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
darkhire21: 2016-04-19 16:20:36

try same problem on codechef for better testcases -> https://www.codechef.com/problems/TALCA

darkhire21: 2016-04-19 15:10:01

Last edit: 2016-04-19 16:20:49
vipul: 2016-03-30 21:23:49

done using sparse table and without sparse table.time limit is enough to get AC with complexity o(t*q*n).

sprof: 2016-02-19 14:10:08

if someone has ac with tarjan offline ,please , give me code on mail sabashavidze@gmail.com thanks.

Last edit: 2016-02-19 14:10:48
Shivam Pandey: 2016-01-28 15:10:05

Nice Problem :)

Last edit: 2016-01-28 15:10:51
maverick_10: 2015-12-29 23:19:20

Wikipedia article is quite helpful!

rk: 2015-12-09 21:58:09

finally done :)

Last edit: 2015-12-09 21:58:59
Afrizal: 2015-09-30 18:19:09

no need to use tarjan offline. and yet there is no significant time difference between those 2 (0.06s for both)

Saurabh Sameer: 2015-09-19 15:37:07

AC in first go :)

:.Mohib.:: 2015-09-18 13:18:56

Nice one..!!


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