codevs 1922 骑士共存问题 网络流

题目链接

给一个n*n的棋盘， 上面有障碍物， 有障碍物的不能放东西。然后往上面放马， 马不能互相攻击， 问最多可以放多少个马。

 

按x+y的奇偶来划分， 如果两个格子可以互相攻击， 就连一条权值为1的边。

 

#include <iostream>
#include <vector>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <complex>
#include <cmath>
#include <map>
#include <set>
#include <string>
#include <queue>
#include <stack>
#include <bitset>
using namespace std;
#define pb(x) push_back(x)
#define ll long long
#define mk(x, y) make_pair(x, y)
#define lson l, m, rt<<1
#define mem(a) memset(a, 0, sizeof(a))
#define rson m+1, r, rt<<1|1
#define mem1(a) memset(a, -1, sizeof(a))
#define mem2(a) memset(a, 0x3f, sizeof(a))
#define rep(i, n, a) for(int i = a; i<n; i++)
#define fi first
#define se second
typedef complex <double> cmx;
typedef pair<int, int> pll;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int mod = 1e9+7;
const int inf = 1061109567;
const int dir[][2] = { {-1, 2}, {-1, -2}, {1, 2}, {1, -2}, {2, -1}, {2, 1}, {-2, -1}, {-2, 1} };
const int maxn = 2e5;
int n, a[205][201];
int q[maxn*2], head[50004], dis[50004], s, t, num, m;
struct node
{
    int to, nextt, c;
    node(){}
    node(int to, int nextt, int c):to(to), nextt(nextt), c(c){}
}e[maxn*2];
void init() {
    num = 0;
    mem1(head);
}
void add(int u, int v, int c) {
    e[num] = node(v, head[u], c); head[u] = num++;
    e[num] = node(u, head[v], 0); head[v] = num++;
}
int bfs() {
    mem(dis);
    dis[s] = 1;
    int st = 0, ed = 0;
    q[ed++] = s;
    while(st<ed) {
        int u = q[st++];
        for(int i = head[u]; ~i; i = e[i].nextt) {
            int v = e[i].to;
            if(!dis[v]&&e[i].c) {
                dis[v] = dis[u]+1;
                if(v == t)
                    return 1;
                q[ed++] = v;
            }
        }
    }
    return 0;
}
int dfs(int u, int limit) {
    if(u == t) {
        return limit;
    }
    int cost = 0;
    for(int i = head[u]; ~i; i = e[i].nextt) {
        int v = e[i].to;
        if(e[i].c&&dis[v] == dis[u]+1) {
            int tmp = dfs(v, min(limit-cost, e[i].c));
            if(tmp>0) {
                e[i].c -= tmp;
                e[i^1].c += tmp;
                cost += tmp;
                if(cost == limit)
                    break;
            } else {
                dis[v] = -1;
            }
        }
    }
    return cost;
}
int dinic() {
    int ans = 0;
    while(bfs()) {
        ans += dfs(s, inf);
    }
    return ans;
}
int check(int x, int y)
{
    if(x >= 0 && y >= 0 && x < n && y < n && !a[x][y])
        return 1;
    return 0;
}
void solve()
{
    init();
    s = n*n, t = s+1;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            if(a[i][j])
                continue;
            if((i+j)%2) {
                add(s, i*n+j, 1);
                for(int k = 0; k < 8; k++) {
                    int x = i+dir[k][0];
                    int y = j+dir[k][1];
                    if(check(x, y)) {
                        add(i*n+j, x*n+y, 1);
                    }
                }
            } else {
                add(i*n+j, t, 1);
            }
        }
    }
    int ans = n*n-dinic()-m;
    cout<<ans<<endl;
}
int main()
{
    int x, y;
    while(~scanf("%d%d", &n, &m)) {
        mem(a);
        for(int i = 0; i < m; i++) {
            scanf("%d%d", &x, &y);
            x--;
            y--;
            a[x][y] = 1;
        }
        solve();
    }
    return 0;
}