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
Shivam Pandey:
2016-01-28 15:10:05
Nice Problem :) Last edit: 2016-01-28 15:10:51 |
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maverick_10:
2015-12-29 23:19:20
Wikipedia article is quite helpful! |
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rk:
2015-12-09 21:58:09
finally done :) Last edit: 2015-12-09 21:58:59 |
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Afrizal:
2015-09-30 18:19:09
no need to use tarjan offline. and yet there is no significant time difference between those 2 (0.06s for both) |
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Saurabh Sameer:
2015-09-19 15:37:07
AC in first go :)
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:.Mohib.::
2015-09-18 13:18:56
Nice one..!! |
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shubham7iitj:
2015-09-16 12:50:50
c in case is capital, cost me 2 WA's :( |
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SangKuan:
2015-08-21 11:12:02
0.26s...why someone use O(logn) got tle |
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SangKuan:
2015-08-21 11:09:55
per Q is O(2n) ac Last edit: 2015-08-21 11:15:10 |
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harkirat:
2015-07-10 08:23:05
Ac in first 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 |