主席树(应用)
主席树(应用)
【树上主席树】：
You are given a tree with N nodes. The tree nodes are numbered from 1 to N. Each node has an integer weight.
We will ask you to perform the following operation:
u v k : ask for the kth minimum weight on the path from node u to node v
Input
In the first line there are two integers N and M. (N, M <= 100000)
In the second line there are N integers. The ith integer denotes the weight of the ith node.
In the next N-1 lines, each line contains two integers u v, which describes an edge (u, v).
In the next M lines, each line contains three integers u v k, which means an operation asking for the kth minimum weight on the path from node u to node v.
Output
For each operation, print its result.
Example Input:
8 5
105 2 9 3 8 5 7 7
1 2
1 3
1 4
3 5
3 6
3 7
4 8
2 5 1
2 5 2
2 5 3
2 5 4
7 8 2
Example Output:
2
8
9
105
7
题目分析：
按照树的DFS顺序建立主席树，设x，y点对应的主席树为 T r e e x , T r e e y Tree_x,Tree_y Treex,Treey，由于主席数搭载是按照树的DFS顺序，为了获取x到y上的结点信息我们可以这样做： T r e e x + T r e e y − T r e e L C A ( x , y ) − T r e e f a [ L C A ( x , y ) ] Tree_x+Tree_y-Tree_{LCA(x,y)}-Tree_{fa[LCA(x,y)]} Treex+Treey−TreeLCA(x,y)−Treefa[LCA(x,y)]。
所以这题为LCA+主席树。
代码：
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