DYNACON1 - Dynamic Tree Connectivity
A forest of unrooted trees initially consists of N (1 ≤ N ≤ 100,000) single-vertex trees. The vertices are numbered from 1 to N.
Your task is to maintain that forest and answer connectivity queries.
All edges in the problem are undirected.
You will receive the following queries, where (1 ≤ A, B ≤ N) :
- add A B : add an edge between vertices A and B, where initially there is no path between A and B.
- rem A B : remove edge between vertices A and B, where initially there is an edge between A and B.
- conn A B : print YES if there is a path between A and B and NO otherwise, where A and B are different.
Input
The first line of input contains the number of initial single-vertex trees N and the number of queries M (1 ≤ M ≤ 100,000). The following M lines contain queries.
Output
For each conn query output YES or NO. Pay attention to letter case.
Example
This example will be the first test case.
Input:
5 11
conn 1 5
add 1 2
add 1 3
add 3 4
add 5 4
conn 1 5
rem 4 5
conn 1 5
rem 3 4
add 3 5
conn 1 5
Output:
NO
YES
NO
YES
hide comments
fabijanb:
2019-02-13 20:31:54
very weak test cases, gives AC with a solution that fails on some easy cases |
|
[Rampage] Blue.Mary:
2016-03-22 16:18:56
Test case is too weak. A silly (LCT-like) brute-force approach can get AC. |
|
bakaniner:
2016-02-24 12:47:33
got AC with Union-Find Sets in 0.07s :) |
|
dacin21:
2015-12-11 18:16:54
Great problem to test my Euler-Tour-Tree implementation (although it's armortized O(M*lg^2(N)) ) based on splay-trees!
|
|
Chiang sheng wen:
2015-12-08 08:29:10
Finally got Accepted with Link/Cut Tree implemented with Treap! |
|
ZiYuan:
2012-08-18 10:55:53
Happy to see the time constraint once became 1600s but now drops to 60s Last edit: 2011-09-26 22:38:17 |
|
:D:
2012-08-18 10:55:53
N*N/8 for N=10^5 is 1.25*10^9. That's over a gigabyte in a single array! Memory limit on SPOJ is 256 MB. Even if it was few GB, I'm not sure the system would be able to allocate that big of a structure. |
|
Bojan Rosko:
2012-08-18 10:55:53
it's giving me sigsegv... I've checked it on ideone.com, and it didn't reported any problems. I have in my code an array of (N*N/8) bytes, but it shouldn't be a problem... |
|
Siarhei Kulik:
2012-08-18 10:55:53
Why the TL is so huge? It seems that even O(M*N) can pass. There is O(M*lg(M)) solution for any kind of undirected graph, not only for trees. Last edit: 2011-09-25 14:50:34 |
|
xiaodao:
2012-08-18 10:55:53
..But this is a unrooted tree..
|
Added by: | indy256 |
Date: | 2011-09-23 |
Time limit: | 2s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: ASM64 |