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

hide comments
Aqib Ahmed J: 2016-02-08 14:58:23

Took a while to realize how exactly but AC in one go :) 0.04s !!

bunnycoder: 2016-01-29 22:09:37

Silly error .....
simple bfs traversal

archit saxena: 2016-01-13 06:48:06

done with bfs using 0.03 sec but people might also try solving equation(try on paper and u will get easy graphical solution) mod(x1-x2)+mod(y1-y2)=z;and find the minimum value of z using binary search might work.if it works do comment

dokz: 2016-01-08 14:23:29

Got WA at first, because of input. "then t test cases follow separated by an empty line". Note that there is a new line after every test case.

utkarsh5: 2015-12-22 11:38:19

Can someone provide me some sample test cases, Im getting wrong answer even though my code produces correct answer for all the test cases Ive built so far?

sunil: 2015-11-29 11:44:19

wtf nothing is working neither brute force nor bfs

vedang: 2015-11-27 22:40:26

nice beginner level graph problem...

mdsharique: 2015-10-20 17:47:33

Last edit: 2015-10-27 14:39:10
Advitiya: 2015-10-20 01:35:16

bfs using queue 0.20 AC! :D

agspoj: 2015-09-22 08:58:27

I finally solved it. If someone is interested this is the testcase which caused problem: "1\n4 6\n100001\n100001\n100001\n100001".

Last edit: 2015-10-13 20:36:44

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