poj 1986 Distance Queries（LCA:倍增/离线）

计算树上的路径长度。input要去查poj 1984。

任意建一棵树，利用树形结构，将问题转化为u，v，lca(u,v)三个点到根的距离。输出d[u]+d[v]-2*d[lca(u,v)]。

倍增求解：

 #include<cstdio>
 #include<cstring>
 #include<queue>
 #include<algorithm>
 #define rep(i,a,b) for(int i=a;i<=b;i++)
 #define clr(a,m) memset(a,m,sizeof(a))
 using namespace std;

 const int MAXN=;
 const int POW = ;

 struct Edge{
     int v,next,c;
     Edge(){}
     Edge(int _v,int _c,int _next):v(_v),c(_c),next(_next){}
 }edge[MAXN<<];

 int head[MAXN],tol;
 int p[MAXN][POW],d[MAXN];
 int vis[MAXN],dis[MAXN];
 queue<int>q;

 void init()
 {
     tol=;
     clr(head,-);
 }

 void add(int u,int v,int c)
 {
     edge[tol]=Edge(v,c,head[u]);
     head[u]=tol++;
 }

 void bfs(int x)
 {
     clr(vis,);
     clr(dis,);
     while(!q.empty())
         q.pop();
     q.push(x);
     vis[x]=;
     dis[x]=;
     while(!q.empty())
     {
         int u=q.front();
         q.pop();
         for(int i=head[u];i!=-;i=edge[i].next)
         {
             int v=edge[i].v;
             if(vis[v])
                 continue;
             q.push(v);
             vis[v]=;
             dis[v]=dis[u]+edge[i].c;
         }
     }
 }

 void dfs(int u,int fa){
     d[u]=d[fa]+;
     p[u][]=fa;
     for(int i=;i<POW;i++) p[u][i]=p[p[u][i-]][i-];
     for(int i=head[u];i!=-;i=edge[i].next){
         int v=edge[i].v;
         if(v==fa) continue;
         dfs(v,u);
     }
 }

 int lca( int a, int b ){
     if( d[a] > d[b] ) a ^= b, b ^= a, a ^= b;
     if( d[a] < d[b] ){
         int del = d[b] - d[a];
         for( int i = ; i < POW; i++ ) if(del&(<<i)) b=p[b][i];
     }
     if( a != b ){
         for( int i = POW-; i >= ; i-- )
             if( p[a][i] != p[b][i] )
                  a = p[a][i] , b = p[b][i];
         a = p[a][], b = p[b][];
     }
     return a;
 }

 void LCA(int n)
 {
     clr(p,);
     d[]=;
     dfs(,);

     bfs();

     int k;
     scanf("%d",&k);
     int u,v;
     rep(i,,k){
         scanf("%d%d",&u,&v);
         printf("%d\n",dis[u]+dis[v]-*dis[lca(u,v)]);
     }
 }

 int main()
 {
     int n,m;
     scanf("%d%d",&n,&m);
     init();
     rep(i,,m){
         int u,v,c;
         scanf("%d%d%d%*s",&u,&v,&c);
         add(u,v,c);
         add(v,u,c);
     }

     LCA(n);
     return ;
 }

又用tarjin离线做了一遍= =

 #include<cstdio>
 #include<cstring>
 #include<queue>
 #include<algorithm>
 #define rep(i,a,b) for(int i=a;i<=b;i++)
 #define clr(a,m) memset(a,m,sizeof(a))
 using namespace std;

 const int MAXN=;

 struct Edge{
     int v,next,c;
     Edge(){}
     Edge(int _v,int _c,int _next):v(_v),c(_c),next(_next){}
 }edge[MAXN<<];

 struct EDGE{
     int u,v;
     int ans;
     EDGE(){}
     EDGE(int _u,int _v):u(_u),v(_v),ans(-){}
 };

 int head[MAXN],tol;
 int p[MAXN],vis[MAXN],dis[MAXN];

 queue<int>q;
 vector<int>query[MAXN];
 vector<EDGE>G;

 void init()
 {
     tol=;
     clr(head,-);
 }

 void add(int u,int v,int c)
 {
     edge[tol]=Edge(v,c,head[u]);
     head[u]=tol++;
 }

 void build(int m)
 {
     init();
     rep(i,,m){
         int u,v,c;
         scanf("%d%d%d%*s",&u,&v,&c);
         add(u,v,c);
         add(v,u,c);
     }

     int k;
     scanf("%d",&k);
     rep(i,,k){
         int u,v,siz;
         scanf("%d%d",&u,&v);

         G.push_back(EDGE(u,v));
         siz=G.size();
         query[u].push_back(siz-);

         G.push_back(EDGE(v,u));
         siz=G.size();
         query[v].push_back(siz-);
     }
 }

 void bfs(int x)
 {
     clr(vis,);
     clr(dis,);
     while(!q.empty())
         q.pop();
     q.push(x);
     vis[x]=;
     dis[x]=;
     while(!q.empty())
     {
         int u=q.front();
         q.pop();
         for(int i=head[u];i!=-;i=edge[i].next)
         {
             int v=edge[i].v;
             if(vis[v])
                 continue;
             q.push(v);
             vis[v]=;
             dis[v]=dis[u]+edge[i].c;
         }
     }
 }

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

 void dfs(int x)
 {
     vis[x]=;
     for(int i=head[x];i!=-;i=edge[i].next)
     {
         int v=edge[i].v;
         if(vis[v])
             continue;
         dfs(v);
         p[v]=x;
     }

     int siz =query[x].size()-;
     rep(i,,siz)
     {
         int t=query[x][i];
         if(vis[G[t].v]){
             G[t].ans=find(G[t].v);
         }
     }
 }

 void LCA(int rt,int n)
 {
     clr(vis,);
     rep(i,,n)
         p[i]=i;
     dfs(rt);
 }

 void PRT()
 {
     int siz=G.size();
     for(int i=;i<siz;i+=)
     {
         int u=G[i].u;
         int v=G[i].v;
         if(G[i].ans!=-)
             printf("%d\n",dis[u]+dis[v]-*dis[G[i].ans]);
         else
             printf("%d\n",dis[u]+dis[v]-*dis[G[i^].ans]);
     }
 }

 int main()
 {
     int n,m;
     scanf("%d%d",&n,&m);
     build(m);
     bfs();
     LCA(,n);
     PRT();
     return ;
 }