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
hitesh87: 2017-10-19 11:45:22

Time limit is huge can be done using brute force with adjacency list.

shubham9261: 2017-09-22 11:21:34

has anybody done it through dp??
recursively traversing the matrix and using memoization,,can anybody suggest something??

suman_biswas95: 2017-08-28 15:10:57

>= does matter

kxingh: 2017-08-21 11:19:06

used brute force AC in 10th go

anurag31: 2017-07-04 15:12:29

bottom up dp rocks....AC in 0.01 sec

sipian: 2017-06-03 22:19:12

a good question

botstar: 2017-05-29 22:43:09

got 15 TLEs....mistake == using iosbase and scnf together...fkcu...c++..

akash619j: 2017-05-29 09:20:25

Little tricky even after you know its bfs!

s407189: 2017-04-03 12:01:56

it could use some more examples. Does it even test for more than one data set ?

vengatesh15: 2017-03-27 12:35:45

AC in 1 go using BFS


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