hdu1565方格取数(1) (最大权独立集)

这个就是一个求最大权独立集，以为这个图是一个二分图，所以可以转换成求对偶问题，也就是最小割。

那么answer ＝ ∑val[i][j] - 最小割。

/*****************************************
Author      :Crazy_AC(JamesQi)
Time        :2016
File Name   :
*****************************************/
// #pragma comment(linker, "/STACK:1024000000,1024000000")
#include <iostream>
#include <algorithm>
#include <iomanip>
#include <sstream>
#include <string>
#include <stack>
#include <queue>
#include <deque>
#include <vector>
#include <map>
#include <set>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <climits>
using namespace std;
#define MEM(x,y) memset(x, y,sizeof x)
#define pk push_back
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> ii;
typedef pair<ii,int> iii;
const double eps = 1e-10;
const int inf = 1 << 30;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
int n;
int val[21][21];
int dis[21*21];
struct Edge {
    int from, to, cap, flow, nxt;
    Edge(){}
    Edge(int from, int to,int cap, int flow,int nxt) : 
        from(from), to(to),cap(cap), flow(flow), nxt(nxt) {}
}edges[10010];
int head[21*21];
int ecnt;
int dx[] = {-1, 0, 1, 0};
int dy[] = {0, -1, 0, 1};
int s, t;
bool spfa(int s,int t) {
    queue<int> que;
    memset(dis, -1,sizeof dis);
    dis[s] = 0;
    que.push(s);
    while(!que.empty()) {
        int u = que.front();
        que.pop();
        for (int i = head[u];~i;i = edges[i].nxt) {
            Edge& e = edges[i];
            if (e.cap > e.flow && dis[e.to] == -1) {
                dis[e.to] = dis[u] + 1;
                que.push(e.to);
            }
        }
    }
    return dis[t] != -1;
}
int dfs(int u,int a) {
    if (u == t || a == 0) return a;
    int flow = 0, f;
    for (int i = head[u];~i;i = edges[i].nxt) {
        Edge& e = edges[i];
        if (dis[e.to] == dis[u] + 1 && (f = dfs(e.to, min(a, e.cap - e.flow))) > 0) {
            flow += f;
            a -= f;
            e.flow += f;
            edges[i^1].flow -= f;
            if (a <= 0) break;
        }
    }
    if (flow == 0) dis[u] = 0;
    return flow;
}
int dinic(int s,int t) {
    int ret = 0;
    while(spfa(s, t)) {
        ret += dfs(s, INF);
    }
    return ret;
}
int main()
{    
    // freopen("in.txt","r",stdin);
    // freopen("out.txt","w",stdout);
    while(~scanf("%d",&n)) {
        int sum = 0;
        for (int i = 1;i <= n;++i) 
            for (int j = 1;j <= n;++j) {
                scanf("%d",&val[i][j]);
                sum += val[i][j];
            }
        memset(head, -1,sizeof head);
        ecnt = 0;
        s = 0,t = n*n + 1;
        for (int i = 1;i <= n;++i) {
            for (int j = 1;j <= n;++j) {
                if (val[i][j] >= 0) {
                    int u = (i-1)*n+j;
                    // printf("u = %d: ", u);
                    edges[ecnt] = Edge(s, u, val[i][j], 0, head[s]), head[s] = ecnt++;
                    edges[ecnt] = Edge(u, s, 0, 0, head[u]), head[u] = ecnt++;
                    // val[i][j] = -1;//
                    for (int k = 0;k < 4;++k) {
                        int nx = i + dx[k];
                        int ny = j + dy[k];
                        if (nx < 1 || nx > n || ny < 1 || ny > n) continue;
                            // printf("%d ", v);
                            int v = (nx - 1)*n+ny;
                            // printf("%d ", v);
                            edges[ecnt] = Edge(v, t, val[nx][ny], 0,head[v]), head[v] = ecnt++;
                            edges[ecnt] = Edge(t, v, 0, 0, head[t]), head[t] = ecnt++;

                            edges[ecnt] = Edge(u, v, INF, 0,head[u]), head[u] = ecnt++;
                            edges[ecnt] = Edge(v, u, 0, 0, head[v]), head[v] = ecnt++;
                            val[nx][ny] = -1;//
                    }
                    // printf("\n");
                }
            }
        }
        int ans = sum - dinic(s, t);
        // cout << sum << endl;
        cout << ans << endl;
    }
    return 0;
}