计算最小费用最大流,网络中可以有负边,但不能存在负权圈。如果要固定流量k,可以在增广的时候检查一下,在flow+a>=k的时候只增广k-flow单位的流量,然后终止程序
#include<bits/stdc++.h>
using namespace std;
const int inf=2e9;
const int maxn=10050;
struct Edge{
int from,to,cap,flow,cost;
Edge(int u,int v,int c,int f,int co):from(u),to(v),cap(c),flow(f),cost(co){}
};
struct MCMF{
int n,m,s,t;
vector<Edge> edges;
vector<int> g[maxn];
int inq[maxn]; //是否在队列中
int d[maxn]; //Bellman-Ford
int p[maxn]; //上一条弧
int a[maxn]; //可改进量
void init(int n){
this->n=n;
for(int i=0;i<n;++i) g[i].clear();
edges.clear();
}
void add(int from,int to,int cap,int cost){
edges.push_back(Edge(from,to,cap,0,cost));
edges.push_back(Edge(to,from,0,0,-cost));
m=edges.size();
g[from].push_back(m-2);
g[to].push_back(m-1);
}
bool BellmanFord(int s,int t,int& flow,int& cost){
for(int i=0;i<n;++i) d[i]=inf;
memset(inq,00,sizeof(inq));
d[s]=0;
inq[s]=1;
p[s]=0;
a[s]=inf;
queue<int> que;
que.push(s);
while(!que.empty()){
int u=que.front();
que.pop();
inq[u]=0;
for(int i=0;i<g[u].size();++i){
Edge& e=edges[g[u][i]];
if(e.cap>e.flow && d[e.to]>d[u]+e.cost){
d[e.to]=d[u]+e.cost;
p[e.to]=g[u][i];
a[e.to]=min(a[u],e.cap-e.flow);
if(!inq[e.to]){ que.push(e.to);inq[e.to]=1; }
}
}
}
if(d[t]==inf) return false;//s-t不联通,失败退出
flow+=a[t];
cost+=d[t]*a[t];
int u=t;
while(u!=s){
edges[p[u]].flow+=a[t];
edges[p[u]^1].flow-=a[t];
u=edges[p[u]].from;
}
return true;
}
int Mincost(int s,int t){
int flow=0,cost=0;
while(BellmanFord(s,t,flow,cost));
return cost;
}
};