<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 rows = mat.size();
        int cols = mat[0].size();
        queue<pair<int,int>> q;
        vector<pair<int,int>> directions = {{-1,0},{1,0},{0,-1},{0,1}} ;
        for(int i = 0; i < rows; i++){
            for(int j =0; j < cols; j++){
                if(mat[i][j] == 0) q.push({i,j});
                else mat[i][j] = INT_MAX;
            }
        }

        while(!q.empty()){
            auto [r,c] = q.front();
            q.pop();
            for(auto dir:directions){
                int nrow = r + dir.first;
                int ncol = c + dir.second;
                if(nrow >= 0 && nrow < rows && ncol >= 0 && ncol < cols && mat[nrow][ncol] > mat[r][c]){
                    mat[nrow][ncol] = mat[r][c]  +1;
                    q.push({nrow, ncol});

                }
            }
        }
        return mat;

    }
};
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