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
fuadul_hasan: 2021-09-01 07:08:17

easy one

kryptonite28: 2021-07-25 14:49:25

input corresponding to the given diagram:
13
3 2 3 4
0
3 5 6 7
0
0
2 8 9
2 10 11
0
0
2 12 13
0
0
0

yasser1110: 2021-07-23 12:25:44

Check this test case:-
Input
1
1
0
1
1 1
Output
1

manito: 2021-06-30 08:47:52

why I am getting TLE in lca in binary lifting

tahoangquan2: 2021-03-28 08:38:18

output of the input below:
Case 1:
1
1
3
3
3
3
3
Case 2:
1
Case 3:
3
6
1
7

sayskar: 2021-03-07 08:08:18

I am getting an RE .... anyone else also facing the same??

hackerakhil: 2021-02-04 11:57:45

https://www.spoj.com/submit/LCA/id=27389011
Please help i am getting runtime error i have changes constraint of N to 1005,10005,100005 but getting runtime error in all please help me out. Thankx in advance

harshiscoding: 2021-01-23 15:13:42

@up_in_smoke ,use if(n===0) break

princemishra: 2020-12-31 18:35:09

even LCA with O(n) works and rooted at node 1

Last edit: 2020-12-31 18:35:33
satyamkr118: 2020-12-27 12:35:12

My 100th 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