# LeetCode 01: Matrix challenge

Recently, I've solved the "01 Matrix" LeetCode problem and the solution was accepted by the LeetCode OJ:

Given a matrix consists of 0 and 1, find the distance of the nearest 0 for each cell.

The distance between two adjacent cells is 1.

Example:

Input:
0 0 0
0 1 0
1 1 1

Output:
0 0 0
0 1 0
1 2 1


Note:

• The number of elements of the given matrix will not exceed 10,000.
• There are at least one 0 in the given matrix.
• The cells are adjacent in only four directions: up, down, left and right.

The idea behind the solution above is to use Dynamic Programming - starting with 0 cells work outwards putting not processed cells on the queue:

from collections import deque

class Solution(object):
def updateMatrix(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: List[List[int]]
"""
if not matrix:
return matrix

row_length = len(matrix)
col_length = len(matrix)

queue = deque()

# put all 0 cells on queue, set all other cells to a big number
for row_index in range(row_length):
for col_index in range(col_length):
if matrix[row_index][col_index] == 0:
queue.append((row_index, col_index))
else:
matrix[row_index][col_index] = 10000

# work from the 0 cells outwards while the queue is not empty
while queue:
row_index, col_index = queue.popleft()
for i, j in [(row_index - 1, col_index),
(row_index + 1, col_index),
(row_index, col_index - 1),
(row_index, col_index + 1)]:
if 0 <= i < row_length and \
0 <= j < col_length and \
matrix[i][j] > matrix[row_index][col_index] + 1:
matrix[i][j] = matrix[row_index][col_index] + 1
queue.append((i, j))

return matrix


Even though the code works, I am not happy with the readability, in particular:

• setting the non-zero cells to "magical" 10000 does not look good
• getting the cell neighbors and checking if they are not out-of-bounds seems overly complicated

What would you improve code style and organization or time and space complexity wise?

By storing the return value in a different variable and placing the distance in the queue, the magic number can be avoided:

class Solution(object):
def updateMatrix(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: List[List[int]]
"""
if not matrix:
return matrix

row_length = len(matrix)
col_length = len(matrix)

result = [[None for j in range(col_length)] for i in range(row_length)]

queue = deque()

# put all 0 cells in queue, set all other cells to a big number
for row_index in range(row_length):
for col_index in range(col_length):
if 0 == matrix[row_index][col_index]:
queue.append((row_index, col_index, 0))

# work from the 0 cells outwards while the queue is not empty
while queue:
i, j, dist = queue.popleft()
if 0 <= i < row_length and 0 <= j < col_length and result[i][j] is None:
result[i][j] = dist
queue.append((i-1, j, dist+1))
queue.append((i+1, j, dist+1))
queue.append((i, j-1, dist+1))
queue.append((i, j+1, dist+1))

return result