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
wslord: 2020-12-29 21:05:32

Loved this question.... Take care, priority queue is not needed ;)

kanishkverma_1: 2020-11-17 17:29:49

If ur having NZEC in java then try the same solution in c++ . Worked like a charm for me. :P

varuntumbe: 2020-10-23 10:01:08

one good optimization is needed in multi source bfs. calculate the no of iterations and compare.

gnomegeek: 2020-08-04 23:42:49

No need to use BFS. Applyting Brute Force works. AC in one go.

satish7978: 2020-07-06 23:14:47

waah. multisource bfs is best.

akt_114: 2020-06-19 21:44:06

AC in one go ! Multisource BFS :)

egor091: 2020-06-19 16:45:24

AC in one go

yash_999: 2020-06-16 10:03:06

can be done without multisource bfs using only bfs shortest path with a little optimization ran in 0.5 s
although using multisource bfs ran in 0.03 s

Last edit: 2020-06-16 10:24:13
gaur_gaur: 2020-05-31 08:44:05

simple mutisource bfs question :)

joaoabrantes: 2020-05-28 14:52:57

Please take care after output each test, you need to read a empty line after every output, otherwise you gonna get RE


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