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2019-12-21 19:47:00
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此题与网络流24题中的骑士共存问题一致

最大流=最小割

用点数-去可以攻击的最大匹配

可以使用网络流或二分图

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define rg register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i=x;i<=y;i++)
    #define Fdr(i,x,y) for(int i=x;i>=y;i--)
    #define fl(i,x) for(int i=head[x],to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) (int(log2(n)))
    #define inf 0x3f3f3f3f
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const char* ln="\n";const int str=1<<20;struct IN{char buf[str],*s,*t;bool _;IN():s(buf),t(buf),_(0){}il char gc(){return s==t&&((t=(s=buf)+fread(buf,1,str,stdin))==s)?EOF:(*s++);}IN&operator>>(char&ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)_=1;else ch=c;return *this;}IN& operator>>(char* ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)_=1;return *this;}IN& operator>>(string& ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)_=1;return *this;}template<typename T>IN&operator>>(T&x){if(_)return *this;char c=gc();bool ff=0;while(c!=EOF&&(c<'0'||c>'9'))ff^=(c=='-'),c=gc();if(c==EOF){_=1;return *this;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=(x<<3)+(x<<1)+c-48,c=gc();if(c==EOF)_=1;if(ff)x=-x;return *this;}}in;struct OUT{char buf[str],*s,*t;OUT():s(buf),t(buf+str){}~OUT(){fwrite(buf,1,s-buf,stdout);}void pt(char c){(s==t)?(fwrite(s=buf,1,str,stdout),*s++=c):(*s++=c);}OUT&operator<<(const char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(string s){for(int i=0;s[i];i++)pt(s[i]);return *this;}template<typename T>OUT&operator<<(T x){if(!x)return pt('0'),*this;if(x<0)pt('-'),x=-x;char a[30],t=0;while(x)a[t++]=x%10,x/=10;while(t--)pt(a[t]+'0');return *this;}}out;}using namespace IO;
#define N 233
int n,head[N*N],d[N*N],q[N*N],cnt=1,st,ed;
int dx[8] = {-2, -1, 1, 2, 2, 1, -1, -2},dy[8] = {-1, -2, -2, -1, 1, 2, 2, 1}; 
bool b[N][N];
struct edge{
    int to,nxt,w;
}e[N*N*2];
void add(int x,int y,int w){
    e[++cnt].to=y;e[cnt].w=w;e[cnt].nxt=head[x];head[x]=cnt;
    e[++cnt].to=x;e[cnt].w=0;e[cnt].nxt=head[y];head[y]=cnt;
}
bool bfs(){
    int h=0,t=1;
    clr(d,0);
    d[q[h]=st]=1;   
    while(h<t){
        int x=q[h++];
        if(x==ed)return 1;
        fl(i,x)if(e[i].w&&!d[to]){
            d[to]=d[x]+1;
            q[t++]=to;
        }
    }
    return 0;
}
int dfs(int x,int mf){
    if(x==ed)return mf;
    int us=0,w;
    fl(i,x)
    if(e[i].w&&d[to]==d[x]+1){
        w=dfs(to,MIN(mf-us,e[i].w));
        e[i].w-=w;e[i^1].w+=w;
        us+=w;
        if(us==mf)return mf;
    }
    if(!us)d[x]=-1;
    return us;
}
int dinic(){
    int ans=0;
    while(bfs())ans+=dfs(st,inf);
    return ans;
}
#define id(x,y) ((x-1)*n+y)
int main(){
    in>>n;
    st=n*n+1;ed=n*n+2;
    int tt=0;
    char ch[N];
    Fur(i,1,n){
        in>>(ch+1);
        Fur(j,1,n)
        tt+=(b[i][j]=ch[j]-48);
    }
    Fur(i,1,n)
        Fur(j,1,n)
        if(!b[i][j]){
            if((i+j)&1){
                add(st,id(i,j),1);
                Fur(k,0,7){
                    int nx=i+dx[k],ny=j+dy[k];
                    if(nx<1||nx>n||ny<1||ny>n||b[nx][ny])continue;
                    add(id(i,j),id(nx,ny),inf);
                }
            }
            else add(id(i,j),ed,1);
        }
    out<<n*n-tt-dinic()<<ln;
}
LG 4304 [TJOI2013]攻击装置
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