#6226. 「网络流 24 题」骑士共存问题

/*加了当前弧优化和读入优化，快了不少
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#define maxn 40010
#define INF 1000000000
int n,m,head[maxn],dis[maxn],num=1,S,T,cur[maxn];
bool vis[maxn],mark[maxn];
struct node{int to,pre,v;}e[maxn*50];
using namespace std;
int count(int x,int y){return n*(x-1)+y;}
void Insert(int from,int to,int v){e[++num].to=to;e[num].v=v;e[num].pre=head[from];head[from]=num;e[++num].to=from;e[num].v=0;e[num].pre=head[to];head[to]=num;
}
bool bfs(){for(int i=S;i<=T;i++)dis[i]=-1,cur[i]=head[i];queue<int>q;q.push(S);dis[S]=0;while(!q.empty()){int now=q.front();q.pop();for(int i=head[now];i;i=e[i].pre){int to=e[i].to;if(e[i].v>0&&dis[to]==-1){dis[to]=dis[now]+1;if(to==T)return 1;q.push(to);}}}return dis[T]!=-1;
}
int dinic(int x,int flow){if(x==T||flow==0){return flow;}int rest=flow;for(int &i=cur[x];i;i=e[i].pre){int to=e[i].to;if(dis[to]==dis[x]+1&&e[i].v>0){int delta=dinic(to,min(rest,e[i].v));e[i].v-=delta;e[i^1].v+=delta;rest-=delta;}}return flow-=rest;
}
bool check(int x,int y){if(x<=n&&x>=1&&y<=n&&y>=1&&!mark[count(x,y)])return 1;return 0;
}
int qread(){int i=0,j=1;char ch=getchar();while(ch<'0'||ch>'9'){if(ch=='-')j=-1;ch=getchar();}while(ch<='9'&&ch>='0'){i=i*10+ch-'0';ch=getchar();}return i*j;
}
int main(){n=qread();m=qread();S=0,T=n*n+1;int x,y;for(int i=1;i<=m;i++){x=qread();y=qread();mark[count(x,y)]=1;}for(int i=1;i<=n;i++){for(int j=1;j<=n;j++){if(mark[count(i,j)])continue;if((i+j)&1){Insert(S,count(i,j),1);if(check(i-1,j-2))Insert(count(i,j),count(i-1,j-2),1);if(check(i-1,j+2))Insert(count(i,j),count(i-1,j+2),1);if(check(i+1,j-2))Insert(count(i,j),count(i+1,j-2),1);if(check(i+1,j+2))Insert(count(i,j),count(i+1,j+2),1);if(check(i-2,j-1))Insert(count(i,j),count(i-2,j-1),1);if(check(i-2,j+1))Insert(count(i,j),count(i-2,j+1),1);if(check(i+2,j-1))Insert(count(i,j),count(i+2,j-1),1);if(check(i+2,j+1))Insert(count(i,j),count(i+2,j+1),1);}else Insert(count(i,j),T,1);}}int ans=0;while(bfs())ans+=dinic(S,INF);printf("%d",n*n-ans-m);
}