卧薪尝胆,厚积薄发。
Date: Fri Aug 24 17:03:33 CST 2018 In Category: NoCategory

Description:

询问在一个棋盘上最多能放多少互不攻击的马,有些位置不能放。
$1\le n,m \le 200$

Solution:

黑白染色,那么马能攻击到的位置一定和当前颜色不同,连边后一条边的两端点不能同时选,求二分图最大独立集即可。

Code:


#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<cstring>
using namespace std;
int n,m;
#define MAXN 210
int p[MAXN][MAXN];
int mx[8] = {-1,-2,-2,-1,1,2,2,1};
int my[8] = {-2,-1,1,2,2,1,-1,-2};
int to(int i,int j){return (i - 1) * m + j;}
struct edge
{
int to,nxt;
}e[MAXN * MAXN * 8];
int edgenum = 0;
int lin[MAXN * MAXN] = {0};
void add(int a,int b)
{
++edgenum;e[edgenum].to = b;e[edgenum].nxt = lin[a];lin[a] = edgenum;
return;
}
bool v[MAXN * MAXN];
int match[MAXN * MAXN];
bool dfs(int k)
{
for(int i = lin[k];i != 0;i = e[i].nxt)
{
if(!v[e[i].to])
{
v[e[i].to] = true;
if(match[e[i].to] == -1 || dfs(match[e[i].to]))
{
match[e[i].to] = k;
return true;
}
}
}
return false;
}
int main()
{
scanf("%d%d",&n,&m);
int tot = 0;
for(int i = 1;i <= n;++i)
{
for(int j = 1;j <= m;++j)
{
scanf("%d",&p[i][j]);
if(p[i][j] == 0)++tot;
}
}
for(int i = 1;i <= n;++i)
{
for(int j = 1;j <= m;++j)
{
if(p[i][j] == 1)continue;
if((i + j) % 2 == 0)continue;
for(int k = 0;k < 8;++k)
{
int ni = i + mx[k],nj = j + my[k];
if(ni <= n && ni >= 1 && nj <= m && nj >= 1 && p[ni][nj] == 0)
{
add(to(i,j),to(ni,nj));
}
}
}
}
int ans = 0;
memset(match,-1,sizeof(match));
for(int i = 1;i <= n;++i)
{
for(int j = 1;j <= m;++j)
{
if(p[i][j] == 1 || (i + j) % 2 == 0)continue;
memset(v,0,sizeof(v));
if(dfs(to(i,j)))++ans;
}
}
cout << tot - ans << endl;
return 0;
}
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