HDU - 4289 Control (最小割 MCMF)

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题目大意：有一个间谍要将一些机密文件送到目的地
现在给出间谍的初始位置和要去的目的地，要求你在间谍的必经路上将其拦获且费用最小

解题思路：最小割最大流的应用，具体可以看网络流–最小割最大流

建图的话
超级源点–起始城市，容量为INF
城市拆成两点(u, v),容量为监视该城市的代价
能连通的城市连接，容量为INF
目的地和超级汇点相连，容量为INF

#include <cstdio>#include <cstring>#include <algorithm>#include <vector>#include <queue>using namespace std;#define N 1010#define INF 0x3f3f3f3fstruct Edge {    int from, to, cap, flow;    Edge() {}    Edge(int from, int to, int cap, int flow): from(from), to(to), cap(cap), flow(flow) {}};struct ISAP {    int p[N], num[N], cur[N], d[N];    int t, s, n, m;    bool vis[N];    vector<int> G[N];    vector<Edge> edges;    void init(int n) {        this->n = n;        for (int i = 0; i <= n; i++) {            G[i].clear();            d[i] = INF;        }        edges.clear();    }    void AddEdge(int from, int to, int cap) {        edges.push_back(Edge(from, to, cap, 0));        edges.push_back(Edge(to, from, 0, 0));        m = edges.size();        G[from].push_back(m - 2);        G[to].push_back(m - 1);    }    bool BFS() {        memset(vis, 0, sizeof(vis));        queue<int> Q;        d[t] = 0;        vis[t] = 1;        Q.push(t);        while (!Q.empty()) {            int u = Q.front();            Q.pop();            for (int i = 0; i < G[u].size(); i++) {                Edge &e = edges[G[u][i] ^ 1];                if (!vis[e.from] && e.cap > e.flow) {                    vis[e.from] = true;                    d[e.from] = d[u] + 1;                    Q.push(e.from);                }            }        }        return vis[s];    }    int Augment() {        int u = t, flow = INF;        while (u != s) {            Edge &e = edges[p[u]];            flow = min(flow, e.cap - e.flow);            u = edges[p[u]].from;        }        u = t;        while (u != s) {            edges[p[u]].flow += flow;            edges[p[u] ^ 1].flow -= flow;            u = edges[p[u]].from;        }        return flow;    }    int Maxflow(int s, int t) {        this->s = s; this->t = t;        int flow = 0;        BFS();        if (d[s] > n)            return 0;        memset(num, 0, sizeof(num));        memset(cur, 0, sizeof(cur));        for (int i = 0; i < n; i++)            if (d[i] < INF)                num[d[i]]++;        int u = s;        while (d[s] <= n) {            if (u == t) {                flow += Augment();                u = s;            }            bool ok = false;            for (int i = cur[u]; i < G[u].size(); i++) {                Edge &e = edges[G[u][i]];                if (e.cap > e.flow && d[u] == d[e.to] + 1) {                    ok = true;                    p[e.to] = G[u][i];                     cur[u] = i;                    u = e.to;                    break;                }            }            if (!ok) {                int Min = n;                for (int i = 0; i < G[u].size(); i++) {                    Edge &e = edges[G[u][i]];                    if (e.cap > e.flow)                        Min = min(Min, d[e.to]);                }                if (--num[d[u]] == 0)                    break;                num[d[u] = Min + 1]++;                cur[u] = 0;                if (u != s)                    u = edges[p[u]].from;            }        }        return flow;    }};ISAP isap;int n, m;void solve() {    int source = 0, sink = 2 * n + 1;    int s, t;    isap.init(sink);    scanf("%d%d", &s, &t);    isap.AddEdge(source, s, INF);    isap.AddEdge(t + n, sink, INF);    int x, y;    for (int i = 1; i <= n; i++) {        scanf("%d", &x);        isap.AddEdge(i, i + n, x);    }    for (int j = 0; j < m; j++) {        scanf("%d%d", &x, &y);        isap.AddEdge(x + n, y, INF);        isap.AddEdge(y + n, x, INF);    }    printf("%d\n", isap.Maxflow(source, sink));}int main() {    while (scanf("%d%d", &n, &m) != EOF) {        solve();    }    return 0;}

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