The correct, optimal and working solution for programming question coin-change on hackerrank

/* * Author: Arpit Bhayani * https://arpitbhayani.me */ #include <cmath> #include <cstdio> #include <cstdlib> #include <climits> #include <deque> #include <iostream> #include <list> #include <limits> #include <map> #include <queue> #include <set> #include <stack> #include <vector> #define ll long long #define MIN(a, b) a < b ? a : b #define MAX(a, b) a > b ? a : b using namespace std; int readline(char *str) { int i = 0; char ch; while((ch = getchar()) != '\n') { str[i++] = ch; } str[i] = '\0'; return i; } #define MAX_COINS 51 #define MAX_SUM 251 int arr[51]; ll int dp[251][51]; ll int count(int sum, int n) { if(sum < 0) { return 0; } if(n < 0 && sum >= 1) { return 0; } if(dp[sum][n] != -1) { return dp[sum][n]; } if(sum == 0) { dp[sum][n] = 1; return 1; } dp[sum][n] = count(sum, n - 1) + count(sum - arr[n], n); return dp[sum][n]; } int main(int argc, char *argv[]) { int sum, n; scanf("%d%d", &sum, &n); for(int i = 0 ; i < n; i++) { scanf("%d", &arr[i]); } for(int i = 0 ; i < MAX_SUM; i++) { for(int j = 0 ; j < MAX_COINS; j++) { dp[i][j] = -1; } } ll int ans = 0; ans = count(sum, n-1); printf("%lld\n", ans); return 0; }