卧薪尝胆,厚积薄发。
      
    
            国家集训队 人员雇佣
        
        
        Description:
雇第
$i$
个人花费
$A_i$
,如果雇了
$i$
并且雇了
$j$
收益
$E_{i,j}$
,雇了
$i$
没雇
$j$
损失
$E_{i,j}$
,求最大收益。
$1\leqslant n\leqslant 10^3$
Solution:
比较容易想到是二元关系最小割,然后列方程就行了。
Code:
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<queue>
#include<cctype>
#include<cstring>
using namespace std;
inline int rd()
{
	register int res = 0,f = 1;register char c = getchar();
	while(!isdigit(c)){if(c == '-')f = -1;c = getchar();}
	while(isdigit(c))res = (res << 1) + (res << 3) + c - '0',c = getchar();
	return res * f;
}
int n;
#define MAXN 1010
int A[MAXN];
int E[MAXN][MAXN];
struct edge
{
	int to,nxt,f;
}e[(MAXN * MAXN + MAXN * 2) * 2];
int edgenum = 0;
int lin[MAXN];
void add(int a,int b,int f)
{
	e[edgenum] = (edge){b,lin[a],f};lin[a] = edgenum++;
	e[edgenum] = (edge){a,lin[b],0};lin[b] = edgenum++;
	return;
}
typedef long long ll;
int ch[MAXN];
int s,t;
bool BFS()
{
	queue<int> q;q.push(s);
	memset(ch,-1,sizeof(ch));ch[s] = 0;
	while(!q.empty())
	{
		int k = q.front();q.pop();
		for(int i = lin[k];i != -1;i = e[i].nxt)
		{
			if(ch[e[i].to] == -1 && e[i].f)
			{
				ch[e[i].to] = ch[k] + 1;
				q.push(e[i].to);
			}
		}
	}
	return (ch[t] != -1);
}
ll flow(int k,ll f)
{
	if(k == t)return f;
	ll r = 0;
	for(int i = lin[k];i != -1 && f > r;i = e[i].nxt)
	{
		if(ch[e[i].to] == ch[k] + 1 && e[i].f)
		{
			int l = flow(e[i].to,min(1ll * e[i].f,f - r));
			e[i].f -= l;r += l;e[i ^ 1].f += l;
		}
		lin[k] = i;
	}
	if(r == 0)ch[k] = -1;
	return r;
}
#define INF 0x3f3f3f3f3f3f3f3f
int cur[MAXN];
ll dinic()
{
	ll ans = 0,r;
	memcpy(cur,lin,sizeof(cur));
	while(BFS())
	{
		ans += flow(s,INF);
		memcpy(lin,cur,sizeof(cur));
	}
	return ans;
}
int main()
{
	memset(lin,-1,sizeof(lin));
	scanf("%d",&n);
	for(int i = 1;i <= n;++i)A[i] = rd();
	for(int i = 1;i <= n;++i)for(int j = 1;j <= n;++j)E[i][j] = rd();
	s = n + 1;t = s + 1;
	ll ans = 0;
	for(int i = 1;i <= n;++i)for(int j = 1;j <= n;++j)ans += E[i][j];
	for(int i = 1;i <= n;++i)
	{
		int sum = 0;
		for(int j = 1;j <= n;++j)sum += E[i][j];
		add(s,i,sum - E[i][i]);
		add(i,t,A[i]);
	}
	for(int i = 1;i <= n;++i)for(int j = 1;j <= n;++j)add(i,j,E[i][j] + E[j][i]);
	cout << ans - dinic() << endl;
	return 0;
}
 In tag:
图论-最小割
          In tag:
图论-最小割 
          
        
        Copyright © 2020
        
          wjh15101051
        
      
      ღゝ◡╹)ノ♡
     Date: Wed Mar 20 11:31:23 CST 2019
          Date: Wed Mar 20 11:31:23 CST 2019
           In Category:
          In Category:
           
         Timeline
            Timeline
           About
            About
           Toolbox
            Toolbox
           Friends
              Friends