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
masterchef2209: 2018-12-02 17:09:08

AC in 1 go :D

The way i solved this is by storing the pair of indices of all cells where value is 1;
and than iterating on array and checking distance of current cell with all points with '1' and saving minimum. solution is O(n^3) but n is small so it works.

manishjoshi394: 2018-11-07 08:48:08

Do a Multi-source bfs from white pixels, it works like a charm!

harry_shit: 2018-11-02 14:12:11

why tle for bfs??

devninja8: 2018-10-17 08:21:13

DO NOT LISTEN TO OTHERS WHILE SOLVING PROBLEM....everyone was saying multisource bfs and i feared cause i have not even heard of that .............i applied simple bfs approach and it got accepted...so ddont listen to anyone else and keep solving your problem....hAPPY Coding!!

sachinspoj: 2018-10-08 02:36:48

Use multisource bfs :)
else you will get TLE
Visited array not required.

vjvjain0: 2018-10-05 18:16:22

input can be:
1
3 4
0001
0011
0110

or
1
3 4
0 0 0 1
0 0 1 1
0 1 1 0

jmr99: 2018-09-27 13:40:35

multisource BFS do the job.

abdelhameedddd: 2018-07-23 03:52:27

ac

rohitnarayan: 2018-07-01 15:57:25

hint - use multisource BFS!! :-)

rajcoolaryan: 2018-06-28 12:32:02

ac in one go
bfs rocks...


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