【toj1163】Gone Fishing

最新推荐文章于 2017-08-02 20:47:04 发布

原创最新推荐文章于 2017-08-02 20:47:04 发布 · 799 阅读

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本文介绍了一个关于钓鱼问题的动态规划算法实现。该问题设定在多个湖中钓鱼，每个湖的鱼数量随时间减少，目标是在规定时间内最大化钓鱼数量。通过使用三维动态规划数组来跟踪最优解，并记录达到该状态的前驱状态。

说有个人钓鱼，好多湖，湖里的鱼从开始钓计时，每 $5$ 分钟减少一定量，搞啊搞。。。最后可以在任何湖停止。问最多可以钓多少鱼。
直接 $dp$ 即可。。。
应该可以贪心做，或者分组做，总之直接 $dp$ 比较慢一点，复杂度是..

$O (144 n h 2)$ $O(144nh^2)$

/* **********************************************

    File Name: 1163.cpp

    Auther: zhengdongjian@tju.edu.cn

    Created Time: 2015/8/26 星期三 下午 1:08:38

*********************************************** */
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> P;

const int INF = 0xfffffff;
const int MAX_T = 207;
const int MAX_L = 26;
struct State {
    int i, j, k;
};
int dp[MAX_L][MAX_T][MAX_T];
State dad[MAX_L][MAX_T][MAX_T];
int daisy[MAX_L];
int f[MAX_L], d[MAX_L], t[MAX_L];
/*
 * dp[i][j][0] = dp[i-1][j - t_{i-1}][..]
 * dp[i][j][k] = max{dp[i][j - 1][k - 1] + max(0,fi-(k-1)di)}
 */
int main() {
    int n, h;
    bool black = false;
    while (~scanf(" %d", &n) && n) {
        scanf(" %d", &h);
        h *= 12;
        for (int i = 1; i <= n; ++i) {
            scanf(" %d", f + i);
        }
        for (int i = 1; i <= n; ++i) {
            scanf(" %d", d + i);
        }
        for (int i = 1; i < n; ++i) {
            scanf(" %d", t + i);
        }
        t[0] = 0;
        //memset(dp, 0, sizeof(dp));
        for (int k = 0; k <= n; ++k) {
            for (int i = 0; i <= h; ++i) {
                for (int j = 0; j <= h; ++j) {
                    dp[k][i][j] = -INF;
                }
            }
        }
        dp[0][0][0] = 0;
        dad[0][0][0] = (struct State){-1, -1, -1};
        //memset(dp[0], 0, sizeof(dp[0]));
        int use = 0;
        for (int i = 1; i <= n; ++i) {
            for (int j = use; j <= h; ++j) {
                for (int k = 0; k <= h - use; ++k) {
                    if (k == 0) {
                        if (j < t[i - 1]) continue;
                        for (int r = 0; r <= h; ++r) {
                            if (dp[i - 1][j - t[i - 1]][r] > dp[i][j][k]) {
                                dp[i][j][k] = dp[i - 1][j - t[i - 1]][r];
                                dad[i][j][k] = (struct State){i - 1, j - t[i - 1], r};
                            }
                        }
                    } else {
                        if (j) {
                            int vl = dp[i][j - 1][k - 1] + max(0, f[i] - (k - 1) * d[i]);
                            if (dp[i][j][k] < vl) {
                                dp[i][j][k] = vl;
                                dad[i][j][k] = (struct State){i, j - 1, k - 1};
                            }
                        }
                    }
                }
            }
            use += t[i];
        }
        int ans = 0;
        P mom = P(0, 0);
        for (int i = 1; i <= n; ++i) {
            for (int j = 0; j <= h; ++j) {
                if (dp[i][h][j] > ans) {
                    ans = dp[i][h][j];
                    mom = P(i, j);
                }
            }
        }
        memset(daisy, 0, sizeof(daisy));
        State now = (struct State){mom.first, h, mom.second};
        //daisy[mom.first] = mom.second;
        while (now.i != -1) {
            daisy[now.i] = max(daisy[now.i], now.k);
            now = dad[now.i][now.j][now.k];
        }
        int sum = 0;
        for (int i = 1; i <= n; ++i) {
            sum += daisy[i];
        }
        for (int i = n; i >= 1; --i) {
            if (daisy[i]) {
                for (int j = i - 1; j >= 1; --j) {
                    sum += t[j];
                }
                break;
            }
        }
        daisy[1] += h - sum > 0 ? h - sum : 0;

        if (black) puts("");
        for (int i = 1; i < n; ++i) {
            printf("%d, ", daisy[i] * 5);
        }
        printf("%d\n", daisy[n] * 5);
        printf("Number of fish expected: %d\n", ans);
        black = true;
    }
    return 0;
}