coin change

/*
Given a value N, if we want to make change for N cents, and we have infinite supply of each of S = { S1, S2, .. , Sm} valued coins, how many ways can we make the change? The order of coins doesn’t matter.
For example, for N = 4 and S = {1,2,3}, there are four solutions: {1,1,1,1},{1,1,2},{2,2},{1,3}. So output should be 4. For N = 10 and S = {2, 5, 3, 6}, there are five solutions: {2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} and {5,5}. So the output should be 5.
/*

// Recursive C program for 
// coin change problem. 
#include<stdio.h> 
  
// Returns the count of ways we can  
// sum S[0...m-1] coins to get sum n 
int count( int S[], int m, int n ) 
{ 
    // If n is 0 then there is 1 solution  
    // (do not include any coin) 
    if (n == 0) 
        return 1; 
      
    // If n is less than 0 then no  
    // solution exists 
    if (n < 0) 
        return 0; 
  
    // If there are no coins and n  
    // is greater than 0, then no 
    // solution exist 
    if (m <=0 && n >= 1) 
        return 0; 
  
    // count is sum of solutions (i)  
    // including S[m-1] (ii) excluding S[m-1] 
    return count( S, m - 1, n ) + count( S, m, n-S[m-1] ); 
} 
  
// Driver program to test above function 
int main() 
{ 
    int i, j; 
    int arr[] = {1, 2, 3}; 
    int m = sizeof(arr)/sizeof(arr[0]); 
    printf("%d ", count(arr, m, 4)); 
    getchar(); 
    return 0; 
}