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
Resource:6th Polish Olympiad in Informatics, stage 2

hide comments
monkz: 2015-07-31 17:56:57

will O(n^3) solution work??

Vikrant Singh: 2015-07-26 18:19:57

@Ashish
Brute Force, really ?

Ashish: 2015-07-08 15:21:58

Can be done by simple brute force! I will try doing it by BFS though.

shravinson: 2015-07-08 13:38:40

it is giving WA
my code : https://ideone.com/U8VWi3

satyam0542: 2015-07-05 11:43:21

make sure you are taking input of white and black spaces as a character..it costed me 3 wa.

tropicalsurf: 2015-06-27 16:11:05

The input specification is ambiguous: "t test cases follow separated by an empty line"
This could mean that the empty line is after all of the test cases. But apparently it is after each test case.
I would suggest changing the wording, e.g., "t test cases, each of which is followed by an empty line"

Last edit: 2015-06-27 16:11:22
Mayank Jethva: 2015-06-16 16:37:22

Good concept recognition question

SangKuan: 2015-06-16 09:02:58

use bfs.and be care of the index of array

Last edit: 2015-06-16 10:11:48
Rakesh: 2015-06-14 22:12:43

My first with dp using iteration...

reggaeguitar: 2015-04-29 16:59:33

"here 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." See the last part of the sentence, "at least one is white"