semwal.

C#

using System;
  
public class GFG {
      
    // Function to calculate x raised to the power y
    static int power(int x, int y)
    {
        if (y == 0)
            return 1;
        else if (y % 2 == 0)
            return power(x, y / 2) * power(x, y / 2);
        else
            return x * power(x, y / 2) * power(x, y / 2);
    }
  
    // Program to test function power
    public static void Main()
    {
        int x = 2;
        int y = 3;
  
        Console.Write(power(x, y));
    }
}
  
// This code is contributed by shiv_bhakt.

PHP

<?php
// Function to calculate x 
// raised to the power y
function power($x, $y)
{
    if ($y == 0)
        return 1;
    else if ($y % 2 == 0)
        return power($x, (int)$y / 2) * 
               power($x, (int)$y / 2);
    else
        return $x * power($x, (int)$y / 2) * 
                    power($x, (int)$y / 2);
}
  
// Driver Code
$x = 2;
$y = 3;
  
echo power($x, $y);
      
// This code is contributed by ajit
?>

Output :

8

Time Complexity: O(n)
Space Complexity: O(1)
Algorithmic Paradigm: Divide and conquer.

Above function can be optimized to O(logn) by calculating power(x, y/2) only once and storing it.

/* Function to calculate x raised to the power y in O(logn)*/
int power(int x, unsigned int y)
{
    int temp;
    if( y == 0)
        return 1;
    temp = power(x, y/2);
    if (y%2 == 0)
        return temp*temp;
    else
        return x*temp*temp;
}

Time Complexity of optimized solution: O(logn)
Let us extend the pow function to work for negative y and float x.

C

/* Extended version of power function that can work
 for float x and negative y*/
#include<stdio.h>
  
float power(float x, int y)
{
    float temp;
    if( y == 0)
       return 1;
    temp = power(x, y/2);       
    if (y%2 == 0)
        return temp*temp;
    else
    {
        if(y > 0)
            return x*temp*temp;
        else
            return (temp*temp)/x;
    }
}  
  
/* Program to test function power */
int main()
{
    float x = 2;
    int y = -3;
    printf("%f", power(x, y));
    return 0;
}

Java

/* Java code for extended version of power function
that can work for float x and negative y */
class GFG {
      
    static float power(float x, int y)
    {
        float temp;
        if( y == 0)
            return 1;
        temp = power(x, y/2); 
          
        if (y%2 == 0)
            return temp*temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    
      
    /* Program to test function power */
    public static void main(String[] args)
    {
        float x = 2;
        int y = -3;
        System.out.printf("%f", power(x, y));
    }
}
  
// This code is contributed by  Smitha Dinesh Semwal.

Python3

# Python3 code for extended version
# of power function that can work
# for float x and negative y
  
def power(x, y):
  
    if(y == 0): return 1
    temp = power(x, int(y / 2)) 
      
    if (y % 2 == 0):
        return temp * temp
    else:
        if(y > 0): return x * temp * temp
        else: return (temp * temp) / x
      
# Driver Code
x, y = 2, -3
print('%.6f' %(power(x, y)))
  
# This code is contributed by Smitha Dinesh Semwal. 

C#

// C# code for extended version of power function
// that can work for float x and negative y
  
using System;
  
public class GFG{
      
    static float power(float x, int y)
    {
        float temp;
          
        if( y == 0)
            return 1;
        temp = power(x, y/2); 
          
        if (y % 2 == 0)
            return temp * temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    
      
    // Program to test function power 
    public static void Main()
    {
        float x = 2;
        int y = -3;
          
        Console.Write(power(x, y));
    }
}
  
// This code is contributed by shiv_bhakt.

PHP

<?php
// Extended version of power
// function that can work
// for float x and negative y
  
function power($x, $y)
{
    $temp;
    if( $y == 0)
    return 1;
    $temp = power($x, $y / 2);     
    if ($y % 2 == 0)
        return $temp * $temp;
    else
    {
        if($y > 0)
            return $x
                   $temp * $temp;
        else
            return ($temp
                    $temp) / $x;
    }
  
// Driver Code
$x = 2;
$y = -3;
echo power($x, $y);
  
// This code is contributed by ajit
?>

Output :

0.125000


Write an iterative O(Log y) function for pow(x, y)
Modular Exponentiation (Power in Modular Arithmetic)

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up

Improved By : jit_t