UVA - 1658 Admiral （最小费用最大流）

最短路对应费用，路径数量对应流量。为限制点经过次数，拆点为边。跑一次流量为2的最小费用最大流。

最小费用最大流和最大流EK算法是十分相似的，只是把找增广路的部分换成了求费用的最短路。

 

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

const int maxv = 2000+5;
const int maxe = 22000+5;

struct Edge
{
    int v,cap,cost,nxt;
    void IN(int V,int C,int c,int N)
    {
        v = V; cap = C; cost = c; nxt = N;
    }
}edges[maxe];


int head[maxv],ecnt,vcnt;


void AddEdge(int u,int v,int C,int c)
{
    edges[ecnt].IN(v,C,c,head[u]);
    head[u] = ecnt++;
    edges[ecnt].IN(u,0,-c,head[v]);
    head[v] = ecnt++;
}
const int INF = 0x3f3f3f3f;
int S,T;
bool vis[maxv];
int d[maxv],p[maxv],a[maxv];
bool spfa()
{
    memset(d,0x3f,sizeof(int)*vcnt);
    memset(vis,0,sizeof(bool)*vcnt);

    queue<int> q; q.push(S); d[S] = 0;
    a[S] = INF;
    while(q.size()){
        int u = q.front(); q.pop();
        vis[u] = false;
        for(int i = head[u]; ~i; i = edges[i].nxt){
            Edge &e = edges[i];
            if(e.cap&& d[e.v] > d[u]+e.cost){
                d[e.v] = d[u] + e.cost;
                p[e.v] = i;
                a[e.v] = min(a[u],e.cap);
                if(!vis[e.v]) { q.push(e.v); vis[e.v] = true; }
            }
        }
    }
    return d[T] != INF;
}

ll MinCostMaxFlow()
{
    ll cost = 0;
    while(spfa()){
        cost += d[T];
        for(int i = T; i != S; i = edges[p[i]^1].v){
            edges[p[i]].cap -= a[T];
            edges[p[i]^1].cap += a[T];
        }
    }
    return cost;
}

int pin[maxv],pout[maxv];



int main()
{
    //freopen("in.txt","r",stdin);
    int v,e;
    int S = 0; T = 1;
    while(~scanf("%d%d",&v,&e)){

        vcnt = 2; ecnt = 0;
        pin[1] = pout[1] = vcnt++;
        pin[v] = pout[v] = vcnt++;
        for(int i = 2; i < v; i++) {
            pin[i] = vcnt++;
            pout[i] = vcnt++;
        }
        memset(head,-1,sizeof(int)*(vcnt));
        AddEdge(S,pin[1],2,0);
        AddEdge(pout[v],T,2,0);
        for(int i = 2; i < v; i++) AddEdge(pin[i],pout[i],1,0);
        while(e--){
            int u,v,c; scanf("%d%d%d",&u,&v,&c);
            AddEdge(pout[u],pin[v],1,c);
        }
        printf("%lld\n",MinCostMaxFlow());
    }
    return 0;
}