Check if a number is a power of another number

Given two positive numbers x and y, check if y is a power of x or not.
Examples :

Input:  x = 10, y = 1
Output: True
x^0 = 1

Input:  x = 10, y = 1000
Output: True
x^3 = 1

Input:  x = 10, y = 1001
Output: False

A simple solution is to repeatedly compute the powers of x. If a power becomes equal to y, then y is a power, else not. 

C++

// C++ program to check if a number is power of
// another number
#include <bits/stdc++.h>
using namespace std;

/* Returns 1 if y is a power of x */
bool isPower(int x, long int y)
{
    // The only power of 1 is 1 itself
    if (x == 1)
        return (y == 1);

    // Repeatedly compute power of x
    long int pow = 1;
    while (pow < y)
        pow *= x;

    // Check if power of x becomes y
    return (pow == y);
}

/* Driver program to test above function */
int main()
{
    cout << isPower(10, 1) << endl;
    cout << isPower(1, 20) << endl;
    cout << isPower(2, 128) << endl;
    cout << isPower(2, 30) << endl;
    return 0;
}

Java

// Java program to check if a number is power of
// another number
public class Test {
    // driver method to test power method
    public static void main(String[] args)
    {
        // check the result for true/false and print.
        System.out.println(isPower(10, 1) ? 1 : 0);
        System.out.println(isPower(1, 20) ? 1 : 0);
        System.out.println(isPower(2, 128) ? 1 : 0);
        System.out.println(isPower(2, 30) ? 1 : 0);
    }
    /* Returns true if y is a power of x */
    public static boolean isPower(int x, int y)
    {
        // The only power of 1 is 1 itself
        if (x == 1)
            return (y == 1);

        // Repeatedly compute power of x
        int pow = 1;
        while (pow < y)
            pow = pow * x;

        // Check if power of x becomes y
        return (pow == y);
    }
}

// This code is contributed by Jyotsna.

Python3

# python program to check
# if a number is power of
# another number

# Returns true if y is a
# power of x
def isPower (x, y):

    # The only power of 1
    # is 1 itself
    if (x == 1):
        return (y == 1)

    # Repeatedly compute
    # power of x
    pow = 1
    while (pow < y):
        pow = pow * x

    # Check if power of x
    # becomes y
    return (pow == y)


# Driver Code
# check the result for
# true/false and print.
if(isPower(10, 1)):
    print(1)
else:
    print(0)

if(isPower(1, 20)):
    print(1)
else:
    print(0)
if(isPower(2, 128)):
    print(1)
else:
    print(0)
if(isPower(2, 30)):
    print(1)
else:
    print(0)

# This code is contributed
# by Sam007.

C#

// C# program to check if a number
// is power of another number
using System;

class GFG
{

    // Returns true if y is a power of x
    public static bool isPower (int x, int y)
    {
        // The only power of 1 is 1 itself
        if (x == 1)
        return (y == 1);

        // Repeatedly compute power of x
        int pow = 1;
        while (pow < y)
        pow = pow * x;

        // Check if power of x becomes y
        return (pow == y);
    }

    // Driver Code
    public static void Main ()
    {
        //check the result for true/false and print.
        Console.WriteLine(isPower(10, 1) ? 1 : 0);
        Console.WriteLine(isPower(1, 20) ? 1 : 0);
        Console.WriteLine(isPower(2, 128) ? 1 : 0);
        Console.WriteLine(isPower(2, 30) ? 1 : 0);
    }

}

// This code is contributed by Sam007

PHP

<?php
// PHP program to check if a
// number is power of another number

/* Returns 1 if y is a power of x */
function isPower($x, $y)
{
    // The only power of 1 is 1 itself
    if ($x == 1)
        return ($y == 1 ? 1 : 0);

    // Repeatedly comput power of x
    $pow = 1;
    while ($pow < $y)
        $pow *= $x;

    // Check if power of x becomes y
    return ($pow == $y ? 1 : 0);
}

// Driver Code
echo isPower(10, 1) . "\n";
echo isPower(1, 20) . "\n";
echo isPower(2, 128) . "\n";
echo isPower(2, 30) . "\n";

// This code is contributed by mits
?>

Javascript

<script>

// JavaScript program to check if a number
// is power of another number

/* Returns true if y is a power of x */
    function isPower(x, y)
    {
        // The only power of 1 is 1 itself
        if (x == 1)
            return (y == 1);

        // Repeatedly compute power of x
        let pow = 1;
        while (pow < y)
            pow = pow * x;

        // Check if power of x becomes y
        return (pow == y);
    }


// Driver Code

        //check the result for true/false and print.
        document.write((isPower(10, 1) ? 1 : 0) + "<br/>");
           document.write((isPower(1, 20) ? 1 : 0) + "<br/>");
        document.write((isPower(2, 128) ? 1 : 0) + "<br/>");
        document.write((isPower(2, 30) ? 1 : 0) + "<br/>");

</script>

Output

1
0
1
0

Time complexity: O(Log_xy)
Auxiliary space: O(1)

Optimization:
We can optimize above solution to work in O(Log Log y). The idea is to do squaring of power instead of multiplying it with x, i.e., compare y with x^2, x^4, x^8, …etc. If x becomes equal to y, return true. If x becomes more than y, then we do binary search for power of x between previous power and current power, i.e., between x^i and x^(i/2).
Following are detailed step. 

1) Initialize pow = x, i = 1
2) while (pow < y)
   {
      pow = pow*pow 
      i *= 2
   }    
3) If pow == y
     return true;
4) Else construct an array of powers
   from x^i to x^(i/2)
5) Binary Search for y in array constructed
   in step 4. If not found, return false. 
   Else return true.

Alternate Solution : 
The idea is to take log of y in base x. If it turns out to be an integer, we return true. Else false. 

C++

// CPP program to check given number y
// is power of x
#include <iostream>
#include <math.h>
using namespace std;

bool isPower(int x, int y)
{
    // logarithm function to calculate value
    float res1 = log(y) / log(x);
    return res1==floor(res1);
}

// Driven program
int main()
{
    cout << isPower(2, 128) << endl;
    return 0;
}
//This code is contributed by Anand Agarwal

Java

// Java program to check given
// number y is power of x

class GFG
{
    static boolean isPower(int x,
                           int y)
    {
        // logarithm function to
        // calculate value
        float res1 = (float)(Math.log(y) /
                   Math.log(x));

        return (res1%1==0);
    }

    // Driver Code
    public static void main(String args[])
    {
        if(isPower(2, 128))
            System.out.println("1");
        else
            System.out.println("0");
    }
}

// This code is contributed by Sam007
// This code is Corrected by Anand Agarwal

Python3

# Python program to check if given number y
# is power of x
import math

def is_power(x, y):
    # logarithm function to calculate value
    res1 = math.log(y) / math.log(x)
    res2 = math.log(y) / math.log(x) # Note: this is float

    # compare to the result1 or result2 both are equal
    return res1 == res2

# Driven program
if __name__ == "__main__":
    print(is_power(2, 128))

C#

using System;

namespace ConsoleApp1
{
  class Program
  {

    // Function to check if a number is power of another number
    static bool IsPower(int x, int y)
    {

      // Use logarithm function to calculate the value
      double res1 = Math.Log(y) / Math.Log(x);

      // Note : this is double
      double res2 = Math.Log(y) / Math.Log(x);

      // Compare the result1 or result2, they should be equal
      return (res1 == res2);
    }

    static void Main(string[] args)
    {
      // Check if 128 is power of 2
      if (IsPower(2, 128))
        Console.WriteLine("1");
      else
        Console.WriteLine("0");
    }
  }
}

// This code is contributed by vinayetbi1.

PHP

<?php
// PHP program to check
// given number y
function isPower($x, $y)
{
    // logarithm function to
    // calculate value
    $res1 = log($y) / log($x);

    // Note : this is double
    $res2 = log($y) / log($x);

    // compare to the result1 or
    // result2 both are equal
    return ($res1 == $res2);
}

// Driver Code
echo isPower(2, 128) ;

// This code is contributed by Sam007
?>

Javascript

// JavaScript program to check given number y
// is power of x

function isPower(x, y) {
    // logarithm function to calculate value
    const res1 = Math.log(y) / Math.log(x);
    const res2 = Math.log(y) / Math.log(x);

    // compare to the result1 or result2 both are equal
    return (res1 === res2);
}

// Driven program
console.log(isPower(2, 128));

Output

1

Time complexity: O(log Y)
Auxiliary space: O(1)