Count ways to express a number as sum of powers in C++

Given two numbers num and power as input. The goal is to find the ways in which num can be represented as a sum of unique natural numbers raised to the given power. If num is 10 and power is 2 then we can represent 10 as 12+32. So total 1 way.

For Example

Input

num=30

Output

Count of ways to express a number as sum of powers are: 2

Explanation

The ways in which we can express 30 as sum of powers:
1<sup>2</sup> + 2<sup>2</sup> + 5<sup>2</sup> and 1<sup>2</sup> + 2<sup>2</sup> + 3<sup>2</sup> + 4<sup>2</sup>

Input

num=35

Output

Count of ways to express a number as sum of powers are: 1

Explanation

The ways in which we can express ‘num’ as sum of powers: 2<sup>2</sup> + 3<sup>2</sup>

Approach used in the below program is as follows −

In this approach we first check if the number is itself the power of any num^power. If yes then return ways as 1, if not then recursively check for sum num^power + (num+1)^power.

• Take two integers num and power as input.

• Function sum_of_powers(int num, int power, int val) takes a num and returns the count of ways to express ‘num’ as sum of unique natural numbers raised to the given power.

• Take check=(num − pow(val, power)). If check is 0 then return 1 as the number itself is val^power.

• If check is less than 0 then return 0.

• Otherwise take temp=val+1.

• Return sum of ( sum_of_powers(check, power, temp) + sum_of_powers(num, power, temp) ).

• At the end we will get ways to return value.

Example

#include <bits/stdc++.h>
using namespace std;
int sum_of_powers(int num, int power, int val){
   int check = (num − pow(val, power));
   if(check == 0){
      return 1;
   }
   else if(check < 0){
      return 0;
   } else {
      int temp = val + 1;
      return sum_of_powers(check, power, temp) + sum_of_powers(num, power, temp);
   }
}
int main(){
   int num = 25, power = 2;
   cout<<"Count of ways to express a number as sum of powers are: "<<sum_of_powers(num, power, 1);
   return 0;
}

Output

If we run the above code it will generate the following output −

Count of ways to express a number as sum of powers are: 2