HDU 2586 How far away?-优快云博客

本文介绍了两种图遍历算法：深度优先搜索（DFS）和最近公共祖先（LCA）算法，并提供了完整的C++实现代码。这两种算法常用于解决图论问题中的路径查找和最短路径问题。

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用dfs和lca均可，贴上两份代码

dfs

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#include <map>
#include <queue>
#include <ctime>
#include <set>
#define ll long long
#define MP make_pair
#define PB push_back
#define SZ(x) ((int)(x).size())
#define REP(i,n) for (int i=0; (i)<(int)n; ++(i))
#define FOR(it,c) for ( __typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it )
using namespace std;

const int N=40010;
struct Edge{
    int next,w;
    Edge(int a,int b):next(a),w(b){}
};
vector<Edge> e[N];
int ans,t,n,m;
bool found,vis[N];

void dfs(int u,int v,int cnt){
    if(found) return;
    if(u==v){
        ans=cnt;
        found=true;
        return;
    }
    FOR(it,e[u]){
        if(vis[it->next]) continue;
        vis[it->next]=true;
        dfs(it->next,v,cnt+it->w);
        if(found) return;
    }
}

int main(){
#ifndef ONLINE_JUDGE
    freopen("a.in","r",stdin);
    freopen("a.out","w",stdout);
#endif
    cin>>t;
    while(t--){
        int u,v,w;
        cin>>n>>m;
        REP(i,n-1){
            scanf("%d%d%d",&u,&v,&w);
            e[u].PB(Edge(v,w));
            e[v].PB(Edge(u,w));
        }
        while(m--){
            scanf("%d%d",&u,&v);
            found=false;
            memset(vis,0,sizeof(vis));
            vis[u]=true;
            ans=0;
            dfs(u,v,0);
            printf("%d\n",ans);
        }
        REP(i,n+1) e[i].clear();
    }
    return 0;
}

lca

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#include <map>
#include <queue>
#include <ctime>
#include <set>
#define ll long long
#define MP make_pair
#define PB push_back
#define SZ(x) ((int)(x).size())
#define REP(i,n) for (int i=0; (i)<(int)n; ++(i))
#define FOR(it,c) for ( __typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it )
using namespace std;

const int N=40010;
struct Edge{
    int next,w;
    Edge(int a,int b):next(a),w(b){}
};
vector<Edge> e[N],q[N];
int ans,t,n,m,p[N],u[210],v[210],dis[N],lca[N];
bool found,vis[N];

int find(int x){ return p[x]==x?x:p[x]=find(p[x]); }

void tarjan(int u){
    vis[u]=true;
    FOR(it,q[u]) if(vis[it->next]) lca[it->w]=find(it->next);
    FOR(it,e[u]){
        if(vis[it->next]) continue;
        dis[it->next]=dis[u]+it->w;
        tarjan(it->next);
        p[it->next]=u;
    }
}

int main(){
#ifndef ONLINE_JUDGE
    freopen("a.in","r",stdin);
    freopen("a.out","w",stdout);
#endif
    cin>>t;
    while(t--){
        cin>>n>>m;
        REP(i,n) p[i]=i;
        REP(i,n-1){
            int a,b,c;
            scanf("%d%d%d",&a,&b,&c);
            a--;b--;
            e[a].PB(Edge(b,c));
            e[b].PB(Edge(a,c));
        }
        REP(i,m){
            scanf("%d%d",u+i,v+i);
            u[i]--;v[i]--;
            q[u[i]].PB(Edge(v[i],i));
            q[v[i]].PB(Edge(u[i],i));
        }
        memset(vis,false,sizeof(vis));
        tarjan(0);
        REP(i,m) printf("%d\n",dis[u[i]]-2*dis[lca[i]]+dis[v[i]]);
        REP(i,n){ e[i].clear(); q[i].clear(); }
    }
    return 0;
}