poj 2987 Firing ------最大权闭合图

网络流里的最大权闭合图和最大密度子图还是挺有意思的

方法：s连接正权点，点权赋给边，t连接负权点，点权的绝对值赋给边，原图两点之间的边用inf64正向容量连接，逆向为0.

这样就能把每一个最小割和每一个闭合图一一对应，利用最小割的性质很好证明。然后求出最小割，用所有正权和减去得到最大获利。因为最小割把图分成了两部分，所以最后求最小人数可以用一个贪心，方法是从s出发广度优先搜索，能达到的节点都是需要开除的，这样就能统计出最大获利时的最小人数！

#include<iostream>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<cmath>
#include<cassert>
#include<cstring>
#include<iomanip>
using namespace std;

#ifdef _WIN32
#define i64 __int64
#define out64 "%I64d\n"
#define in64 "%I64d"
#else
#define i64 long long
#define out64 "%lld\n"
#define in64 "%lld"
#endif

#define FOR(i,a,b)      for( int i = (a) ; i <= (b) ; i ++)
#define FF(i,a)         for( int i = 0 ; i < (a) ; i ++)
#define FFD(i,a)        for( int i = (a)-1 ; i >= 0 ; i --)
#define S64(a)          scanf(in64,&a)
#define SS(a)           scanf("%d",&a)
#define LL(a)           ((a)<<1)
#define RR(a)           (((a)<<1)+1)
#define SZ(a)           ((int)a.size())
#define PP(n,m,a)		puts("---");FF(i,n){FF(j,m)cout << a[i][j] << ' ';puts("");}
#define pb              push_back
#define CL(Q)           while(!Q.empty())Q.pop()
#define MM(name,what)   memset(name,what,sizeof(name))
#define read            freopen("in.txt","r",stdin)
#define write           freopen("out.txt","w",stdout)

const int inf = 0x3f3f3f3f;
const i64 inf64 = 0x3f3f3f3f3f3f3f3fLL;
const double oo = 10e9;
const double eps = 10e-8;
const double pi = acos(-1.0);
const int maxn=5011;
const int end=5001;

struct zz
{
    int from;
    int to;
    i64 c;
    int id;
}zx,tz;

int n,m,tx,ty;
i64 pro,total;
int cost[maxn];
vector<zz>g[maxn];
queue<int>q;
int cen[maxn];
bool vis[maxn];

bool bfs()
{
    CL(q);
    MM(cen,-1); 
    q.push(0);
    cen[0] = 0;
    int now,to;
    while(!q.empty())
    {
        now = q.front();
        q.pop();
        FF(i,g[now].size())
        {
            to = g[now][i].to;
            if(cen[to] == -1 && g[now][i].c > 0)
            {
                cen[to] = cen[now] + 1;
                q.push(to);
            }
        } 
    }
    return cen[end] != -1;         
}

i64 dfs(i64 flow = inf , int now = 0 )
{
    if(now == end)
    {
        return flow;
    }                   
    i64 temp,sum=0;
    int to;
    FF(i,g[now].size())
    {
        to = g[now][i].to;
        if (g[now][i].c > 0 && flow > sum && cen[to] == cen[now] + 1 ) 
        {
            temp = dfs ( min ( flow - sum , g[now][i].c ) , to );
            sum += temp;    
            g[now][i].c -= temp;
            g[to][g[now][i].id].c += temp;           
        }
    }                                            
    if(!sum) cen[now] = -1;
    return sum;
}

void dinic()
{
    i64 ans = 0;
    while(bfs())
    {
        ans += dfs();
    }
    pro = total - ans;  
    return ;
}

void bfs2()
{
    int ans = 0;
    CL(q);  
    MM(vis,false);
    vis[0] = true;
    q.push(0);
    int now,to;
    while(!q.empty())
    {
        now = q.front();
        q.pop();
        FF(i,g[now].size())
        {
            to = g[now][i].to;
            if(g[now][i].c > 0 && !vis[to] )
            {
                vis[to] = true; 
                ans++;
                q.push(to);
                
            }
        }     
    }
    cout<<ans<<" ";
    return ;
}
           
int main()
{
    total = 0; 
    cin>>n>>m;
    FOR(i,1,n)
    {
        SS(cost[i]);
        if(cost[i] > 0)
        {
            total += cost[i];
        }
    }    
    FOR(i,1,m)
    {
        SS(tx);
        SS(ty);
        zx.from = tx;
        zx.to = ty;
        zx.c = inf64;
        zx.id = g[ty].size();
        g[tx].pb(zx);
        swap(zx.from,zx.to);    
        zx.c = 0;
        zx.id = g[tx].size() - 1; 
        g[zx.from].pb(zx);
    }
    FOR(i,1,n)
    {
        if(cost[i]>0)
        {
            zx.from = 0;
            zx.to = i; 
            zx.c = cost[i];
            zx.id = g[i].size();
            g[0].pb(zx);
            swap(zx.from,zx.to);
            zx.c = 0;
            zx.id = g[0].size()-1;  
            g[i].pb(zx);         
        }    
        else if(cost[i]<0)
        {
            zx.from = i;
            zx.to = end;
            zx.c = -cost[i]; 
            zx.id = g[end].size();
            g[i].pb(zx);    
            swap(zx.from,zx.to);
            zx.c = 0;
            zx.id = g[i].size() - 1;
            g[end].pb(zx);
        }  
    }
    dinic();
    bfs2();  
    cout<<pro<<endl;
    return 0;   
}