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
Ayush Mishra: 2015-01-19 05:17:43

The iterative way to find LCA got me accepted (3.58 s), the similar recurisve function gave TLE! Strange! o.O

Tây Cuồng: 2015-01-19 05:17:43

WA because the Query u u, out 0 but the answer is u... hic :((

S: 2015-01-19 05:17:43

test_cases * Q * N solution passed if implemented efficiently :D

S: 2015-01-19 05:17:43

I used assert and find that the number of test cases are atleast 100 but no more than 150.

S: 2015-01-19 05:17:43

Although i have solved this question but still i would like to know upper_bound on the number of test cases.

Yash Sadhwani: 2015-01-19 05:17:43

take care of tree size........caused me a wa

Last edit: 2014-10-22 00:57:22
hamza007: 2015-01-19 05:17:43

Remember to clear the arrays!! Not doing so caused me a lot of TLEs :/ Damn I am stupid ...

Last edit: 2014-08-05 09:40:17
kelaseek: 2015-01-19 05:17:43

i think my code's complexity is q*(logn+logn) and 2.26s

Tây Cuồng: 2015-01-19 05:17:43

forget to print "CASE C:"... 2WA and AC

tapopadma: 2015-01-19 05:17:43

AC ! in one Go ! :)


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