Use C++ to solve: I got the solution, but don't understand how it works.

My question is how can the program count the ways?

And what does " return number_of_ways(value, N, number + 1) + number_of_ways(X, N, number + 1);" mean in this function?

#include

using namespace std;

int number_of_ways(int X, int N, int number)

{

/* While calling the function from the main, we have to initialize num=1 */

int value = (X - pow(number, N));

/*If X is itself the nth power of num, the we count 1*/

if (value == 0)

return 1;

/*If X is lesser than nth power of num, the we discard thet*/

if (value

return 0;

/*Now recurssively call the function with two possibilities, one in which num is included and the other in which num is not included.*/

return number_of_ways(value, N, number + 1) +

number_of_ways(X, N, number + 1);

}

int main()

{

int X, N;

cin>>X>>N;

cout

return 0;

}

4 No answer yet (25 points) The user input consists of two positive integers X and N. Determine the number of ways in which X can be written as the sum of perfect N-th powers of distinct positive integers. Example 1: Input: 200 2 Output: 9 Explanation: There are nine ways in which 200 can be written as the sum of perfect squares. They are 200 = 12 +22 + 32 +42 +52 +82 +92, 200 = 12 +22 + 32 +42 +72 +112, 200 = 12 +22+52 + 72 +112, 200 = 12 + 32 +42 +52 +62 +72 +82, 200 = 12 + 32 +42 +52 + 72 +102, 200 = 22 +42 +62 +122, 200 = 22 +14, 200 = 32 +52 +62 +7+92, and 200 = 62 +82 + 10%. Example 2: Input: 1008 3 Output: 2 Explanation: There are two ways in which 1008 can be written as the sum of perfect cubes. They are 1008 = 12 +33 +53 + 7 + 83 and 1008 = 23 + 10%