Number of arrays of size N whose elements are positive integers and sum is K in C++

We are given two numbers n and k. We need to find the count of arrays that can be formed using the n numbers whose sum is k.

The number of arrays of size N with sum K is $\dbinom{k - 1}{n - 1}$.

This a straightforward formula to find the number arrays that can be formed using n elements whose sum k. Let's see an example.

Input

n = 1
k = 2

Output

1

The only array that can be formed is [2]

Input

n = 2
k = 4

Output

3

The arrays that can be formed are [1, 3], [2, 2], [3, 1].

Algorithm

• Initialise the numbers n and k.
• Write a function to calculate the factorial of a number.
• Now, write our main function to compute the binomial as seen above.
• Return the answer.

Implementation

Following is the implementation of the above algorithm in C++

#include <bits/stdc++.h>
using namespace std;
int factorial(int n) {
   int result = 1;
   for (int i = 2; i <= n; i++) {
      result *= i;
   }
   return result;
}
int getNumberOfArraysCount(int n, int k) {
   return factorial(n) / (factorial(k) * factorial(n - k));
}
int main() {
   int N = 5, K = 8;
   cout << getNumberOfArraysCount(K - 1, N - 1) << endl;
   return 0;
}

Output

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

35