HDU 5889 Barricade

最短路，最小割，网络流。

可以根据$dis[u]+1$与$dis[v]$的大小关系判断$<u,v>$是否为最短路上的边，可以处理出一个只包含最短路的$DAG$，然后求这个$DAG$的最小割就可以了。

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
typedef long long LL;
const double pi=acos(-1.0),eps=1e-6;
void File()
{
    freopen("D:\\in.txt","r",stdin);
    freopen("D:\\out.txt","w",stdout);
}
template <class T>
inline void read(T &x)
{
    char c=getchar(); x=0;
    while(!isdigit(c)) c=getchar();
    while(isdigit(c)) {x=x*10+c-‘0‘; c=getchar();}
}

const int maxn = 30000 + 10;
const int INF = 0x7FFFFFFF;
struct Edge
{
    int from, to, cap, flow;
    Edge(int u, int v, int c, int f) :from(u), to(v), cap(c), flow(f){}
};
vector<Edge>edges;
vector<int>G[maxn];
bool vis[maxn];
int d[maxn];
int cur[maxn];
int n, m, s, t;

void init()
{
    for (int i = 0; i < maxn; i++)
        G[i].clear();
    edges.clear();
}
void AddEdge(int from, int to, int cap)
{
    edges.push_back(Edge(from, to, cap, 0));
    edges.push_back(Edge(to, from, 0, 0));
    int w = edges.size();
    G[from].push_back(w - 2);
    G[to].push_back(w - 1);
}
bool BFS()
{
    memset(vis, 0, sizeof(vis));
    queue<int>Q;
    Q.push(s);
    d[s] = 0;
    vis[s] = 1;
    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)
        {
            edges[G[x][i]].flow+=f;
            edges[G[x][i] ^ 1].flow-=f;
            flow+=f;
            a-=f;
            if(a==0) break;
        }
    }
    if(!flow) d[x] = -1;
    return flow;
}
int dinic(int s, int t)
{
    int flow = 0;
    while (BFS())
    {
        memset(cur, 0, sizeof(cur));
        flow += DFS(s, INF);
    }
    return flow;
}

int h[maxn],sz,T;
struct X
{
    int u,v,w,nx;
}ee[maxn];
int dis[maxn],flag[maxn];

void add(int a,int b,int c)
{
    ee[sz].u=a; ee[sz].v=b; ee[sz].w=c;
    ee[sz].nx=h[a]; h[a]=sz++;
}

void spfa()
{
    for(int i=1;i<=n;i++) dis[i]=INF ,flag[i]=0;
    dis[1]=0; queue<int>Q; Q.push(1); flag[1]=1;

    while(!Q.empty())
    {
        int top=Q.front(); Q.pop(); flag[top]=0;
        for(int i=h[top];i!=-1;i=ee[i].nx)
        {
            if(dis[top]+1<dis[ee[i].v])
            {
                dis[ee[i].v]=dis[top]+1;
                if(flag[ee[i].v]==0)
                {
                    flag[ee[i].v]=1;
                    Q.push(ee[i].v);
                }
            }
        }
    }
}

int main()
{
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&n,&m); sz=0;
        memset(h,-1,sizeof h);
        for(int i=1;i<=m;i++)
        {
            int u,v,w; scanf("%d%d%d",&u,&v,&w);
            add(u,v,w); add(v,u,w);
        }
        spfa();

        init();
        for(int i=0;i<sz;i++)
        {
            if(dis[ee[i].u]+1==dis[ee[i].v])
            {
                AddEdge(ee[i].u,ee[i].v,ee[i].w);
            }
        }
        s=1; t=n;
        printf("%d\n",dinic(s,t));
    }
    return 0;
}