<p>You are given an <code>m x n</code> binary matrix <code>grid</code>, where <code>0</code> represents a sea cell and <code>1</code> represents a land cell.</p>

<p>A <strong>move</strong> consists of walking from one land cell to another adjacent (<strong>4-directionally</strong>) land cell or walking off the boundary of the <code>grid</code>.</p>

<p>Return <em>the number of land cells in</em> <code>grid</code> <em>for which we cannot walk off the boundary of the grid in any number of <strong>moves</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/enclaves1.jpg" style="width: 333px; height: 333px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,0,0],[1,0,1,0],[0,1,1,0],[0,0,0,0]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are three 1s that are enclosed by 0s, and one 1 that is not enclosed because its on the boundary.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/enclaves2.jpg" style="width: 333px; height: 333px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,0,1,0],[0,0,1,0],[0,0,0,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All 1s are either on the boundary or can reach the boundary.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
    int DR[4] = {0,-1,0,1};
    int DC[4] = {1,0,-1,0};
    bool isValid(int x, int y, vector<vector<int>>& vis, vector<vector<int>>& grid){
        int m = grid.size(), n = grid[0].size();
        return x < m && y < n && x>=0 && y >= 0 && !vis[x][y] && grid[x][y]==1;
    }
    void dfs(int x, int y, vector<vector<int>>& vis, vector<vector<int>>& grid){
        vis[x][y] = 1;
        for(int k=0; k<4; k++){
            int nx = x + DR[k];
            int ny = y + DC[k];
            if(isValid(nx,ny,vis,grid))
                dfs(nx,ny,vis,grid);
        }
    }
public:
    int numEnclaves(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector<vector<int>> vis(m,vector<int>(n,0));
        int count = 0;
        for(int j=0; j<n; j++){
            if(grid[0][j]==1 && !vis[0][j])
                dfs(0,j,vis,grid);
            if(grid[m-1][j]==1 && !vis[m-1][j])
                dfs(m-1,j,vis,grid);
        }
        for(int i=0; i<m; i++){
            if(grid[i][0]==1 && !vis[i][0])
                dfs(i,0,vis,grid);
            if(grid[i][n-1]==1 && !vis[i][n-1])
                dfs(i,n-1,vis,grid);
        }
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                if(grid[i][j]==1 && !vis[i][j]) count++;
            }
        }
        return count;
    }
};
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