UVA 1349 Optimal Bus Route Design （二分图最小权完美匹配）

恰好属于一个圈，那等价与每个点有唯一的前驱和后继，这让人想到了二分图，

把一个点拆开，点的前驱作为S集和点的后继作为T集，然后连边，跑二分图最小权完美匹配。

写的费用流。。最大权完美匹配KM算法没看懂

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

const int maxn = 200+6;
struct Edge
{
    int v,cap,cost,nxt;
};

vector<Edge> edges;
#define PB push_back
int head[maxn];

void addEdge(int u,int v,int C,int c)
{
    edges.PB(Edge{v,C,c,head[u]});
    head[u] = edges.size()-1;
}

void AddEdge(int u,int v,int C,int c)
{
    addEdge(u,v,C,c);
    addEdge(v,u,0,-c);
}
typedef int ll;
int S = 0,T = 1,vcnt;
int d[maxn],p[maxn],a[maxn];
bool vis[maxn];
const int INF = 0x3f3f3f3f;

ll MCMF(ll &cost)
{
    cost = 0;
    ll flow = 0;
    while(true){
        memset(vis,0,sizeof(bool)*vcnt);
        memset(d,0x3f,sizeof(int)*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(e.cap,a[u]);
                    if(!vis[e.v]){
                        vis[e.v] = true;
                        q.push(e.v);
                    }
                }
            }
        }
        if(d[T] == INF) return flow;
        flow += a[T];
        cost += a[T]*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 -1;
}

void init()
{
    memset(head,-1,sizeof(int)*vcnt);
    edges.clear();
}

int main()
{
    //freopen("in.txt","r",stdin);
    int n;
    S = 0;
    while(scanf("%d",&n),n){
        vcnt = 2*n+2;
        init(); T = 2*n+1;
        for(int i = 1; i <= n; i++){
            AddEdge(S,i,1,0);
            AddEdge(i+n,T,1,0);
        }
        for(int i = 1; i <= n; i++){
            int v,c;
            while(scanf("%d",&v),v){
                scanf("%d",&c);
                AddEdge(i,v+n,1,c);
            }
        }
        int cost;
        int flow = MCMF(cost);
        if(flow<n) puts("N");
        else printf("%d
",cost);
    }
    return 0;
}