Check if a number is power of k using base changing method

This program checks whether a number n can be expressed as power of k and if yes, then to what power should k be raised to make it n. Following example will clarify :

Examples:

Input :   n = 16, k = 2 
Output :  yes : 4
Explanation : Answer is yes because 16 can 
be expressed as power of 2. 
                        
Input :   n = 27, k = 3 
Output :  yes : 3
Explanation : Answer is yes as 27 can be
expressed as power of 3.

Input :  n = 20, k = 5
Output : No
Explanation : Answer is No as 20 cannot 
be expressed as power of 5.  

We have discussed two methods in below post
:Check if a number is a power of another number

In this post, a new Base Changing method is discussed.

In Base Changing Method, we simply change the base of number n to k and check if the first digit of Changed number is 1 and remaining all are zero.

Example for this : Let’s take n = 16 and k = 2.
Change 16 to base 2. i.e. (10000)2. Since first digit is 1 and remaining are zero. Hence 16 can be expressed as power of 2. Count the length of (10000)2 and subtract 1 from it, that’ll be the number to which 2 must be raised to make 16. In this case 5 – 1 = 4.

Another example : Let’s take n = 20 and k = 3.
20 in base 3 is (202)3. Since there are two non-zero digit, hence 20 cannot be expressed as power of 3.

// CPP program to check if a number can be
// raised to k
#include <iostream>
#include <algorithm>
using namespace std;

bool isPowerOfK(unsigned int n, unsigned int k)
{
    // loop to change base n to base = k
    bool oneSeen = false;
    while (n > 0) {

        // Find current digit in base k
        int digit = n % k;

        // If digit is neither 0 nor 1 
        if (digit > 1)
            return false;

        // Make sure that only one 1
        // is present. 
        if (digit == 1)
        {
            if (oneSeen)
            return false;
            oneSeen = true;
        }     

        n /= k;
    }
    
    return true; 
}

// Driver code
int main()
{
    int n = 64, k = 4;

    if (isPowerOfK(n ,k))
        cout << "Yes";
    else
        cout << "No";
}

Output:

Yes

This article is contributed by Shubham Rana. 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.

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