HDU - 1733 Escape(网络流层次模型)

题目大意：给出一张地图，每个位置每个时刻只能有一个人，现在问这些人都跑到门那边的最短时间

解题思路：网络流的层次模型，因为每个点每个时刻只能有一个人，所以拆成边，容量为1

再把每个结点每秒当成一个结点，接着枚举时间

连边的话有几种状态，一种是走到相邻格子的，如果能走的话，就把该点的出点连向下一个格子的下一秒的时态的入点

有可能该点的人不走，所以该点的出点要连接到该点的下一时刻的入点

[code]#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
const int MAXNODE = (1 << 17) + 10;
const int MAXEDGE = MAXNODE * 10;
typedef int Type;
const Type INF = 0x3f3f3f3f;

struct Edge{
    int u, v, next;
    Type cap, flow;
    Edge() {}
    Edge(int u, int v, Type cap, Type flow, int next) : u(u), v(v), cap(cap), flow(flow), next(next){}
};

struct Dinic{
    int n, m, s, t;
    Edge edges[MAXEDGE];
    int head[MAXNODE];
    int cur[MAXNODE];
    bool vis[MAXNODE];
    Type d[MAXNODE];
    vector<int> cut;

    void init(int n) {
        this->n = n;
        memset(head, -1, sizeof(head));
        m = 0;
    }

    void AddEdge(int u, int v, Type cap) {
        edges[m] = Edge(u, v, cap, 0, head[u]);
        head[u] = m++;
        edges[m] = Edge(v, u, 0, 0, head[v]);
        head[v] = m++;
    } 

    bool BFS() {
        memset(vis, 0, sizeof(vis));
        queue<int> Q;
        Q.push(s);
        d[s] = 0;
        vis[s] = 1;

        while (!Q.empty()) {
            int u = Q.front(); Q.pop();
            for (int i = head[u]; ~i; i = edges[i].next) {
                Edge &e = edges[i];
                if (!vis[e.v] && e.cap > e.flow) {
                    vis[e.v] = true;
                    d[e.v] = d[u] + 1;
                    Q.push(e.v);
                }
            }
        }
        return vis[t];
    }

    Type DFS(int u, Type a) {
        if (u == t || a == 0) return a;

        Type flow = 0, f;
        for (int &i = cur[u]; i != -1; i = edges[i].next) {
            Edge &e = edges[i];
            if (d[u] + 1 == d[e.v] && (f = DFS(e.v, min(a, e.cap - e.flow))) > 0) {
                e.flow += f;
                edges[i ^ 1].flow -= f;
                flow += f;
                a -= f;
                if (a == 0) break;
            }
        }
        return flow;
    }

    Type Maxflow(int s, int t) {
        this->s = s; this->t = t;
        Type flow = 0;
        while (BFS()) {
            for (int i = 0; i < n; i++)
                cur[i] = head[i];
            flow += DFS(s, INF);
        }
        return flow;
    }

    void Mincut() {
        cut.clear();
        for (int i = 0; i < m; i += 2) {
            if (vis[edges[i].u] && !vis[edges[i].v]) 
                cut.push_back(i);
        }
    }
}dinic;

#define maxn 20

struct Node {
    int x, y;
    Node() {}
    Node(int x, int y): x(x), y(y) {}
};

int n, m, num;
char map[maxn][maxn];
int dir[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
bool vis[maxn][maxn];

void init() {
    for (int i = 0; i < n; i++) 
        scanf("%s", map[i]);
}

bool bfs(int i, int j) {
    queue<Node> Q;
    memset(vis, 0, sizeof(vis));
    Q.push(Node(i, j));
    vis[i][j] = true;
    while (!Q.empty()) {
        Node t = Q.front(); Q.pop();
        if (map[t.x][t.y] == '@') return true;

        for (int i = 0; i < 4; i++) {
            int tx = t.x + dir[i][0];
            int ty = t.y + dir[i][1];
            if (tx < 0 || tx >= n || ty < 0 || ty >= m || vis[tx][ty] || map[tx][ty] == '#') continue;
            vis[tx][ty] = true;
            Q.push(Node(tx, ty));
        }
    }
    return false;
}

bool judge() {
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            if (map[i][j] == 'X' && !bfs(i, j)) return false;
    return true;
}

void solve() {
    if (!judge()) {
        printf("-1\n");
        return ;
    }

    int source = n * m * 2 * 100, sink = n * m * 2 * 100+ 1; 
    dinic.init(sink + 1);

    int tx, ty;
    num = 0;
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) 
            if (map[i][j] == 'X') {
                dinic.AddEdge(source, i * m + j, 1);
                num++;
            }

    int Time = 0;
    while (1) {
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)  {
                if (map[i][j] == '#') continue;
                int in = Time * n * m * 2 + i * m + j;
                int out = in + n * m;   
                dinic.AddEdge(in, out, 1);
                dinic.AddEdge(out, out + n * m, 1);
                if (map[i][j] == '@') dinic.AddEdge(out, sink, 1);
                for (int k = 0; k < 4; k++) {
                    int tx = i + dir[k][0];
                    int ty = j + dir[k][1];
                    if (tx < 0 || tx >= n || ty < 0 || ty >= m || map[tx][ty] == '#') continue;
                    dinic.AddEdge(out, (Time + 1) * n * m * 2 + tx * m + ty, 1);
                }
            }
        int Maxflow = dinic.Maxflow(source, sink);
        if (Maxflow == num) {
            printf("%d\n", Time);
            return ;
        }
        num -= Maxflow;
        Time++;
    }
}

int main() {
    while (scanf("%d%d", &n, &m) != EOF) {
        init();
        solve();
    }
    return 0;
}