<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) {
        vector<vector<int>> dst(mat.size(), vector<int>(mat[0].size(), 0));

        std::queue<vector<int>> steps;
        for (int i = 0; i < mat.size(); ++i) {
            for (int j = 0; j < mat[0].size(); ++j) {
                if (mat[i][j] != 1) continue;
                if (isValid(mat, i - 1, j) && mat[i - 1][j] == 0 ||
                    isValid(mat, i + 1, j) && mat[i + 1][j] == 0 ||
                    isValid(mat, i, j - 1) && mat[i][j - 1] == 0 ||
                    isValid(mat, i, j + 1) && mat[i][j + 1] == 0) {
                    steps.push({i, j, 1});
                    dst[i][j] = 1;
                }
            }
        }

        while (!steps.empty()) {
            auto step = steps.front();
            steps.pop();

            int i = step[0], j = step[1], ds = step[2];
            if (isValid(mat, i - 1, j) && mat[i - 1][j] == 1 &&
               (dst[i - 1][j] == 0 || dst[i - 1][j] > ds + 1)) {
                steps.push({i - 1, j, ds + 1});
                dst[i - 1][j] = ds + 1;
            }
            if (isValid(mat, i + 1, j) && mat[i + 1][j] == 1 &&
                       (dst[i + 1][j] == 0 || dst[i + 1][j] > ds + 1)) {
                steps.push({i + 1, j, ds + 1});
                dst[i + 1][j] = ds + 1;
            }
            if (isValid(mat, i, j - 1) && mat[i][j - 1] == 1 &&
                       (dst[i][j - 1] == 0 || dst[i][j - 1] > ds + 1)) {
                steps.push({i, j - 1, ds + 1});
                dst[i][j - 1] = ds + 1;
            }
            if (isValid(mat, i, j + 1) && mat[i][j + 1] == 1 &&
                       (dst[i][j + 1] == 0 || dst[i][j + 1] > ds + 1)) {
                steps.push({i, j + 1, ds + 1});
                dst[i][j + 1] = ds + 1;
            }
        }

        return dst;
    }

    bool isValid(vector<vector<int>>& mat, int i, int j) {
        return i >= 0 && i < mat.size() &&
               j >= 0 && j < mat[0].size();
    }
};
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