Find ways an Integer can be expressed as sum of n-th power of unique natural numbers in C++

In this tutorial, we are going to write a program that find the number of ways a integer can be expressed as sum of given n-th power of unique numbers.

We have two integers number and power. And we need to find in how many ways can we represent the given number as sum of n-th power of unique natural numbers. Let's see an example.

Input − number = 50, power = 2

Output − 3

There is only possible way we can write 4 as sum of 2 powers.

We will be using recursion to solve the problem. Let's see the steps to solve the problem.

  • Initialize the number and power.

  • Write a recursive function with a suitable name. It accepts number, power and i as arguments.

  • If the number is less than zero or pow(i, power) is greater than number, then return 0.

  • If the number is zero or pow(i, power) is equal to the number, then return 1.

  • We have two recursive calls for the functions to compute the total number of ways

    • Increment the i.

    • In the first recursive call, check for the numbers less than given number.

    • In the second recursive call, check for the given number.


Let's see the code.

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int findPossibleWaysCount(int number, int power, int i = 1) {
   if(number < 0 || number < pow(i, power)) {
      return 0;
   if(number == 0 || number == pow(i, power)) {
      return 1;
   return findPossibleWaysCount(number - pow(i, power), power, i + 1) + findPossibleWaysCount(number, power, i + 1);
int main() {
   // initializing the number and power
   int number = 50, power = 2;
   cout << findPossibleWaysCount(number, power) << endl;
   return 0;


If you run the above code, then you will get the following result.



If you have any queries in the tutorial, mention them in the comment section.