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
ahmet25:
2019-12-26 21:36:54
euler tour+segment tree works 0.05s ~ 26mb |
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wolf3h2h2:
2019-12-19 00:27:59
if you are getting wa check this case
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starboy_jb:
2019-09-21 15:27:39
the constraint of n is wrong. |
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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. |
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prismbreak1155:
2019-07-14 11:25:50
Binary Lifting C++ 0.03 nice |
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arjun_9426:
2019-07-09 05:31:54
using binary lifting in 0.06sec |
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rohanku_537:
2019-07-02 10:32:53
AC in one go....using array implementation like union find |
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pratham_1:
2019-06-19 16:04:42
AC with HLD in 0.36s using Java ;) |
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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 |
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islingr:
2019-06-02 22:47:33
Last edit: 2019-06-02 23:43:55 |
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 |