734. [网络流24题] 方格取数问题 二分图点权最大独立集/最小割/最大流

/* 
 * Problem: 线性规划与网络流24题 #9 方格取数问题
 * Author: Guo Jiabao
 * Time: 2009.6.27 19:06
 * State: Solved
 * Memo: 网络最大流 二分图点权最大独立集
*/
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
using namespace std;
const int MAXL=50,MAXN=50*50,MAXM=MAXN*8,INF=~0U>>1;
const int dx[]={0,0,-1,1},dy[]={-1,1,0,0};
struct edge
{
    edge *next,*op;
    int t,c;
}*V[MAXN],*P[MAXN],ES[MAXM],*Stae[MAXN];
int N,M,S,T,C,EC,Ans,Maxflow,Total;
int Lv[MAXN],Stap[MAXN],Map[MAXL][MAXL];
inline void addedge(int a,int b,int c)
{
    ES[++EC].next = V[a]; V[a]=ES+EC; V[a]->t=b; V[a]->c=c;
    ES[++EC].next = V[b]; V[b]=ES+EC; V[b]->t=a; V[b]->c=0;
    V[a]->op = V[b]; V[b]->op = V[a];
}
void init()
{
    int i,j,k,c;
    freopen("grid.in","r",stdin);
    freopen("grid.out","w",stdout);
    scanf("%d%d",&M,&N);
    S=0; T=N*M+1;
    for (i=1;i<=M;i++)
    {
        for (j=1;j<=N;j++)
        {
            scanf("%d",&c);
            Total += c;
            Map[i][j] = ++C;
            if ((i+j)%2==0)
                addedge(S,C,c);
            else
                addedge(C,T,c);
        }
    }
    for (i=1;i<=M;i++)
    {
        for (j=1;j<=N;j++)
        {
            if ((i+j)%2==0)
            {
                for (k=0;k<4;k++)
                {
                    int x=i+dx[k],y=j+dy[k];
                    if (x>=1 && x<=M && y>=1 && y<=N)
                        addedge(Map[i][j],Map[x][y],INF);
                }
            }
        }
    }
}
bool Dinic_Label()
{
    int head,tail,i,j;
    Stap[head=tail=0]=S;
    memset(Lv,-1,sizeof(Lv));
    Lv[S]=0;
    while (head<=tail)
    {
        i=Stap[head++];
        for (edge *e=V[i];e;e=e->next)
        {
            j=e->t;
            if (e->c && Lv[j]==-1)
            {
                Lv[j] = Lv[i]+1;
                if (j==T)
                    return true;
                Stap[++tail] = j;
            }
        }
    }
    return false;
}
void Dinic_Augment()
{
    int i,j,delta,Stop;
    for (i=S;i<=T;i++)
        P[i] = V[i];
    Stap[Stop=1]=S;
    while (Stop)
    {
        i=Stap[Stop];
        if (i!=T)
        {
            for (;P[i];P[i]=P[i]->next)
                if (P[i]->c && Lv[i] + 1 == Lv[j=P[i]->t])
                    break;
            if (P[i])
            {
                Stap[++Stop] = j;
                Stae[Stop] = P[i];
            }
            else
                Stop--,Lv[i]=-1;
        }
        else
        {
            delta = INF;
            for (i=Stop;i>=2;i--)
                if (Stae[i]->c < delta)
                    delta = Stae[i]->c;
            Maxflow += delta;
            for (i=Stop;i>=2;i--)
            {
                Stae[i]->c -= delta;
                Stae[i]->op->c += delta;
                if (Stae[i]->c==0)
                    Stop = i-1;
            }
        }
    }
}
void Dinic()
{
    while (Dinic_Label())
        Dinic_Augment();
}
int main()
{
    init();
    Dinic();
    Ans = Total - Maxflow;
    printf("%d\n",Ans);
    return 0;
}