POJ - 1787 Charlie\'s Change(完全背包和路径纪录)

题目大意：给出五种硬币的价值和数量，问如何用最多的硬币组成另一个数

解题思路：完全背包问题加纪录路径

#include <cstdio>
#include <cstring>
const int N = 10010;

int val[4] = {1, 5, 10, 25};
int dp[N], path[N], use[N], num[4], ans[30];
int n;

void solve() {
    memset(dp, -1, sizeof(dp));
    memset(path, -1, sizeof(path));

    dp[0] = 0;
    path[0] = 0;
    for (int i = 0; i < 4; i++) { 
        memset(use, 0, sizeof(use));
        for (int j = val[i]; j <= n; j++) {
            if (dp[j] < dp[j - val[i]] + 1 && dp[j - val[i]] != -1 && use[j - val[i]] < num[i]) {
                dp[j] = dp[j - val[i]] + 1;
                use[j] = use[j - val[i]] + 1;
                path[j] = j - val[i];
            }
        }
    }

    if (dp[n] == -1) {
        printf("Charlie cannot buy coffee.\n");
        return ;
    }
    memset(ans, 0, sizeof(ans));
    int t = n;

    while (t != 0) {
        ans[t - path[t]]++;
        t = path[t];
    }
    printf("Throw in %d cents, %d nickels, %d dimes, and %d quarters.\n", ans[1], ans[5], ans[10], ans[25]);

}

int main() {
    while (scanf("%d", &n)) {
        int Sum = n;
        for (int i = 0; i < 4; i++) {
            scanf("%d", &num[i]);
            Sum += num[i];
        }

        if (!Sum) break;
        solve();
    }
    return 0;
}