Check if one integer is an integer power of another

In this blog post, I will teach you how to write Program to check whether a given integer is an integer power of another. That means a general solution to check if any number X is a power of Y or not, where Y is another integer number. After reading this post you able to check whether given integer number is power of another integer number or not.

An integer X is a power of Y, if there exists an integer p such that X == Y^p.

Let’s see the problem statements and constraints for this question.

Problem Statement: Given an integer X, return 1 if it is a power of Y. Otherwise, return 0.

Constraints:

➤ -2³¹ <= n <= 2³¹ -1

Ways to check whether a number X is a power of another number Y:

Using Logarithm (Math Approach).
Using while loop.

Let’s discuss each of them to find whether given number is power of three or not.

C program that checks if a number X is a power of another number Y:

Using Logarithm (Math Approach):

In the below C code, we find whether a given number X is a power of another number Y or not using log function. Below C function returns 1 if given number X is a power of another number Y otherwise returns 0.

/**
 C Program to find whether a given number x
 is power of y.
*/
#include <stdio.h>
#include <math.h>

int checkPowerOfY(int x, int y)
{
    int checkPowerOfY = 0;

    if((x==1) && (y==1))
    {
        checkPowerOfY = 1;
    }
    else
    {
        if ((x > 0) && (y > 0))
        {
            const double denominator  = 1.0;
            
            // Calculate logarithm base x of y
            double logarithm = (log(x) / log(y));
            
            // Check if the result is an integer
            checkPowerOfY = (fmod(logarithm, denominator) == 0);
        }
    }
    return checkPowerOfY;
}

int main()
{
    int x, y;
    printf("Enter the number X: ");
    scanf("%d", &x);
    printf("Enter the base number Y: ");
    scanf("%d", &y);

    if (checkPowerOfY(x, y))
    {
        printf("%d is a power of %d.\n", x, y);
    }
    else
    {
        printf("%d is not a power of %d.\n", x, y);
    }

    return 0;
}

Output:

Enter the number X: 32
Enter the base number Y: 2
32 is a power of 2.

Explanation:

In the above C code, we have put special handling for 1 and for other numbers that is greater than 0; we are calculating their logarithmic value. If result of expression log(x) / log(y) is integer, then x is power of y. We are verifying the integer with the help of fmod().

Note: You need to be careful of rounding issues with floating point numbers when comparing them.

Using while loop:

It is one of simplest approach in which you need to divide y into x. This means here, conceptualized as repeatedly subtracting y from x until the remainder obtained is less than y. If the first time you get a non-zero remainder you know x is not an integer power of y.

/**
 C Program to find whether a given number x
 is power of y.
*/
#include <stdio.h>

int checkPowerOfY(int x, int y)
{
    if((x>0) && (y > 0))
    {
        while (x % y == 0)
        {
            x /= y;
        }
    }

    // if x = 1 only then it is power of y
    return (x == 1);
}



int main()
{
    int x, y;
    printf("Enter the number X: ");
    scanf("%d", &x);
    printf("Enter the base number Y: ");
    scanf("%d", &y);
    if (checkPowerOfY(x, y))
    {
        printf("%d is a power of %d.\n", x, y);
    }
    else
    {
        printf("%d is not a power of %d.\n", x, y);
    }
    return 0;
}