BZOJ 4443 小凸玩矩阵

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题意：中文题

思路：二分答案，然后比较显然的网络流建图之后看看最大流是否大于n-k+1就可以了

#include<bits/stdc++.h>using namespace std;#define INF 1e9+100const int maxn = 250*250+100;struct Edge{int from,to,cap,flow;Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}};struct Dinic{int n,m,s,t;vector<Edge>edges;vector<int> G[maxn];bool vis[maxn];int d[maxn];int cur[maxn];void AddEdge(int from,int to,int cap){edges.push_back(Edge(from,to,cap,0));edges.push_back(Edge(to,from,0,0));m = edges.size();G[from].push_back(m-2);G[to].push_back(m-1);}void init(int n){for (int i = 0;i<=n;i++)G[i].clear();edges.clear();}bool BFS(){memset(vis,0,sizeof(vis));queue<int>q;q.push(s);d[s]=0;vis[s]=1;while (!q.empty()){int x = q.front();q.pop();for (int i = 0;i<G[x].size();i++){Edge &e = edges[G[x][i]];if (!vis[e.to] && e.cap>e.flow){vis[e.to]=1;d[e.to]=d[x]+1;q.push(e.to);}}}return vis[t];}int DFS(int x,int a){if (x==t || a==0)return a;int flow = 0,f;for (int &i=cur[x];i<G[x].size();i++){Edge&e = edges[G[x][i]];if (d[x]+1==d[e.to] && (f=DFS(e.to,min(a,e.cap-e.flow)))>0){e.flow+=f;edges[G[x][i]^1].flow-=f;flow+=f;a-=f;if (a==0)break;}}return flow;}int Maxflow(int s,int t){this->s=s;this->t=t;int flow = 0;while (BFS()){memset(cur,0,sizeof(cur));flow+=DFS(s,INF);}return flow;}}di;int mp[252][252];int n,m,k;bool check(int x){    di.init(n+m+10);int s= 0;int t = n+m+1;for (int i = 1;i<=n;i++){di.AddEdge(s,i,1);for (int j= 1;j<=m;j++)if (mp[i][j] <= x)di.AddEdge(i,n+j,1);}for (int j = 1;j<=m;j++)di.AddEdge(n+j,t,1);if (di.Maxflow(s,t)>=n-k+1)return 1;return 0;}int main(){while (scanf("%d%d%d",&n,&m,&k)!=EOF){         for (int i = 1;i<=n;i++) for (int j= 1;j<=m;j++) scanf("%d",&mp[i][j]);         int l = 0,r=INF,ans=-1; while (l<=r) { int m = (l+r)>>1; if (check(m)) r=m-1,ans=m; else l=m+1; } printf("%d\n",ans);}}

Description

小凸和小方是好朋友，小方给小凸一个N*M（N<=M)的矩阵A,要求小秃从其中选出N个数，其中任意两个数字不能在同一行或同一列，现小凸想知道选出来的N个数中第K大的数字的最小值是多少。

Input

第一行给出三个整数N,M,K

接下来N行，每行M个数字，用来描述这个矩阵

Output

如题

Sample Input

3 4 21 5 6 6 8 3 4 36 8 6 3

Sample Output

Hint

1<=K<=N<=M<=250,1<=矩阵元素<=10^9

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