<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>

class Solution {
public:
    vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {
        int n = mat.size(), m = mat[0].size();
        std::queue<std::pair<int,int>> q;
        std::vector<std::vector<bool>> vis(n, std::vector<bool>(m, false));
        int cnt = 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (mat[i][j] == 0) continue;
                if (i > 0 && mat[i-1][j] == 0) { q.push({i, j}); vis[i][j] = true; continue; }
                if (i < n - 1 && mat[i+1][j] == 0) { q.push({i, j}); vis[i][j] = true; continue; }
                if (j > 0 && mat[i][j-1] == 0) { q.push({i, j}); vis[i][j] = true; continue; }
                if (j < m - 1 && mat[i][j+1] == 0) { q.push({i, j}); vis[i][j] = true; continue; }
            }
        }
        while (q.size()) {
            int q_len = q.size();
            cnt++;
            for (int i = 0; i < q_len; i++) {
                auto [row, col] = q.front(); q.pop();
                if (row > 0 && mat[row-1][col] == 1 && !vis[row-1][col]) {
                    mat[row-1][col] = cnt;
                    vis[row-1][col] = true;
                    q.push({row-1,col});
                }
                if (row < n - 1 && mat[row+1][col] == 1 && !vis[row+1][col]) {
                    mat[row+1][col] = cnt;
                    vis[row+1][col] = true;
                    q.push({row+1,col});
                }
                if (col > 0 && mat[row][col-1] == 1 && !vis[row][col-1]) {
                    mat[row][col-1] = cnt;
                    vis[row][col-1] = true;
                    q.push({row,col-1});
                }
                if (col < m - 1 && mat[row][col+1] == 1 && !vis[row][col+1]) {
                    mat[row][col+1] = cnt;
                    vis[row][col+1] = true;
                    q.push({row,col+1});
                }
            }
        }
        return mat;
    }
};
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