ADASEA - Ada and Island

Ada the Ladybug just read a book from famous author Dobsonfly Daffoedil. It is about Robinson's Cicada, who was flying over sea. Suddenly she had an accident and fell to island below her. Luckily the island was big enough, so she could recover and fly home till Friday night... or something like that.

As Ada was reading through the book, she fell asleep and started dreaming. She was thinking about how lucky the Cicada was, that she fell into such big island. She could have fallen into a smaller one or even to sea.

It keeps bugging her, so she has asked you to tell her the expected size of island, the Cicada will fall to (considering equal probability for all coordinates). Since Ada is not friend of floating point numbers, she wants the answer in some "nice" form.

Island is considered to be union of any '#' characters, which share side.


The first line contains an integer T, the number of test-cases.

Each test-case begins with two integers N, M, 1 ≤ N, M ≤ 1000

Afterward N lines follow, with M characters. Each of the characters is either '#' (island) or '~' (sea).


For each test-case print the expected size of island. Output it as p / q, where p and q has no common divisor. If p / q can be printed as an integer (not as fraction), do so!

Example Input

3 4
3 3
4 5
1 1
4 4

Example Output

7 / 5
9 / 4

hide comments
mahmoud_acm5: 2019-03-26 22:22:20

until now i can't know what do you mean by q / p
what is q and p mean ??

nadstratosfer: 2018-02-04 22:13:20

Too big for Python. Through some antiprogramming I've managed to push my solution past a few more testfiles but my best effort needs over 4.5s on Ideone for a worst-case file. I guess unless Python 4 comes out one day with C-style arrays, there's no fun to be had with big graphs here :(

Edit: Got several ideas while solving other graph problems and.. AC!! Can't believe my Python code gets past 1000x1000 grids.

Last edit: 2018-02-27 20:20:53
kaushalag29: 2018-02-04 10:01:13

@morass: are there spaces between numbers and slash?
Got It..#3 WA because of that..

Last edit: 2018-02-04 13:54:17
roberttz: 2017-12-29 12:40:47

Don't forget to use long long

morass: 2017-04-05 21:51:03

@anonymous: Well: Maximum number of test-cases is "200" and maximum sum of "N*M" is 9498720

anonymous: 2017-04-03 17:44:53

An overall limit on the input size would be nice to have (limit on t or sum of all n*m, etc.)

morass: 2017-02-11 10:28:09

ANNOUNCEMENT: I'm sorry for inconvenience, but I've found wrong input. It shall be hopefully solved now! (my apologies go to "Prec" who tried to solve it with it [sorry])

Last edit: 2017-02-11 10:28:48
morass: 2017-02-11 10:01:55

@Vipul Srivastava: Hope you are right - erasing "Harsh warning" then. Thank you for piloting as first-to-solve ^_^

Vipul Srivastava: 2017-02-11 08:15:28

I think the test cases are right.

Last edit: 2017-02-11 08:23:10

Added by:Morass
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)