hdu 3682

二分 + 状压dp

dp[i][j]表示终点为i，访问状态为j剩余的最大能量

二分一个上限能量

dp[i][j]  可以由dp[k][s]转移过来，表示从k点走到i点，如果k点是一个电池的话那么只要满足dp[k][s]剩余的能量 >= 0，否则则是dp[k][s] - dist[i][k]

#include <cstdio>
#include <cstring>
#include <queue>

using namespace std;
const int maxn = 30;
const int INF = 10007;


struct Point {
    int x, y, d;
};
int tot;
struct Point point[maxn];
int type[maxn], num[maxn][maxn];
int dp[17][1 << (16)];
int goal;
int n, m;
int step[4][2] = {{0, 1}, {0,-1},{-1, 0}, {1, 0}};
char maps[maxn][maxn];
queue<struct Point> que;
int dist[maxn][maxn], vis[maxn][maxn];
int pre[17][1 << 16];
void bfs(int source) {
    memset(vis, 0, sizeof(vis));
    for (int i = 0; i <= tot; i++) {
        dist[source][i] = INF;
    }
    memset(vis, 0, sizeof(vis));
    dist[source][source] = 0;
    point[source].d = 0;
    que.push(point[source]);
    vis[point[source].x][point[source].y] = 1;
    while (!que.empty()) {
        struct Point p = que.front();
        que.pop();
        for (int k = 0; k < 4; k++) {
            int next_x = p.x + step[k][0];
            int next_y = p.y + step[k][1];
            if (next_x >= 0 && next_x < n && next_y >= 0 && next_y < m && !vis[next_x][next_y] && maps[next_x][next_y] != 'D') {
                vis[next_x][next_y] = 1;
                struct Point a;
                a.x = next_x;
                a.y = next_y;
                a.d = p.d + 1;
                if (num[next_x][next_y] != -1) {
                    dist[source][num[next_x][next_y]] = p.d + 1;
                }
                que.push(a);
            }
        }
    }
}
bool check(int p) {
    memset(dp, -1, sizeof(dp));
    dp[0][1] = p;
    for (int i = 1; i < (1 << tot); i++) {
        for (int j = 0; j < tot; j++) {
            if (!(i & (1 << j))) {
                continue;
            }
            for (int k = 0; k < tot; k++) {
                if (i & (1 << k) && k != j) {
                    if (type[k] == 1) {
                        if (dp[k][i ^ (1 << j)] < 0) {
                            continue;
                        }
                        dp[j][i] = max(dp[j][i], p - dist[k][j]);
                    }
                    else {
                        dp[j][i] = max(dp[j][i], dp[k][i ^ (1 << j)] - dist[k][j]);
                    }
                }
            }
            if (((i & goal) == goal) && dp[j][i] >= 0) {
                return true;
            }
        }
    }
    return false;
}
int main() {
//    freopen("in.txt", "r", stdin);
    while (scanf("%d%d", &n, &m) != EOF) {
        if (!n && !m) {
            break;
        }
        for (int i = 0; i < n; i++) {
            scanf("%s", maps[i]);
        }
        tot = 1;
        goal = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                num[i][j] = -1;
                if (maps[i][j] == 'F') {
                    point[0].x = i;
                    point[0].y = j;
                    num[i][j] = 0;
                }
                else if (maps[i][j] == 'G') {
                    point[tot].x = i;
                    point[tot].y = j;
                    num[i][j] = tot;
                    type[tot] = 1;
                    tot++;
                }
                else if (maps[i][j] == 'Y') {
                    point[tot].x = i;
                    point[tot].y = j;
                    type[tot] = 2;
                    num[i][j] = tot;
                    goal |= (1 << tot);
                    tot++;
                }
            }
        }
        for (int i = 0; i < tot; i++) {
            bfs(i);
        }
        int flag = 0;
        for (int i = 1; i < tot; i++) {
            if (type[i] == 2 && dist[0][i] == INF) {
                flag = 1;
                break;
            }
        }
        if (flag) {
            puts("-1");
            continue;
        }
        int low = 0;
        int high = INF;
        while (low <= high) {
            int mid = (low + high) >> 1;
            if (check(mid)) {
                high = mid - 1;
            }
            else {
                low = mid + 1;
            }
        }
        printf("%d\n", low);
    }
    return 0;
}