POJ - 3436 ACM Computer Factory （ISAP EK Dinic）

题目大意：有N台机器，每台机器能处理相应型态的电脑，处理完后，电脑将变成另一种形态。
每台机器有相应的工作限度，每次至多处理K台
现在问，在一次流水线生产中，最多可以产生多少台完整的电脑（流水线指的是在每一台机器的工作限度下）

解题思路：题目比较难理解，理解题目的话，就比较好做了
首先，将每台机器的点拆成两个点，权值为工作限度
如果机器能处理的电脑的状态全是0的话，就将其和超级源点连接，表示该机器进行第一步加工
如果机器处理完后的形态与另一台机器能处理的最初形态相同，就将其连线，表示下一台机器可以将其处理完的电脑再进一步加工
如果机器处理完后形态都为1，表示完工，将其和超级汇点相连，接着跑最大流

ISAP

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
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) {}
};
int g[70][70];

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));
        int 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 - 1 ;
                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;

#define M 70
#define P 20
int in[M][P], out[M][P], f[M];
int n, m;

bool NullJudge(int cur) {
    for (int i = 1; i <= n; i++)
        if (in[cur][i] == 1)
            return false;
    return true;
}

bool FullJudge(int cur) {
    for (int i = 1; i <= n; i++)
        if (!out[cur][i])
            return false;
    return true;
}

bool connect(int x, int y) {
    for (int i = 1; i <= n; i++)
        if (out[x][i] + in[y][i] == 1)
            return false;
    return true;
}

void init() {

    for (int i = 1; i <= m; i++) {
        scanf("%d", &f[i]);

        for (int j = 1; j <= n; j++)
            scanf("%d", &in[i][j]);

        for (int j = 1; j <= n; j++)
            scanf("%d", &out[i][j]);
    }
    int s = 2 * m + 1;
    int t = 2 * m + 2;
    isap.init(t);

    for (int i = 1; i <= m; i++) {
        isap.AddEdge(i, i + m, f[i]);
        if (NullJudge(i))
            isap.AddEdge(s, i, f[i]);
        if (FullJudge(i))
            isap.AddEdge(i + m, t, f[i]);

        for (int j = 1; j <= m; j++) 
            if (i != j && connect(i, j))
                isap.AddEdge(i + m, j, f[i]);
    }

    int ans[M][P];
    int flow = isap.Maxflow(s, t);
    int cnt = 0;
    for (int i = m + 1; i <= m + m; i++)
        for (int j = 0; j < isap.G[i].size(); j++) {
            int v = isap.G[i][j];
            Edge &e = isap.edges[v];

            if (e.flow > 0 && e.to <= m) {
                ans[cnt][0] = i - m;
                ans[cnt][1] = e.to;
                ans[cnt][2] = e.flow;
                cnt++;
            }
        }

    printf("%d %d\n", flow, cnt);
    for (int i = 0; i < cnt; i++)
        printf("%d %d %d\n", ans[i][0], ans[i][1], ans[i][2]);
}

int main() {
    while (scanf("%d%d", &n, &m) == 2) {
        init();
    }
    return 0;
}

EK

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
#include <vector>
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<int> G[N];
    vector<Edge> 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<int> 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;

#define M 70
#define P 20
int in[M][P], out[M][P], f[M];
int n, m;

bool NullJudge(int cur) {
    for (int i = 1; i <= n; i++)
        if (in[cur][i] == 1)
            return false;
    return true;
}

bool FullJudge(int cur) {
    for (int i = 1; i <= n; i++)
        if (!out[cur][i])
            return false;
    return true;
}

bool connect(int x, int y) {
    for (int i = 1; i <= n; i++)
        if (out[x][i] + in[y][i] == 1)
            return false;
    return true;
}

void init() {

    for (int i = 1; i <= m; i++) {
        scanf("%d", &f[i]);

        for (int j = 1; j <= n; j++)
            scanf("%d", &in[i][j]);

        for (int j = 1; j <= n; j++)
            scanf("%d", &out[i][j]);
    }
    int s = 2 * m + 1;
    int t = 2 * m + 2;
    ek.init(t);

    for (int i = 1; i <= m; i++) {
        ek.AddEdge(i, i + m, f[i]);
        if (NullJudge(i))
            ek.AddEdge(s, i, f[i]);
        if (FullJudge(i))
            ek.AddEdge(i + m, t, f[i]);

        for (int j = 1; j <= m; j++) 
            if (i != j && connect(i, j))
                ek.AddEdge(i + m, j, f[i]);
    }

    int ans[M][P];
    int flow = ek.Maxflow(s, t);
    int cnt = 0;
    for (int i = m + 1; i <= m + m; i++)
        for (int j = 0; j < ek.G[i].size(); j++) {
            int v = ek.G[i][j];
            Edge &e = ek.edges[v];

            if (e.flow > 0 && e.to <= m) {
                ans[cnt][0] = i - m;
                ans[cnt][1] = e.to;
                ans[cnt][2] = e.flow;
                cnt++;
            }
        }

    printf("%d %d\n", flow, cnt);
    for (int i = 0; i < cnt; i++)
        printf("%d %d %d\n", ans[i][0], ans[i][1], ans[i][2]);
}

int main() {
    while (scanf("%d%d", &n, &m) == 2) {
        init();
    }
    return 0;
}

Dinic

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
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<Edge> edges;
    vector<int> 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<int> 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;



#define M 70
#define P 20
int in[M][P], out[M][P], f[M];
int n, m;

bool NullJudge(int cur) {
    for (int i = 1; i <= n; i++)
        if (in[cur][i] == 1)
            return false;
    return true;
}

bool FullJudge(int cur) {
    for (int i = 1; i <= n; i++)
        if (!out[cur][i])
            return false;
    return true;
}

bool connect(int x, int y) {
    for (int i = 1; i <= n; i++)
        if (out[x][i] + in[y][i] == 1)
            return false;
    return true;
}

void init() {

    for (int i = 1; i <= m; i++) {
        scanf("%d", &f[i]);

        for (int j = 1; j <= n; j++)
            scanf("%d", &in[i][j]);

        for (int j = 1; j <= n; j++)
            scanf("%d", &out[i][j]);
    }
    int s = 2 * m + 1;
    int t = 2 * m + 2;
    dinic.init(t);

    for (int i = 1; i <= m; i++) {
        dinic.AddEdge(i, i + m, f[i]);
        if (NullJudge(i))
            dinic.AddEdge(s, i, f[i]);
        if (FullJudge(i))
            dinic.AddEdge(i + m, t, f[i]);

        for (int j = 1; j <= m; j++) 
            if (i != j && connect(i, j))
                dinic.AddEdge(i + m, j, f[i]);
    }

    int ans[M][P];
    int flow = dinic.Maxflow(s, t);
    int cnt = 0;
    for (int i = m + 1; i <= m + m; i++)
        for (int j = 0; j < dinic.G[i].size(); j++) {
            int v = dinic.G[i][j];
            Edge &e = dinic.edges[v];

            if (e.flow > 0 && e.to <= m) {
                ans[cnt][0] = i - m;
                ans[cnt][1] = e.to;
                ans[cnt][2] = e.flow;
                cnt++;
            }
        }

    printf("%d %d\n", flow, cnt);
    for (int i = 0; i < cnt; i++)
        printf("%d %d %d\n", ans[i][0], ans[i][1], ans[i][2]);
}

int main() {
    while (scanf("%d%d", &n, &m) == 2) {
        init();
    }
    return 0;
}