hdu 3416 Marriage Match IV 最大流 最短路径

在无向图上求s到t最短路径的条数且最短路径间不能有重边（即弱独立轨）

#include <cstdio>
#include <vector>
#include <queue>
#include <cstring>
using namespace std;
#define maxn 2100
#define INF 100000
struct node
{
    int u,v,dis;
};
struct Edge
{
    int from, to, cap, flow;
};

int n, m, s, t;
vector <node> map[maxn];
vector<Edge> edges;    // 边数的两倍
vector<int> G[maxn];   // 邻接表，G[i][j]表示结点i的第j条边在e数组中的序号
bool vis[maxn];        // BFS使用
int d[maxn];           // 从起点到i的距离
int cur[maxn];         // 当前弧指针
int dist[maxn];
int min(int a,int b)
{
    if(a<b) return a;
    else return b;
}
void AddEdge(int from, int to, int cap)
{
    int len;
    Edge temp;
    temp.from=from;temp.to=to;temp.cap=cap;temp.flow=0;
    edges.push_back(temp);
    temp.from=to;temp.to=from;temp.cap=0;temp.flow=0;
    edges.push_back(temp);
    len = edges.size();
    G[from].push_back(len-2);
    G[to].push_back(len-1);
}
bool BFS()
{
    memset(vis, 0, sizeof(vis));
    queue<int> Q;
    Q.push(s);
    vis[s] = 1;
    d[s] = 0;
    while(!Q.empty())
    {
        int x = Q.front(); Q.pop();
        for(int i = 0; i < G[x].size(); i++)
        {
            Edge& e = edges[G[x][i]];
            if(!vis[e.to] && e.cap > e.flow)
            {
                vis[e.to] = 1;
                d[e.to] = d[x] + 1;
                Q.push(e.to);
            }
        }
    }
    return vis[t];
}
int DFS(int x, int a)
{
    if(x == t || a == 0) return a;
    int flow = 0, f;
    for(int& i = cur[x]; i < G[x].size(); i++)
    {
        Edge& e = edges[G[x][i]];
        if(d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap-e.flow))) > 0)
        {
            e.flow += f;
            edges[G[x][i]^1].flow -= f;
            flow += f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}
int Maxflow()
{
    int flow = 0;
    while(BFS())
    {
        memset(cur, 0, sizeof(cur));
        flow += DFS(s, INF);
    }
    return flow;
}
void spfa()
{
    int i,v,u;
    memset(vis,0,sizeof(vis));
    for(i=1;i<=n;i++)
        dist[i]=INF;
    queue<int> Q;
    dist[s]=0;
    Q.push(s);
    while(!Q.empty())
    {
        u=Q.front();
        Q.pop();
        vis[u]=0;
        for(i=0;i<map[u].size();i++)
        {
            v=map[u][i].v;
            if(dist[v]>dist[u]+map[u][i].dis)
            {
                dist[v]=dist[u]+map[u][i].dis;
                if(!vis[v])
                {
                    vis[v]=1;
                    Q.push(v);
                }
            }
        }
    }
}

int main()
{
    int cas;
    scanf("%d",&cas);
    while(cas--)
    {
        node temp;
        int i,j,x,y,z;
        scanf("%d%d",&n,&m);
        for(i=0;i<=n+5;i++)
        {
            map[i].clear();
            G[i].clear();
        }
        for(i=1;i<=m;i++)
        {
            scanf("%d%d%d",&x,&y,&z);
            if(x==y)
                continue;
            temp.u=x;
            temp.v=y;
            temp.dis=z;
            map[x].push_back(temp);
        }
        scanf("%d%d",&s,&t);
        spfa();
        for(i=1;i<=n;i++)
        {
            for(j=0;j<map[i].size();j++)
            {
                if(dist[i]+map[i][j].dis==dist[map[i][j].v])
                    AddEdge(i,map[i][j].v,1);
            }
        }
        int ans=Maxflow();
        printf("%d
",ans);
    }
    return 0;
}