BITMAP - Bitmap

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There is given a rectangular bitmap of size n*m. Each pixel of the bitmap is either white or black, but at least one is white. The pixel in i-th line and j-th column is called the pixel (i,j). The distance between two pixels p1=(i1,j1) and p2=(i2,j2) is defined as:

d(p1,p2)=|i1-i2|+|j1-j2|.

Task

Write a program which:

  • reads the description of the bitmap from the standard input,
  • for each pixel, computes the distance to the nearest white pixel,
  • writes the results to the standard output.

Input

The number of test cases t is in the first line of input, then t test cases follow separated by an empty line. In the first line of each test case there is a pair of integer numbers n, m separated by a single space, 1<=n <=182, 1<=m<=182. In each of the following n lines of the test case exactly one zero-one word of length m, the description of one line of the bitmap, is written. On the j-th position in the line (i+1), 1 <= i <= n, 1 <= j <= m, is '1' if, and only if the pixel (i,j) is white.

Output

In the i-th line for each test case, 1<=i<=n, there should be written m integers f(i,1),...,f(i,m) separated by single spaces, where f(i,j) is the distance from the pixel (i,j) to the nearest white pixel.

Example

Sample input:
1
3 4
0001
0011
0110

Sample output:
3 2 1 0
2 1 0 0
1 0 0 1

Added by:Piotr Ɓowiec
Date:2004-09-13
Time limit:4s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel Pentium G860 3GHz)
Languages:All except: SCM chicken
Resource:6th Polish Olympiad in Informatics, stage 2

hide comments
Rachit: 2015-03-15 12:44:42

" but at least one is white "
@David

David: 2015-03-03 00:53:34

What if there are no white pixels in the bitmap, what should I print?

scyther: 2015-01-27 13:10:35

you just need one word to understand the ques: minesweeper

Last edit: 2015-01-27 13:12:46
the_imp: 2015-01-24 17:48:08

getting sigxfsz runtime error .....somebody plz help
*********
--edit(Francky)--> Please see the notes below.
Notes:
1. Don't post any source code here.
--edit
sorry about that but can u help me as to why i might be getting that error...

Last edit: 2015-01-24 20:02:01
Arafat dad Khan: 2015-01-22 17:54:01

A brilliant problem with a brilliant solution--- Absolutely loved it

Rajat (1307086): 2015-01-22 13:42:27

Exactly @ Master_Card

Francky: 2015-01-02 14:14:34

Is anybody have old Pyramid best timings ? I don't remember my own best time. I think there were several near 0.01s too with Pyramid.

Kishlay Raj: 2015-01-02 09:55:26

hw can one solve this in 0.0 , _/\_

Master_Card: 2014-10-10 12:21:53

Very good question!!

Jagatheesvaran Palanisamy: 2013-03-26 10:12:34

@reggaeguitar:
Each of these n lines has length m and contains 0 and/or 1's.

Last edit: 2014-08-18 18:08:57