[最小费用最大流]UVa1658

这种问题难点仅在于建模

理解透彻原模型！

#include<bits/stdc++.h>
using namespace std;
const int maxn = 10000 + 100;
const int INF = 0x7f7f7f7f;
typedef long long LL;
struct Edge{
int from,to,cap,flow,cost;

Edge(int u,int v,int c,int f,int w):from(u),to(v),cap(c),flow(f),cost(w) {}
};
struct MCMF{
int n,m;
vector<Edge> edges;
vector<int> G[maxn];
int inq[maxn];
int d[maxn];
int p[maxn];
int a[maxn];

void init(int n){
this->n=n;
for(int i=0;i<n;i++) G[i].clear();
edges.clear();
}
void AddEdge(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,LL & cost){
for(int i=0;i<n;i++) d[i]=INF;
memset(inq,0,sizeof(inq));
d[s]=0; inq[s]=1; p[s]=0; a[s]=INF;

queue<int> Q;
Q.push(s);
while(!Q.empty()){
int u=Q.front(); Q.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]) { Q.push(e.to); inq[e.to]=1; }
}
}
}
if(d[t]==INF) return false;
flow+=a[t];
cost+=(LL) d[t]*(LL)a[t];
for(int u=t;u!=s;u=edges[p[u]].from){
edges[p[u] ].flow+=a[t];
edges[p[u]^1 ].flow-=a[t];

}
return true;
}
int MincostMaxdflow(int s,int t,int limit,LL & cost){
int flow=0; cost=0;
while(flow<limit && BellmanFord(s,t,flow,cost));
return flow;
}
}g;
int main()
{
int n,m;
while(~scanf("%d%d",&n,&m)){
g.init(2*n-2);
for(int i=2;i<=n-1;i++){
g.AddEdge(i-1,n-2+i,1,0);
}
for(int i=0;i<m;i++){
int u,v,w;
scanf("%d%d%d",&u,&v,&w); v-=1;
if(u!=1&&u!=n) u+=n-2;
else u-=1;
g.AddEdge(u,v,1,w);
}
LL cost;
g.MincostMaxdflow(0,n-1,2,cost);
printf("%lld\n",cost);
}
return 0;
}