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 perfrom 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

hide comments
an09mous: 2020-03-11 17:31:40

Did it using binary lifting. A must do problem if you're learning LCA.

fayedanik: 2020-02-22 15:48:43

Updated:AC
I don't know why i am getting wrong answer probably not even passed the sample test case. But running in local machine my code gives right output. Can anybody help me please?

Last edit: 2020-02-22 16:58:08
hkyiitd: 2019-08-03 09:02:01

Don't forget to print one blank line after each test case.

viskey: 2019-05-22 22:16:44

Easy to solve with sqrt decompostion, as there are no updates.

tarungupta: 2019-04-11 10:33:26

Don't forget to clear graph before each test case, if taken globally. Costed me many WA. :/
Binary Lifting implementation works.

vickyand_27: 2019-02-04 19:08:54

Took sosoo long

hacker_sk: 2018-12-29 23:17:51

No need to use long long, int is enough.

alucard_01: 2018-12-24 06:50:25

just use binary lifting

Last edit: 2018-12-24 08:01:13
lamia2658: 2018-11-13 20:16:11

a must do LCA problem after learning

vaishcr7: 2018-08-01 13:18:40

i am getting nzec error in this , i have tried taking input in many different ways. Is anybody else also facing the same problem ?


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