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
fuadul_hasan:
20210901 07:08:17
easy one 

kryptonite28:
20210725 14:49:25
input corresponding to the given diagram:


yasser1110:
20210723 12:25:44
Check this test case:


manito:
20210630 08:47:52
why I am getting TLE in lca in binary lifting 

tahoangquan2:
20210328 08:38:18
output of the input below:


sayskar:
20210307 08:08:18
I am getting an RE .... anyone else also facing the same?? 

hackerakhil:
20210204 11:57:45
https://www.spoj.com/submit/LCA/id=27389011


harshiscoding:
20210123 15:13:42
@up_in_smoke ,use if(n===0) break 

princemishra:
20201231 18:35:09
even LCA with O(n) works and rooted at node 1 Last edit: 20201231 18:35:33 

satyamkr118:
20201227 12:35:12
My 100th one!! 
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 