题目链接:https://ac.nowcoder.com/acm/contest/5961/E
题目大意:
思路:拆点,在出点向进点连接q条边。第k条边的流量为1,费用为a+(k-1)*b。对于原图的边,出点到入点连接流量为q。费用为0的边。
然后源点0到所有x的入点连接费用为0,流量为1的边。同理:所以y的出点到汇点点2n+1连接费用为0,流量为1的边。跑个最小费用最大流。
#include<bits/stdc++.h>
#define MAXN_ 5050
#define INF 0x3f3f3f3f
#define P pair<int,int>
using namespace std;
struct edge
{
int to,cap,cost,rev;
};
int n,N,m,flow,s,t,cap,res,cost,from,to,h[MAXN_];
std::vector<edge> G[MAXN_];
int dist[MAXN_],prevv[MAXN_],preve[MAXN_]; // 前驱节点和对应边
inline void add()
{
//cout<<from<<" "<<to<<" "<<cap<<" "<<cost<<endl;
G[from].push_back((edge)
{
to,cap,cost,(int)G[to].size()
});
G[to].push_back((edge)
{
from,0,-cost,(int)G[from].size()-1
});
} // 在vector 之中找到边的位置所在!
inline int read()
{
int x=0;
char c=getchar();
bool flag=0;
while(c<'0'||c>'9')
{
if(c=='-')flag=1;
c=getchar();
}
while(c>='0'&&c<='9')
{
x=(x<<3)+(x<<1)+c-'0';
c=getchar();
}
return flag?-x:x;
}
inline void min_cost_flow(int s,int t,int f)
{
memset(h,0,sizeof(h));
while(f > 0)
{
priority_queue<P,vector<P>, greater<P> > D;
memset(dist,INF,sizeof dist);
dist[s] = 0;
D.push(P(0,s));
while(!D.empty())
{
P now = D.top();
D.pop();
if(dist[now.second] < now.first)
{
continue;
}
int v = now.second;
for(int i=0; i<(int)G[v].size(); ++i)
{
edge &e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to])
{
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
D.push(P(dist[e.to],e.to));
}
}
}
// 无法增广 , 就是找到了答案了!
if(dist[t] == INF) break;
for(int i=1; i<=N; ++i)
{
h[i] += dist[i];
}
int d = f;
for(int v = t; v != s; v = prevv[v])
{
d = min(d,G[prevv[v]][preve[v]].cap);
}
f -= d;
flow += d;
res += d * h[t];
for(int v=t; v!=s; v=prevv[v])
{
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
}
int main(){
int q, a, b; scanf("%d%d%d", &n, &m, &q);
s=0, t=2*n+1; N=t;
for(int i=1; i<=n; i++){
scanf("%d%d", &a, &b);
from = i; to = i+n;
for(int k=1; k<=q; k++){
cap = 1;
cost = a+(k-1)*b;
add();
}
}
for(int i=1; i<=m; i++){
scanf("%d%d", &a, &b);
from = a+n; to = b; cap = q; cost = 0;
add();
from = b+n; to = a; cap = q; cost = 0;
add();
}
for(int i=1; i<=q; i++){
scanf("%d", &a);
from = s; to = a; cap = 1; cost = 0;
add();
}
for(int i=1; i<=q; i++){
scanf("%d", &b);
from = b+n; to = t; cap = 1; cost = 0;
add();
}
min_cost_flow(s,t,INF);
printf("%d\n", res);
return 0;
}

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