<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:

    int row[4]={1,0,-1,0};
    int col[4]={0,-1,0,1};
    int n,m;
    void solve(int i,int j,vector<vector<int>>&dis,vector<vector<int>>&mat){

        for(int k=0;k<4;k++){
            int nr=i+row[k];
            int nc=j+col[k];
            if(nr<n and nc<m and nc>=0 and nr>=0 and dis[i][j]+1<dis[nr][nc] and mat[nr][nc]==1){
               dis[nr][nc]=1+dis[i][j];
               solve(nr,nc,dis,mat);
            }
        }
    }

    vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {
        n=mat.size();
        m=mat[0].size();

        vector<vector<int>>dis(n,vector<int>(m,1e9));

        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(mat[i][j]==0){
                    dis[i][j]=0;
                    solve(i,j,dis,mat);
                }
            }
        }

        return dis;
    }
};
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