POJ - 3281 Dining （ISAP EK Dinic）

POJ - 3281 Dining （ISAP EK Dinic）

題目大意：有N頭牛，F種食物，D種飲料，每種食物和飲料都只有一
現在給出每頭牛所喜愛的食物和飲料，問最多有多少頭牛能同時得到自己喜歡的食物和飲料

解題思路：將牛拆成兩點，權值為1，一條和喜歡的食物相連，權值為1，另一條和喜歡的飲料相連，權值為1
然後將所有食物和超級源點相連，權值為1
將所有的飲料喝超級匯點相連，權值為1

ISAP

#include 
#include 
#include 
#include 
#include 
using namespace std;
#define N 1010
#define INF 0x3f3f3f3f

struct 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 G[N];
    vector 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));
        int m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    }

    bool BFS() {
        memset(vis, 0, sizeof(vis));

        queue 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;
    }
};

//cow 1 -- 2 * n
//food 2 * n + 1 --- 2 * n + f
//drink 2 * n + f + 1 --- 2 * n + f + d
//start 0
//sink 2 * n + f + d + 1

ISAP isap;
int n, f, d;

void init() {
    int s = 0, t = 2 * n + d + f + 1;
    isap.init(t);

    for (int i = 1; i <= f; i++) {
        isap.AddEdge(0, 2 * n + i, 1);
    }

    for (int i = 1; i <= d; i++) {
        isap.AddEdge(2 * n + f + i, t, 1);
    }

    int fi, di, x;
    for (int i = 1; i <= n; i++)  {
        scanf(%d%d, &fi, &di);
        isap.AddEdge(i, n + i, 1);

        for (int j = 0; j < fi; j++) {
            scanf(%d, &x);
            isap.AddEdge(2 * n + x, i, 1);
        }

        for (int j = 0; j < di; j++) {
            scanf(%d, &x);
            isap.AddEdge(n + i, 2 * n + f + x, 1);
        }
    }
    int flow = isap.Maxflow(s, t);

    printf(%d
, flow);
}

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

Dinic

#include 
#include 
#include 
#include 
#include 
using namespace std;
#define N 1010
#define INF 0x3f3f3f3f

struct 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 Dinic{
    int n, m, s, t;
    vector edges;
    vector G[N];
    bool vis[N];
    int d[N], cur[N];

    void init(int n) {
        this->n = n;
        for (int i = 0; i <= n; i++) {
            G[i].clear();
        }
        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));
        int m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    } 

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

        while (!Q.empty()) {
            int u = Q.front();
            Q.pop();
            for (int i = 0; i < G[u].size(); i++) {
                Edge &e = edges[G[u][i]];
                if (!vis[e.to] && e.cap > e.flow) {
                    vis[e.to] = true;
                    d[e.to] = d[u] + 1;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }

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

        int flow = 0, f;
        for (int i = cur[x]; i < G[x].size(); i++) {
            Edge &e = edges[G[x][i]];
            if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0) {
                e.flow += f;
                edges[G[x][i] ^ 1].flow -= f;
                flow += f;
                a -= f;
                if (a == 0)
                    break;
            }
        }
        return flow;
    }

    int Maxflow(int s, int t) {
        this->s = s; this->t = t;
        int flow = 0;
        while (BFS()) {
            memset(cur, 0, sizeof(cur));
            flow += DFS(s, INF);
        }
        return flow;
    }
};

Dinic dinic;

//cow 1 -- 2 * n
//food 2 * n + 1 --- 2 * n + f
//drink 2 * n + f + 1 --- 2 * n + f + d
//start 0
//sink 2 * n + f + d + 1

int n, f, d;

void init() {
    int s = 0, t = 2 * n + d + f + 1;
    dinic.init(t);

    for (int i = 1; i <= f; i++) {
        dinic.AddEdge(0, 2 * n + i, 1);
    }

    for (int i = 1; i <= d; i++) {
        dinic.AddEdge(2 * n + f + i, t, 1);
    }

    int fi, di, x;
    for (int i = 1; i <= n; i++)  {
        scanf(%d%d, &fi, &di);
        dinic.AddEdge(i, n + i, 1);

        for (int j = 0; j < fi; j++) {
            scanf(%d, &x);
            dinic.AddEdge(2 * n + x, i, 1);
        }

        for (int j = 0; j < di; j++) {
            scanf(%d, &x);
            dinic.AddEdge(n + i, 2 * n + f + x, 1);
        }
    }
    int flow = dinic.Maxflow(s, t);

    printf(%d
, flow);
}

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

EK

#include 
#include 
#include 
#include 
#include 
using namespace std;
#define N 1010
#define INF 0x3f3f3f3f

struct 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 EK{
    vector G[N];
    vector edges;
    int s, t, n, m, p[N];
    bool vis[N];

    void init(int n) {
        this->n = n;
        for (int i = 0; i <= n; i++)
            G[i].clear();
        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() {
        queue q;
        memset(vis, 0, sizeof(vis));
        vis[s] = 1;
        q.push(s);

        while (!q.empty()) {
            int u = q.front();
            q.pop();

            for (int i = 0; i < G[u].size(); i++) {
                Edge &e = edges[G[u][i]];
                if (!vis[e.to] && e.cap > e.flow) {
                    vis[e.to] = true;
                    p[e.to] = G[u][i];
                    if (e.to == t)
                        return true;
                    q.push(e.to);
                }
            }
        }
        return false;
    }

    int Augment() {
        int flow = INF, u = t;
        while (u != s) {
            Edge &e = edges[p[u]];
            flow = min(flow, e.cap - e.flow);
            u = e.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;

        while (BFS()) {
            flow += Augment();
        }
        return flow;
    }
};

EK ek;

//cow 1 -- 2 * n
//food 2 * n + 1 --- 2 * n + f
//drink 2 * n + f + 1 --- 2 * n + f + d
//start 0
//sink 2 * n + f + d + 1

int n, f, d;

void init() {
    int s = 0, t = 2 * n + d + f + 1;
    ek.init(t);

    for (int i = 1; i <= f; i++) {
        ek.AddEdge(0, 2 * n + i, 1);
    }

    for (int i = 1; i <= d; i++) {
        ek.AddEdge(2 * n + f + i, t, 1);
    }

    int fi, di, x;
    for (int i = 1; i <= n; i++)  {
        scanf(%d%d, &fi, &di);
        ek.AddEdge(i, n + i, 1);

        for (int j = 0; j < fi; j++) {
            scanf(%d, &x);
            ek.AddEdge(2 * n + x, i, 1);
        }

        for (int j = 0; j < di; j++) {
            scanf(%d, &x);
            ek.AddEdge(n + i, 2 * n + f + x, 1);
        }
    }
    int flow = ek.Maxflow(s, t);

    printf(%d
, flow);
}

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