卧薪尝胆,厚积薄发。
国家集训队 人员雇佣
Date: Wed Mar 20 11:31:23 CST 2019 In Category: NoCategory

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;
}
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