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...N1. 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 kth 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 4th 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 N1 lines, the ith line describes the ith 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
ppap_1264589:
20210915 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'


sarkybastard:
20200924 23:41:48
@ sanjitpd_777. its good to know yourself, but really, nobody cares. 

sanjitpd_777:
20200908 06:46:13
I'm a homo Last edit: 20200908 11:28:33 

mhasan01:
20200710 00:46:46
Nice, used HLD, although binary lifting would probably be better 

tarungupta:
20200621 06:43:11
A must do question to learn LCA. Last edit: 20200621 06:43:28 

saurabhshadow:
20200513 19:13:04
Updated: AC


black_shroud:
20200509 15:14:03
just check your preprocessing fn if you are getting segmentation fault 

shahayush457:
20200425 10:36:47
Easy but good problem :) 

an09mous:
20200311 17:31:40
Did it using binary lifting. A must do problem if you're learning LCA. 

fayedanik:
20200222 15:48:43
Updated:AC

Added by:  ThanhVy Hua 
Date:  20060827 
Time limit:  1s 
Source limit:  15000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Special thanks to Ivan Krasilnikov for his alternative solution 