LCA - Lowest Common Ancestor

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A tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree. - Wikipedia 

The lowest common ancestor (LCA) is a concept in graph theory and computer science. Let T be a rooted tree with N nodes. The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself). - Wikipedia

Your task in this problem is to find the LCA of any two given nodes v and w in a given tree T.

For example the LCA of nodes 9 and 12 in this tree is the node number 3.

Input

The first line of input will be the number of test cases. Each test case will start with a number N the number of nodes in the tree, 1 <= N <= 1,000. Nodes are numbered from 1 to N. The next N lines each one will start with a number M the number of child nodes of the Nth node, 0 <= M <= 999 followed by M numbers the child nodes of the Nth node. The next line will be a number Q the number of queries you have to answer for the given tree T, 1 <= Q <= 1000. The next Q lines each one will have two number v and w in which you have to find the LCA of v and w in T, 1 <= v, w <= 1,000.

Input will guarantee that there is only one root and no cycles.

Output

For each test case print Q + 1 lines, The first line will have “Case C:” without quotes where C is the case number starting with 1. The next Q lines should be the LCA of the given v and w respectively.

Example

Input:
1
7
3 2 3 4
0
3 5 6 7
0
0
0
0
2
5 7
2 7

Output:
Case 1:
3
1

hide comments
Abhinav92003: 2015-01-19 05:17:43

Solution accepted! Thanks for the question :)

Last edit: 2013-12-12 14:08:55
NnN: 2015-01-19 05:17:43

got my mistake...working on it...isnt as simple as it seems..

Last edit: 2013-09-02 18:41:00
Amit RC: 2015-01-19 05:17:43

got WA for not writing case!!And spent 30 mins debugging code!!!....nd ya brute force does work here.

Kevin Sebastian: 2015-01-19 05:17:43

pls tell the correct format of output..wen shud each line come

Kevin Sebastian: 2015-01-19 05:17:43

@author please tell me what is wrong with my code getting WA

Pragya Mishra: 2015-01-19 05:17:43

read the question carefully... ;) if u missd anything u will be in hell trouble..
n get TLEs... :P

$!:D: 2015-01-19 05:17:43

@Akash thnxx got AC :)

i ws making my vector array elements set to 0 resulting in TLE
but gt accepted on c++4.3.2
c++4.0.8 gve tle for it :P

Last edit: 2013-06-11 07:57:39
Ouditchya Sinha: 2015-01-19 05:17:43

Finally AC... :)

Last edit: 2013-10-20 12:48:07
Akash: 2015-01-19 05:17:43

@$!:D I did it the same way u did..my solution is accepted..the only problem i found out is that u have printed "Case t" which always gives number of test cases and not the case number..and u have printed it before taking u and v input..try submitting it after correcting this error..and try compiling it with 4.0.0.8 bcos sometimes 4.3.2 gives compilation error or TLE but it compiles with another compiler

Last edit: 2013-06-07 04:37:04

Added by:hossamyosef
Date:2013-05-13
Time limit:0.600s-1.113s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:FCIS/ASU Local Contest 2013