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
starboy_jb:
20190921 15:27:39
the constraint of n is wrong. 

codeblooded20:
20190719 23:43:57
AC :) If you are using 2D vector for adjacency list, make sure that you are clearing it for every test case... Cost me 3 times TLE. 

prismbreak1155:
20190714 11:25:50
Binary Lifting C++ 0.03 nice 

arjun_9426:
20190709 05:31:54
using binary lifting in 0.06sec 

rohanku_537:
20190702 10:32:53
AC in one go....using array implementation like union find 

pratham_1:
20190619 16:04:42
AC with HLD in 0.36s using Java ;) 

toolatetostart:
20190604 20:38:22
my code is getting tle in c++,approach setting parent nodes then visiting from node u to root and making all visited,similarily for node v and stop when encounter a vissited node 

islingr:
20190602 22:47:33
Last edit: 20190602 23:43:55 

kanna_3:
20190324 04:44:33
HLD 0.22s


ab_biswas09:
20190319 22:11:46
NAIVE : 0.41

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 