递归动态编程解决方案太慢

Question

我已经被困了一个多小时，我已经对动态编程问题有了正确的解决方案，但由于某些原因它太慢了。即使我使用的是C ++，我仍然会在hackerrank的测试用例上获得超时（我希望Java会出现这种问题）。

Here is the Coin Change Problem

这是我的问题代码：

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

/*
    N - The amount of change that should be created.
    M - The number of elements in the C array.
    C[] - The array of possible coins to use. Coins can be reused.
    i - The index of the coin to begin with, as to not 
            repeat combinations already used.
*/
unsigned long long coinChangeCombinations(int N, int M, int C[], int i) {
    unsigned long long combinations = 0;
    for (; i < M; i++) {
        int c = C[i];
        if (N == c) {
            combinations++;
        } else if (N > c) {
            combinations += coinChangeCombinations(N - c, M, C, i);
        }
    }
    return combinations;
}

int main() {
    unsigned long long N, M;
    cin >> N;
    cin >> M;
    int C[M];
    for (int i = 0; i < M; i++) {
        int c;
        cin >> c;
        C[i] = c;
    }
    cout << coinChangeCombinations(N, M, C, 0) << endl;
    return 0;
}

大多数讨论都集中在迭代解决方案上 - 迭代总是比递归更快吗？在这种情况下，我认为迭代解决方案没有理由比递归更快。当然，递归会占用更多内存，但这不是我遇到的问题。