【USACO】Money Systems

原理在注释里，自己写的不是这样的，参照答案改的。自己写的是最原始版本的DP。

但这个推理貌似很厉害的样子，记住之。

/*
ID :
LANG: C++11
TASK: money
 */

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <string>
#include <cmath>
#include <set>

using namespace std;

int main()
{
    freopen("money.in", "r", stdin);
    freopen("money.out", "w", stdout);
    std::ios::sync_with_stdio(false);

    int V, N;
    cin >> V >> N;
    int coins[30] = {};
    long long int ways[11000] = {};
    //ways(i, n) = ways(i - 1, n) + sigma<k> ways(i - 1, n - coins[i] * k);
    //ways(i - 1, n - coins[i] * k) = ways(i - 1,
    ways[0] = 1;
    for (int i = 1; i <= V; i ++){
        cin >> coins[i];
        /*
        for (int j = N; i >= 0; i ++){
            ways[j] += ways[j] + sigma ways[j - k * coins[i]];
        }
         */
        for (int j = coins[i]; j <= N; j ++){
            ways[j] += ways[j - coins[i]];
        }
    }
    sort(coins + 1, coins + 1 + V, greater<int>());


    cout << ways[N] << endl;

    return 0;
}