[SCOI2015]小凸玩矩阵

看到这种第(k)大的题面就想到二分答案对吧，问题在于二分后怎么(check)。直接网络流跑就行了。

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<set>
#include<map>
#include<iostream>
using namespace std;
#define re register
#define ll long long
inline int gi(){
	int f=1,sum=0;char ch=getchar();
	while(ch>'9' || ch<'0'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0' && ch<='9'){sum=(sum<<3)+(sum<<1)+ch-'0';ch=getchar();}
	return f*sum;
}
const int N=5010,Inf=1e9+10;
int n,m,k,a[N][N],front[N<<1],cnt,s,t,dep[N];
struct node{int to,nxt,w;}e[N*N<<1];
void Add(int u,int v,int w){e[cnt]=(node){v,front[u],w};front[u]=cnt++;e[cnt]=(node){u,front[v],0};front[v]=cnt++;}
void build(int mid){
	memset(front,-1,sizeof(front));cnt=0;s=0;t=n+m+1;
	for(int i=1;i<=n;i++)Add(s,i,1);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
			if(a[i][j]<=mid)Add(i,j+n,1);
	for(int j=1;j<=m;j++)Add(j+n,t,1);
}
queue<int>Q;
bool bfs(){
	memset(dep,0,sizeof(dep));dep[s]=1;
	Q.push(s);
	while(!Q.empty()){
		int u=Q.front();Q.pop();
		for(int i=front[u];~i;i=e[i].nxt){
			int v=e[i].to;
			if(e[i].w && !dep[v]){
				dep[v]=dep[u]+1;
				Q.push(v);
			}
		}
	}
	return dep[t];
}
int dfs(int u,int flow){
	if(u==t || !flow)return flow;
	for(int i=front[u];~i;i=e[i].nxt){
		int v=e[i].to;
		if(e[i].w && dep[v]==dep[u]+1){
			int di=dfs(v,min(e[i].w,flow));
			if(di){e[i].w-=di;e[i^1].w+=di;return di;}
			else dep[v]=0;
		}
	}
	return 0;
}
int dinic(){
	int fl=0;
	while(bfs())
		while(int d=dfs(s,Inf))fl+=d;
	return fl;
}
bool check(int mid){
	build(mid);
	return dinic()>=n-k+1;
}
int main(){
	n=gi();m=gi();k=gi();int l=1e9+10,r=0;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
			a[i][j]=gi(),l=min(l,a[i][j]),r=max(r,a[i][j]);
	int ans=0;
	while(l<=r){
		int mid=(l+r)>>1;
		if(check(mid)){ans=mid;r=mid-1;}
		else l=mid+1;
	}
	printf("%d
",ans);
	return 0;
}