POJ 3308 最少点集覆盖

Posted 2020-09-28 树的种子

题意：和Uva 11419 类似。

首先最少点集覆盖 = 最大匹配。

我们可以在 S 和行 的边 不是1，有了权值，但是题意要求的是乘积最小，那么可以用 log(a*b) = loga + logb 转换，那么权值就是logr ,logc;

最大匹配 = 最大流（最大流一定经过最小割，最小割=最大流）。那么题目就转换为求最大流了。

 

但是，这个题目很流氓，vector的邻接表超时，数组模拟的G++ WA,C++ AC.

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
#include <cmath>

using namespace std;

/*
const double inf = 1000000.0;
const int maxn = 100;
int dblcmp(double d) {
    if(fabs(d)<1e-5)
        return 1;
    return 0;
}

struct Edge {
    int from,to;
    double cap,flow;
};

struct Dinic
{
    int n,m,s,t;
    vector<Edge> edge;
    vector<int> G[maxn];
    bool vis[maxn];
    int d[maxn];
    int cur[maxn];

    void init()
    {
        for(int i=0;i<maxn;i++)
            G[i].clear();
        edge.clear();
        memset(d,0,sizeof(d));
        memset(vis,0,sizeof(vis));
        memset(cur,0,sizeof(cur));
    }

    void AddEdge (int from,int to,double cap)
    {
        edge.push_back((Edge){from,to,cap,0});
        edge.push_back((Edge){to,from,0,0});
        m = edge.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);
        d[s] = 0;
        vis[s] = 1;
        while(!Q.empty())
        {
            int x = Q.front();
            Q.pop();
            for(int i=0; i<G[x].size(); i++)
            {
                Edge & e = edge[G[x][i]];
                if(!vis[e.to]&&e.cap>e.flow)
                {
                    vis[e.to] = 1;
                    d[e.to] = d[x] + 1;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }

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

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

}sol;
*/

const int N = 105;
const double inf = 1000000.0;

struct Edge{
    int s,e,next;
    double v;
}edge[15*N];

int n,e_num,head[N],d[N],sp,tp;

void AddEdge(int a,int b,double c){
    edge[e_num].s=a; edge[e_num].e=b; edge[e_num].v=c;
    edge[e_num].next=head[a]; head[a]=e_num++;

    edge[e_num].s=b; edge[e_num].e=a; edge[e_num].v=0.0;
    edge[e_num].next=head[b]; head[b]=e_num++;
}

int bfs(){
    queue <int> q;
    memset(d,-1,sizeof(d));
    d[sp]=0;
    q.push(sp);
    while(!q.empty()){
        int cur=q.front();
        q.pop();
        for(int i=head[cur];i!=-1;i=edge[i].next){
            int u=edge[i].e;
            if(d[u]==-1 && edge[i].v>0){//没有标记,且可行流大于0
                d[u]=d[cur]+1;
                q.push(u);
            }
        }
    }
    return d[tp] != -1;//汇点是否成功标号,也就是说是否找到增广路
}

double dfs(int a,double b){//a为起点
    double r=0;
    if(a==tp)return b;
    for(int i=head[a];i!=-1 && r<b;i=edge[i].next){
        int u=edge[i].e;
        if(edge[i].v>0 && d[u]==d[a]+1){
            double x=min(edge[i].v,b-r);
            x=dfs(u,x);
            r+=x;
            edge[i].v-=x;
            edge[i^1].v+=x;
        }
    }
    if(!r)d[a]=-2;
    return r;
}

double dinic(int sp,int tp){
    double total=0.0,t;
    while(bfs()){
        while(t=dfs(sp,inf))
        total+=t;
    }
    return total;
}

int main()
{
    int t;
    scanf("%d",&t);
    int i,m,l,a,b;
    double row[N],col[N];
    while(t--) {

        /*
        //sol.init();
        int m,n,l;
        scanf("%d%d%d",&m,&n,&l);
        sp = 0,tp=m+n+1;
        e_num=0;
        memset(head,-1,sizeof(head));
        for(int i=1;i<=m;i++) {
            double r;
            scanf("%lf",&r);
            //sol.AddEdge(s,i,log(r));
            AddEdge(sp,i,log(r));
        }

        for(int i=1;i<=n;i++) {
            double c;
            scanf("%lf",&c);
            //sol.AddEdge(i+m,t,log(c));
            AddEdge(i+m,tp,log(c));
        }

        for(int i=0;i<l;i++) {
            int u,v;
            scanf("%d%d",&u,&v);
            v+=m;
            //sol.AddEdge(u,v,inf);
            AddEdge(u,v,inf);
        }

        //double ans = sol.Maxflow(s,t);
        double ans = dinic(sp,tp);
        printf("%.4lf\n",exp(ans));
        */

        scanf("%d%d%d",&n,&m,&l);
        for(i=1;i<=n;i++)
            scanf("%lf",&row[i]);
        for(i=1;i<=m;i++)
            scanf("%lf",&col[i]);

        e_num=0;
        memset(head,-1,sizeof(head));
        sp=0; tp=n+m+1;
        for(i=1;i<=n;i++)
            AddEdge(sp,i,log(row[i]));
        for(i=1;i<=m;i++)
            AddEdge(n+i,tp,log(col[i]));
        for(i=1;i<=l;i++){
            scanf("%d%d",&a,&b);
            AddEdge(a,n+b,inf);
        }

        printf("%.4lf\n",exp(dinic(sp,tp)));

    }

    return 0;
}

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