QTREE5 - Query on a tree V


You are given a tree (an acyclic undirected connected graph) with N nodes. The tree nodes are numbered from 1 to N. We define dist(a, b) as the number of edges on the path from node a to node b.

Each node has a color, white or black. All the nodes are black initially.

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

  • 0 i : change the color of i-th node(from black to white, or from white to black).
  • 1 v : ask for the minimum dist(u, v), node u must be white(u can be equal to v). Obviously, as long as node v is white, the result will always be 0.

Input

  • In the first line there is an integer N (N <= 100000)
  • In the next N-1 lines, the i-th line describes the i-th edge: a line with two integers a b denotes an edge between a and b.
  • In the next line, there is an integer Q denotes the number of instructions (Q <= 100000)
  • In the next Q lines, each line contains an instruction "0 i" or "1 v"

Output

For each "1 v" operation, print one integer representing its result. If there is no white node in the tree, you should write "-1".

Example

Input:
10
1 2
1 3
2 4
1 5
1 6
4 7
7 8
5 9
1 10
10
0 6
0 6
0 6
1 3
0 1
0 1
1 3
1 10
1 4
1 6

Output:
2
2
2
3
0


hide comments
Rizvee: 2018-05-10 16:37:48

do O(LogN * LogN) per query get AC ? I am consistently getting TLE. I tried to implement centroid decomposition here.

siva2697: 2018-03-31 15:19:26

BEST QUESTION ON TREES MUST DO. try implementing priority_queue its fun when u get it AC. DID with centroid Decomposition. I wonder how HLD approach would be for this..?

tanavya: 2018-03-05 05:36:29

If anyone wants to learn the algorithm used to solve this problem, read this amazing blog: https://threads-iiith.quora.com/Centroid-Decomposition-of-a-Tree :)
Note: HLD can also be used, but thats a bit more challenging. :)

alejf: 2017-03-03 17:40:07

I'm trying to use a Centroid Decomposition to solve this problem, but still having WA. All the cases i've tested by my own give the right solution, so anyone knows of some border cases??? Thanks.
edit - solved it with cd just an error with the set.

Last edit: 2017-03-08 15:54:36
sinh_ngu_10i: 2017-02-04 06:16:20

Anyone know how to use HLD for this problem ?

Ronak Vaghela: 2016-12-21 23:07:20

Nice Question :-)

Last edit: 2016-12-21 23:07:47
Vadym: 2015-10-17 09:30:09

7 line of statement: "alway" ---> it should be "always"


Added by:Qu Jun
Date:2008-08-13
Time limit:0.714s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:XunYunbo, modified from ZJOI07