最小费用流: uva 1658

来源：互联网发布：windows server版本编辑：程序博客网时间：2024/04/25 15:42

最小费用流可以求

某个流量的最小费用流，

也可以直接求最大流量的最小费用流

某个流量的最小费用流：

 int MincostFlow(int s, int t, int flow_limit, int& cost) {        int flow = 0; cost = 0;        while(flow < flow_limit && BellmanFord(s, t, flow_limit, flow, cost));        return flow;    }

MCMF

int minflow(int s,int t,long long &cost){    int flow=0;cost=0;    while(BellmanFord(s,t,flow,cost));    return flow}

套上模板。。

#include<iostream>#include<string>#include<cstring>#include<algorithm>#include<cstdio>#include<vector>#include<queue>#include<bits/stdc++.h>using namespace std;#define mem(a,b) memset(a,b,sizeof(a));#define sf scanf#define pf printf#define LL long longconst int maxn = 2000 + 10;const int INF = 1000000000;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];         // 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 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_limit, int& flow, int& 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;        if(flow + a[t] > flow_limit) a[t] = flow_limit - flow;        flow += a[t];        cost += d[t] * 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;    }    // 需要保证初始网络中没有负权圈    int MincostFlow(int s, int t, int flow_limit, int& cost) {        int flow = 0; cost = 0;        while(flow < flow_limit && BellmanFord(s, t, flow_limit, flow, cost));        return flow;//返回的流量，但其实是没有用的，求的最小费用在&cost中求了    }};MCMF g;int main(){    int n,m;    while(~sf("%d%d",&n,&m)){       g.init(n*2-2);        for(int i=2;i<=n-1;++i){            g.addedge(i-1,i+n-2,1,0);        }        // 点2~n-1拆成弧i->i'，前者编号为1~n-2，后者编号为n~2n-2        for(int i=1;i<=m;++i){            int u,v,c;            sf("%d%d%d",&u,&v,&c);            if(u!=1&&u!=n)u+=n-2;            else u--;            v--;            g.addedge(u,v,1,c);        }        int cost;        g.MincostFlow(0,n-1,2,cost);//s为0，  t为n-1        pf("%d\n",cost);    }}

0 0