poj 1087.A Plug for UNIX （最大流）

网络流，关键在建图

建图思路在代码里

/*

      最大流SAP

      邻接表

      思路：基本源于FF方法，给每个顶点设定层次标号，和允许弧。

      优化:

      1、当前弧优化（重要）。

      1、每找到以条增广路回退到断点（常数优化）。

      2、层次出现断层，无法得到新流（重要）。

      时间复杂度（m*n^2）

*/

#include <iostream>

#include <cstdio>

#include <cstring>

#include <map>

#define ms(a,b) memset(a,b,sizeof a)

using namespace std;

const int INF = 500;

struct node {

    int v, c, next;

} edge[INF*INF * 4];

int  pHead[INF*INF], SS, ST, nCnt;

void addEdge (int u, int v, int c) {

    edge[++nCnt].v = v; edge[nCnt].c = c, edge[nCnt].next = pHead[u]; pHead[u] = nCnt;

    edge[++nCnt].v = u; edge[nCnt].c = 0, edge[nCnt].next = pHead[v]; pHead[v] = nCnt;

}

int SAP (int pStart, int pEnd, int N) {

    int numh[INF], h[INF], curEdge[INF], pre[INF];

    int cur_flow, flow_ans = 0, u, neck, i, tmp;

    ms (h, 0); ms (numh, 0); ms (pre, -1);

    for (i = 0; i <= N; i++) curEdge[i] = pHead[i];

    numh[0] = N;

    u = pStart;

    while (h[pStart] <= N) {

        if (u == pEnd) {

            cur_flow = 1e9;

            for (i = pStart; i != pEnd; i = edge[curEdge[i]].v)

                if (cur_flow > edge[curEdge[i]].c) neck = i, cur_flow = edge[curEdge[i]].c;

            for (i = pStart; i != pEnd; i = edge[curEdge[i]].v) {

                tmp = curEdge[i];

                edge[tmp].c -= cur_flow, edge[tmp ^ 1].c += cur_flow;

            }

            flow_ans += cur_flow;

            u = neck;

        }

        for ( i = curEdge[u]; i != 0; i = edge[i].next)

            if (edge[i].c && h[u] == h[edge[i].v] + 1)     break;

        if (i != 0) {

            curEdge[u] = i, pre[edge[i].v] = u;

            u = edge[i].v;

        }

        else {

            if (0 == --numh[h[u]]) continue;

            curEdge[u] = pHead[u];

            for (tmp = N, i = pHead[u]; i != 0; i = edge[i].next)

                if (edge[i].c)  tmp = min (tmp, h[edge[i].v]);

            h[u] = tmp + 1;

            ++numh[h[u]];

            if (u != pStart) u = pre[u];

        }

    }

    return flow_ans;

}

/*

       poj1087 最大流

       建图：

       每个种插座和为一个节点，添加源点和汇点

       源点到每个存在的插座连一条容量为插座数量的边

       统计需要每种插座的数量，作为插座到汇点边的容量

       如果有转换器A->B,AB连接一条容量无限的边

*/

int k, m, n, tol;

int sum[INF], need[INF];

map<string, int> mat;

string s,ss;

int main() {

    /*

           前向星存边，表头在pHead[],初始化nCnt=1

           SS,ST分别为源点和汇点

    */

    nCnt = 1;

    cin >> n;

    for (int i = 1; i <= n; i++) {

        cin >> s;

        if (mat.find (s) == mat.end() ) mat[s] = ++tol;

        sum[tol]++;

    }

    cin >> m;

    for (int i = 1; i <= m; i++) {

        cin >> ss >> s;

        if (mat.find (s) == mat.end() ) mat[s] = ++tol;

        need[mat[s]]++;

    }

    cin>>k;

    for (int i=1;i<=k;i++){

           cin>>ss>>s;

           if (mat.find (s) == mat.end() ) mat[s] = ++tol;

           if (mat.find (ss) == mat.end() ) mat[ss] = ++tol;

              int u=mat[s],v=mat[ss];

              addEdge(u,v,100);

    }

    SS=tol+1,ST=tol+2;

    for(int i=1;i<=tol;i++){

              addEdge(SS,i,sum[i]);

              addEdge(i,ST,need[i]);

    }

    int ans=SAP(SS,ST,ST);

    cout<<m-ans<<endl;

       return 0;

}

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