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
starboy_jb: 2019-09-21 15:27:39

the constraint of n is wrong.

codeblooded20: 2019-07-19 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: 2019-07-14 11:25:50

Binary Lifting C++ 0.03 nice

arjun_9426: 2019-07-09 05:31:54

using binary lifting in 0.06sec

rohanku_537: 2019-07-02 10:32:53

AC in one go....using array implementation like union find

pratham_1: 2019-06-19 16:04:42

AC with HLD in 0.36s using Java ;)

toolatetostart: 2019-06-04 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: 2019-06-02 22:47:33

Last edit: 2019-06-02 23:43:55
kanna_3: 2019-03-24 04:44:33

HLD 0.22s
RMQ 0.18s

Last edit: 2019-03-24 04:46:15
ab_biswas09: 2019-03-19 22:11:46

NAIVE : 0.41
SQRT : 0.22
Bin Lifting : 0.20
RMQ remains


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