BTCODE_G - Coloring Trees

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Nivash and Bhoopathi play a game of memory, which goes as follows: There is a tree containing 'N' nodes, all of which are initially uncoloured. In the game, Nivash has 2 moves:

1) Command: Color a particular node with a given color.
2) Query: Ask Bhoopathi if the path from node 'a' to node 'b' (both inclusive), is monochromatic or not.(i.e Whether all nodes on the path have the same color).

Nivash can do these steps in any order he wishes and he colors each node atmost once. Whenever Nivash puts forth a 'Query' at Bhoopathi, Bhoopathi has to recollect the colouring of the tree and reply either "YES" or "NO". Can your help Bhoopathi answer these queries?

Input

The first line of input contains an integer 'N', denoting the number of nodes in the tree. The next 'N-1' lines contain 2 space separated integers 'u' and 'v', denoting an edge between vertex 'u' and vertex 'v'.
The next line contains an integer 'Q', denoting the number of inputs (commands and queries) which Nivash wants to give. The next 'Q' lines contain 3 space separated integers 'x', 'a', 'b'. If 'x' is 1, it denotes a command to color node 'a' with a color 'b'. If 'x' is 2, it denotes a query and Bhoopathi should answer if the path from node 'a' to node 'b' (both inclusive), is monochromatic or not.

All vertices of the tree are 0 based.

Output

For each query, output "YES" or "NO" (quotes for clarity), denoting whether the path from node 'a' to node 'b' (both inclusive), is monochromatic or not.

Output "NO", even if all nodes on the path from node 'a' to node 'b' (both inclusive) are uncolored.

Example

Input:
3
0 1
1 2
7
1 0 11
2 0 1
2 0 2
1 2 12
1 1 11
2 0 1
2 0 2

Output:
NO
NO
YES
NO

Constraints:
1 <= N <= 100000 
1 <= Q <= 200000
1 <= color value <= 30.

Explanation:

Initially node '0' is colored with color '11', so path between node '0' and node '1' is not monochromatic. Hence, the answer is "NO". The same explanation holds for the path between node '0' and node '2'. Then node '2' is colored with color '12' and node '1' with color '11'. Now, all nodes on the path between node '0' and node '1' are colored with only one color ('11'), so the answer is "YES". The path between node '0' and node '2' has 2 colors ('11' and '12'), hence the answer is "NO".


hide comments
DK...: 2019-04-18 02:27:59

I got AC with a simple hld

kshubham02: 2018-10-22 12:19:02

O(Q lg^2 N) fails with fast I/O. Is there any way to optimise HLD-based approach?

spojabhi: 2018-06-19 16:58:17

use simple DSU :}

sifat_15: 2018-05-20 16:52:50

AC in one go! Just figure out Which method should be used!

Last edit: 2018-05-20 16:53:11
julkas: 2017-12-03 12:45:34

Great problem. I suggest also https://www.hackerrank.com/challenges/kundu-and-tree/problem

Last edit: 2017-12-09 12:44:51
Rezaul H Sagar: 2017-10-01 17:10:07

how to optimize HLD?

yogahmad: 2017-08-03 14:57:44

very strict time limit, even HLD solution gives TLE.

EDIT: Needs a little of optimization to AC

Last edit: 2017-08-03 15:03:27
siddharth_0196: 2017-06-10 20:06:56

Last edit: 2017-06-10 20:30:33
conquistador: 2017-05-17 22:01:13

@siddharth @ganda @mohit @banka optimise in every way possible to get AC . I got with 0.36

shubham2305: 2017-05-12 14:35:42

Time limit got strict. I earlier got AC with 0.35 sec but now TLE


Added by:suhash
Date:2011-02-26
Time limit:0.207s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Bytecode 2011, NIT Trichy, India