HDU 3078：Network（LCA之tarjan）

http://acm.hdu.edu.cn/showproblem.php?pid=3078

题意：给出n个点n-1条边m个询问，每个点有个权值，询问中有k，u，v，当k = 0的情况是将u的权值修改成v，当k不为0的情况是问u和v的路径中权值第k大的点的权值是多少。

思路：比较暴力的方法，可能数据太水勉强混过去了。对于每一个询问的时候保留两个点之间的lca，还有计算出两个点之间的点的个数（询问的时候如果点的个数小于k就不用算了），然后tarjan算完之后对每个询问再暴力路径上的每个点放进vector排序输出第k大..

 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <iostream>
 #include <queue>
 #include <cmath>
 #include <map>
 #include <vector>
 using namespace std;
 #define N 80010
 #define M 30010
 struct node
 {
     int u, v, next;
 }edge[N*];
 struct P
 {
     int u, v, next, num, k, lca;
 }Edge[M*];
 int n, m, tot, Tot, head[N], Head[N], a[N], fa[N], dis[N];
 bool vis[N];
 vector<int> vec;

 void init()
 {
     tot = Tot = ;
     memset(head, -, sizeof(head));
     memset(Head, -, sizeof(Head));
     memset(dis, -, sizeof(dis));
     memset(vis, false, sizeof(vis));
     for(int i = ; i <= n; i++) fa[i] = i;
 }

 void add(int u, int v)
 {
     edge[tot].u = u; edge[tot].v = v; edge[tot].next = head[u]; head[u] = tot++;
 }

 void Add(int u, int v, int k)
 {
     Edge[Tot].k = k; Edge[Tot].u = u; Edge[Tot].v = v; Edge[Tot].next = Head[u]; Edge[Tot].num = ; Edge[Tot].lca = -; Head[u] = Tot++;
 }

 int Find(int x)
 {
     while(x != fa[x]) x = fa[x];
     return x;
 }

 void Merge(int u, int v)
 {
     u = Find(u), v = Find(v);
     fa[v] = u;
 }

 void tarjan(int u)
 {
     vis[u] = true;
     for(int i = head[u]; ~i; i = edge[i].next) {
         int v = edge[i].v;
         if(!vis[v]) {
             dis[v] = dis[u] + ;
             tarjan(v);
             fa[v] = u;
         }
     }
     for(int i = Head[u]; ~i; i = Edge[i].next) {
         int v = Edge[i].v, k = Edge[i].k;
         if(vis[v]) {
             int ff = Find(v);
             if(k) {
                 Edge[i].num = Edge[i^].num = dis[u] + dis[v] -  * dis[ff];
                 Edge[i].lca = Edge[i^].lca = ff;
             }
             else a[u] = v;
         }
     }
 }

 int doit(int u, int v, int k, int num, int lca)
 {
     vec.clear();
     while(u != lca) {
         vec.push_back(a[u]); u = fa[u];
     }
     while(v != lca) {
         vec.push_back(a[v]); v = fa[v];
     }
     vec.push_back(a[lca]);
     sort(vec.begin(), vec.end());
     num++;
     return vec[num-k];
 }

 void solve()
 {
     for(int i = ; i < Tot; i += ) {
         int u = Edge[i].u, v = Edge[i].v, k = Edge[i].k, num = Edge[i].num, lca = Edge[i].lca;
         if(k) {
             if(num +  < k) puts("invalid request!");
             else printf("%d\n", doit(u, v, k, num, lca));
         }
     }
 }

 int main()
 {
     scanf("%d%d", &n, &m);
     init();
     for(int i = ; i <= n; i++) scanf("%d", a+i);
     for(int i = ; i < n; i++) {
         int u, v;
         scanf("%d%d", &u, &v);
         add(u, v); add(v, u);
     }
     for(int i = ; i < m; i++) {
         int u, v, k;
         scanf("%d%d%d", &k, &u, &v);
         Add(u, v, k); Add(v, u, k);
     }
     dis[] = ;
     tarjan();
     solve();
     return ;
 }