LABYR1 - Labyrinth


The northern part of the Pyramid contains a very large and complicated labyrinth. The labyrinth is divided into square blocks, each of them either filled by rock, or free. There is also a little hook on the floor in the center of every free block. The ACM have found that two of the hooks must be connected by a rope that runs through the hooks in every block on the path between the connected ones. When the rope is fastened, a secret door opens. The problem is that we do not know which hooks to connect. That means also that the neccessary length of the rope is unknown. Your task is to determine the maximum length of the rope we could need for a given labyrinth.

Input

The input consists of T test cases. The number of them (T) is given on the first line of the input file. Each test case begins with a line containing two integers C and R (3 <= C,R <= 1000) indicating the number of columns and rows. Then exactly R lines follow, each containing C characters. These characters specify the labyrinth. Each of them is either a hash mark (#) or a period (.). Hash marks represent rocks, periods are free blocks. It is possible to walk between neighbouring blocks only, where neighbouring blocks are blocks sharing a common side. We cannot walk diagonally and we cannot step out of the labyrinth.

The labyrinth is designed in such a way that there is exactly one path between any two free blocks. Consequently, if we find the proper hooks to connect, it is easy to find the right path connecting them.

Output

Your program must print exactly one line of output for each test case. The line must contain the sentence "Maximum rope length is X." where Xis the length of the longest path between any two free blocks, measured in blocks.

Example

Sample Input:
2
3 3
###
#.#
###
7 6
#######
#.#.###
#.#.###
#.#.#.#
#.....#
#######

Sample output:
Maximum rope length is 0.
Maximum rope length is 8.
Warning: large Input/Output data, be careful with certain languages

hide comments
dec0dedd: 2020-12-29 21:41:06

Well, that was a really bad problem considering that a programm which couldn't even pass basic test case like that one got AC:

<invalid case removed>

[NG]: "The labyrinth is designed in such a way that there is exactly one path between any two free blocks."

Last edit: 2020-12-30 00:44:25
s_triker9: 2020-12-28 19:02:51

I have tried DFS twice but still, I am not able to figure out the mistake in the code. Any ideas :(
<snip>

[NG]: Use forum for code review & discussion.

[s_triker9]: Ahh! There was a silly mistake. Figured it out. Thank you :)

Last edit: 2020-12-29 07:40:02
bhargav_07: 2020-11-21 14:19:38

Hi, can anyone provide the solution in Python3, I have tried nearly 20 times but getting run time error.

Last edit: 2020-11-21 14:20:11
sachin_19: 2020-10-13 14:21:56

Apply BFS (or DFS) on any (.) block to find the block(where the longest path from start ends). Lets call that block as diameter end.
again use BFS(or DFS) on diameter end block and find max length

tarun_28: 2020-09-21 13:05:27

Use DFS twice

vee_nits123: 2020-09-16 18:42:51

calculate diameter of the tree :)

jrseinc: 2020-08-20 08:51:39

I'm confused about the second test case they have provided. It is clearly visible that the max length should be 9 but the testcase's answer is 8. Can anyone explain this?

Edit: It was my mistake it is actually 8. Think closely and you will figure it out. And also make sure the input format gives Col first then Row.

Last edit: 2020-08-20 09:02:20
robosapien: 2020-05-28 21:36:30

How are some of the submissions so fast?

ankit_code2799: 2020-03-29 14:50:19

AC in one go. Use map and DFS for simplicity.

varuntumbe: 2020-03-27 07:19:41

How can i convert this matrix data in to adjacency list representation ?
Thanks in advance


Added by:adrian
Date:2004-06-06
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:ACM Central European Programming Contest, Prague 1999