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
robosapien:
20200603 13:21:24
Naive LCA : 0.38s :) 

brandonbreyers:
20200527 11:21:06
I am getting SIGABRT error by using euler tour +rmq


pirate_joker1:
20200525 09:03:26
Important:


manimanimani:
20200515 21:29:24
probably the best problem for learning LCA! 

shrey_devep:
20200514 15:51:33
Take Care of long long and for binary lifting intialisation of 2D lifting array Last edit: 20200514 16:09:37 

nayeem_joy:
20200422 21:31:33
Solved by LCA with both sparse table and rmq && sparse table and binary lifting technique Last edit: 20200423 16:43:03 

abid_jawad:
20200403 21:35:49
maybe the constraint of N is wrong in the question, got wa, then simply submitted again by increasing the value of n, got ac 

fahimcp495:
20200331 21:43:17
Required time for various technique using fast I/O:


bhavyarustgi10:
20200331 08:00:17
What root we have to consider 

sagsango:
20200330 14:03:48
Try it :) https://www.codechef.com/problems/TALCA

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 