QTREE2 - Query on a tree II

You are given a tree (an undirected acyclic connected graph) with N nodes, and edges numbered 1, 2, 3 ...N-1. Each edge has an integer value assigned to it, representing its length.

We will ask you to perform some instructions of the following form:

  • DIST a b : ask for the distance between node a and node b
    or
  • KTH a b k : ask for the k-th node on the path from node a to node b

Example:
N = 6
1 2 1 // edge connects node 1 and node 2 has cost 1
2 4 1
2 5 2
1 3 1
3 6 2

Path from node 4 to node 6 is 4 → 2 → 1 → 3 → 6
DIST 4 6 : answer is 5 (1 + 1 + 1 + 2 = 5)
KTH 4 6 4 : answer is 3 (the 4-th node on the path from node 4 to node 6 is 3)

Input

The first line of input contains an integer t, the number of test cases (t <= 25). t test cases follow.

For each test case:

  • In the first line there is an integer N (N <= 10000)
  • In the next N-1 lines, the i-th line describes the i-th edge: a line with three integers a b c denotes an edge between a, b of cost c (c <= 100000)
  • The next lines contain instructions "DIST a b" or "KTH a b k"
  • The end of each test case is signified by the string "DONE".

There is one blank line between successive tests.

Output

For each "DIST" or "KTH" operation, write one integer representing its result.

Print one blank line after each test.

Example

Input:
1

6
1 2 1
2 4 1
2 5 2
1 3 1
3 6 2
DIST 4 6
KTH 4 6 4
DONE

Output:
5
3

Added by:Thanh-Vy Hua
Date:2006-08-27
Time limit:1s
Source limit:15000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Special thanks to Ivan Krasilnikov for his alternative solution

hide comments
2024-08-24 20:10:06
I just spent a whole hour to figure out I'd done (a << i) instead of (1 << i) when doing the binary lifting :(
2024-07-27 13:36:35
use tarnary lifting + log decomposition
ez problem (ac in one go)
2024-07-27 13:35:49
use sqrt decomposition + sparse desk
2024-05-28 20:04:44
i am getting the wrong answer but i dont know why
2023-10-02 16:48:05
Very easy just LCA
2023-09-14 10:16:47
easy one
2023-05-23 10:59:23
DANG , this sounds hard as hell
2022-08-18 07:28:51
what is the root of the tree ?
2021-11-08 14:37:28
How can I get the data of this problem ?
I have got so many WA , but still unable to find my mistake :-(
2021-09-15 19:04:07
If you use LCA for this problem, remember to check if 'a' and 'b' in a same branch and 'a' is closer to the root than 'b'
This case cost me some WA .-.
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