<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 {
    vector<int> rowInd;
    vector<int> colInd;
    void processCell(int row, int col, vector<vector<int>> &mat) const{
        // cout << row << ", " << col << endl;
        int minNeighbor = INT_MAX;
        int n = mat.size();
        int m = mat[0].size();
        for(unsigned int i = 0; i < 4; ++i){
            int r = row + rowInd[i];
            int c = col + colInd[i];
            if(r>=0 && r<n && c>=0 && c<m)
                minNeighbor = min(minNeighbor, mat[r][c]);
        }
        mat[row][col] = minNeighbor + 1;
        for(unsigned int i = 0; i < 4; ++i){
            int r = row + rowInd[i];
            int c = col + colInd[i];
            if(r>=0 && r<n && c>=0 && c<m)
                if(mat[r][c] - 1 > mat[row][col])
                    processCell(r, c, mat);
        }
    }
public:
    vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {
        rowInd = vector<int>({-1, 0, 1, 0});
        colInd = vector<int>({0, -1, 0, 1});
        int n = mat.size();
        int m = mat[0].size();
        for(unsigned int i = 0; i < mat.size(); ++i)
            for(unsigned int j = 0; j < mat[0].size(); ++j)
                if(mat[i][j] == 1)
                    mat[i][j] = INT_MAX;
        for(unsigned int i = 0; i < mat.size(); ++i)
            for(unsigned int j = 0; j < mat[0].size(); ++j)
                if(mat[i][j] == INT_MAX){
                    for(unsigned int ind = 0; ind < 4; ++ind){
                        int r = i + rowInd[ind];
                        int c = j + colInd[ind];
                        if(r>=0 && r<n && c>=0 && c<m)
                            if(mat[r][c] == 0){
                                processCell(i, j, mat);
                                break;
                            }
                    }
                }
        return mat;
    }
};
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