<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:
    void distance(const vector<vector<int>>& mat, vector<vector<int>>& output, int x, int y, int acc) {
        if (x < 0 || x >= mat.size() || y < 0 || y >= mat[x].size()) {
            return;
        }
        if (mat[x][y] == 0) {
            acc = 0;
        } 
        if (acc < output[x][y]) {
            output[x][y] = acc;
            distance(mat, output, x-1, y, acc + 1);
            distance(mat, output, x, y-1, acc + 1);
            distance(mat, output, x, y+1, acc + 1);
            distance(mat, output, x+1, y, acc + 1);
        }
    }
    vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {
        vector<vector<int>> output(mat.size(), vector<int>(mat[0].size(), INT_MAX));
        // spread from 0
        for (int i = 0; i < mat.size(); i++) {
            for (int j = 0; j < mat[i].size(); j++) {
                if (mat[i][j] == 0) {
                    distance(mat, output, i, j, 0);
                    return output;
                }
            }
        }
        return output;
    }
};
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