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
Mayank Ladia: 2015-07-08 16:43:23

Am getting SIGFPE error ? Can someone let me know why its so ?

xxbloodysantaxx: 2015-07-05 13:31:46

They should start writing "Print the case number " too. I am sick of getting WA due to that ....

sourabh: 2015-06-26 14:40:49

Has any one submitted by using spare table ??

ftftfttfat: 2015-05-08 17:05:08

> is node 1 always a root?
@fanatique, yes, root is always node 1.

I got AC, assuming that root may vary. Then, submitted the same code but removed the "search for root" part and assumed root is node 1. I still got AC.

Last edit: 2015-05-08 17:08:59
sai krishna: 2015-03-23 06:25:00

got AC with dp

Siddharth Singh: 2015-03-16 18:33:14

Runtime error , Really Don't Know whats wrong ,AC on LCASQ

Tushar Sinha: 2015-02-21 20:27:28

3 WA due to case :x

fanatique: 2015-01-24 13:40:02

is node 1 always a root?

AKASH GOEL: 2015-01-19 05:17:43

nice one

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

Ohh! It turns out that cin is slower than scanf. Scanf on the previous recursive code got accepted, whereas cin gives TLE


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