Sphere Online Judge

SPOJ Problem Set (classical)

206. Bitmap

Problem code: BITMAP

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:



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.


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.


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.


Sample input:
3 4

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

Added by:Piotr £owiec
Time limit:4s
Source limit:50000B
Memory limit:256MB
Cluster: Pyramid (Intel Pentium III 733 MHz)
Resource:6th Polish Olympiad in Informatics, stage 2

hide comments
2014-07-19 17:36:51 Darren Sun
Good problem. Some optimization needed to overcome TLE
2014-06-26 22:09:41 prakhar
Good one..finally subitted aftr lots of tle.... :D
2014-06-26 12:37:34 Mohan K
the next step from (i,j) , at some instance of time are :
(i,j-1) .. #question nt very clear about this..
2014-02-28 21:27:39 Diana Gonzalez
TLE in python 2.7. Any hint???
--ans(francky)--> There's only one py2.7 visible AC, others are old py+psyco ones (36MB of memory print). You can see in Py3.2, there's only 2 AC ; it is a sign that it is hard to get AC in python here. Good luck.

Last edit: 2014-02-28 21:50:17
2014-02-02 09:49:05 mad
very nice question..learned some new things
2014-01-21 19:31:37 siddhant gupta
Awesome ques..:)
2014-01-11 23:43:41 Martijn Muijsers
That feeling when the only solution you can think of is horrible and you get AC :P

Last edit: 2014-01-11 23:43:51
2014-01-08 19:56:46 rabee
is there any empty line at the end of each test case and at the end of all test case ...
2013-03-26 10:12:34 Jagatheesvaran Palanisamy
Each of these n lines has length m and contains 0 and/or 1's.

Last edit: 2014-08-18 18:08:57
2013-02-22 22:00:32 reggaeguitar
Can someone please make this sentence more comprehensible "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"

Last edit: 2013-02-22 22:00:50
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