LCA  Lowest Common Ancestor
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
ipg_2015054:
20171116 13:48:33
Can anyone tell me how the edges are undirected , as if they are then we can take any node as the root node and answer will differ according to the root node taken. 

Bihan Sen:
20171006 09:50:59
AC :) Last edit: 20171006 10:16:43 

smso:
20170818 18:34:30
I got WA because I neglect the 2 points:


triettt:
20170809 04:34:56
nani 

anupamwadhwa:
20170805 22:49:50
Weak test case.. 

vishesh_345:
20170727 09:04:33
I am getting rte with memory usage of 2000M. Please Help. https://ideone.com/SLL4lN. Using lca + rmq(sparse table) 

mrinal_verma:
20170725 21:41:25
can someone plz tell me what is wrong in my code , im using lca+rmq


sonu:
20170615 11:11:29
build >o(n)


rraj001:
20170530 11:03:13
My 100th :)


anupamwadhwa:
20170515 01:10:57
TAKE "1" as ROOT node always.

Added by:  hossamyosef 
Date:  20130513 
Time limit:  0.600s1.113s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  FCIS/ASU Local Contest 2013 