HDU - 1733 Escape(网络流层次模型)

来源：互联网发布：云存储软件编辑：程序博客网时间：2024/05/18 02:34

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

#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 20struct 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;}

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