### Problem Statement#

Given an m x n binary matrix mat, return the distance of the nearest 0 for each cell.

The distance between two adjacent cells is 1.

``````Input: mat = [[0,0,0],[0,1,0],[1,1,1]]
Output: [[0,0,0],[0,1,0],[1,2,1]]
``````

### BFS: Iterative#

``````from collections import deque
class Solution:
def updateMatrix(self, mat: List[List[int]]) -> List[List[int]]:
ROWS, COLS = len(mat), len(mat[0])
"""
* we need to find the distance to the nearest 0
* we know that m >= n >= 1 ~ no need to check dims
* add zeros to queue
* we can change mat
"""
queue = deque()
# Add locations of zero cells to queue with distance of 0
# T: O(N*M)
# S: O(N*M)
for r in range(ROWS):
for c in range(COLS):
if mat[r][c] == 0:
# (row, col, distance)
queue.append((r, c, 0))
else:
mat[r][c] = 10_001
"""
[
[0,0,0],
[0,1,0],
[1,2,1]
]
queue = []

dist = 2
"""
# T: O(N*M)
# S: O(N*M)
while queue:
for _ in range(len(queue)):
ro, co, dist = queue.popleft()
dist += 1

for dr, dc in [(-1,0),(0,1),(1,0),(0,-1)]:
r = ro + dr
c = co + dc

if 0 <= r < ROWS and 0 <= c < COLS and \
mat[r][c] > mat[ro][co] + 1:
mat[r][c] = dist
queue.append((r, c, dist))
return mat
``````

Leetcode 542 01 Matrix