<p>Given an <code>m x n</code> binary matrix <code>mat</code>, return <em>the distance of the nearest </em><code>0</code><em> for each cell</em>.</p>

<p>The distance between two adjacent cells is <code>1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/24/01-1-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> mat = [[0,0,0],[0,1,0],[0,0,0]]
<strong>Output:</strong> [[0,0,0],[0,1,0],[0,0,0]]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/24/01-2-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> mat = [[0,0,0],[0,1,0],[1,1,1]]
<strong>Output:</strong> [[0,0,0],[0,1,0],[1,2,1]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>4</sup></code></li>
	<li><code>mat[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
	<li>There is at least one <code>0</code> in <code>mat</code>.</li>
</ul>

from collections import deque
from typing import List

class Solution:
    def updateMatrix(self, mat: List[List[int]]) -> List[List[int]]:
        rows,columns = len(mat),len(mat[0])
        queue = deque()
        dist = [[float('inf')]*columns for _ in range(rows)]
        for i in range(rows):
            for j in range(columns):
                if mat[i][j] == 0:
                    dist[i][j] = 0
                    queue.append((i,j))
        dir = [(1,0),(0,1),(-1,0),(0,-1)]
        while queue:
            r,c = queue.popleft()
            for dr,dc in dir:
                nr,nc = r+dr,c+dc
                if 0<=nr<rows and 0<=nc<columns:
                    if dist[nr][nc] > dist[r][c] + 1:
                        dist[nr][nc] = dist[r][c] + 1
                        queue.append((nr, nc))

        return dist


        
19600