HDU1565 方格取数(1) 网络流

//将问题转化为最小割，首先采用奇偶建立二分图，
//最大点独立集=总权-最小点权覆盖集
//二分图最小点权覆盖:从x或y中选取一些点,使这些点覆盖所有的边，
//并且选出来的点权值和最小
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cmath>
#include <ctime>
#include <vector>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 0x3f3f3f3f
#define inf -0x3f3f3f3f
#define lson k<<1, L, mid
#define rson k<<1|1, mid+1, R
#define mem0(a) memset(a,0,sizeof(a))
#define mem1(a) memset(a,-1,sizeof(a))
#define mem(a, b) memset(a, b, sizeof(a))
typedef long long ll;
const int maxn=1000 + 10;

struct Edge{
    int from,to,cap,flow;
    Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}
};


struct Dinic{
    int n,m,s,t;                        //结点数,边数（包括反相弧），源点编号和汇点编号
    vector<Edge>edges;                  //边表，edges[e]和edges[e^1]互为反相弧
    vector<int>G[maxn];                 //邻接表，G[i][j]表示结点i的第j条边在e数组中的序号
    bool vis[maxn];                     //BFS使用
    int d[maxn];                        //从起点到i的距离
    int cur[maxn];                      //当前弧下标
    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);
    }

    void init(int n){
        this->n=n;
        for(int i=0;i<=n;i++)
            G[i].clear();
        edges.clear();
    }

    bool BFS(){
        mem0(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++){                 //只考虑残量网络中的弧
                Edge& e=edges[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];
    }

    ll DFS(int x,int a){
        if(x==t||a==0)
            return a;
        ll 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;
    }

    ll Maxflow(int s,int t){
        this->s=s;
        this->t=t;
        ll flow=0;
        while(BFS()){
            mem0(cur);
            flow+=DFS(s,INF);
        }
        return flow;
    }
};
Dinic solve;
int mp[21][21];

int main(){
    int x,y,z;
    int n,m;
    while(scanf("%d",&n)!=EOF){
        solve.init(n*n+1);                      //初始化不要错误
        int sum=0;
        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++){
                scanf("%d",&mp[i][j]);
                if((i+j)%2==0){
                    solve.AddEdge(0,(i-1)*n+j,mp[i][j]);
                }
                else
                    solve.AddEdge((i-1)*n+j,n*n+1,mp[i][j]);
                sum+=mp[i][j];
            }
        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++){
                if((i+j)%2==0){
                    if(i-1>=1){
                        solve.AddEdge((i-1)*n+j,(i-2)*n+j,INF);
                    }
                    if(i+1<=n){
                        solve.AddEdge((i-1)*n+j,i*n+j,INF);
                    }
                    if(j-1>=1){
                        solve.AddEdge((i-1)*n+j,(i-1)*n+j-1,INF);
                    }
                    if(j+1<=n)
                        solve.AddEdge((i-1)*n+j,(i-1)*n+j+1,INF);
                }
            }
        ll tmp=solve.Maxflow(0,n*n+1);
        printf("%d\n",sum-tmp);
    }
    return 0;
}