<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 {
public:
    void DFS(vector<vector<int>>& grid, 
        vector<vector<bool>>&visited, int row, int col)
    {
        if(row < 0 || col < 0 || row >= grid.size() || col >= grid[0].size()
            || visited[row][col] == true || grid[row][col] == 0)
        {
            return;
        }
        visited[row][col] = true;
        DFS(grid, visited, row - 1, col);
        DFS(grid, visited, row + 1, col);
        DFS(grid, visited, row, col - 1);
        DFS(grid, visited, row, col + 1);
    }
    void traverseBoundary(vector<vector<int>>& grid, 
        vector<vector<bool>>&visited, int startRow, int endRow,
        int startCol, int endCol)
    {
        for(int i = startRow; i < endRow; i++){
            for(int j = startCol; j < endCol; j++){
                if(grid[i][j] == 1 && visited[i][j] == false){
                    DFS(grid, visited, i, j);
                }
            }
        }
    }
    int numEnclaves(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        int ans = 0;
        vector<vector<bool>>visited(n, vector<bool>(m, false));
        traverseBoundary(grid, visited, 0, 1, 0, m);
        traverseBoundary(grid, visited, 0, n, 0, 1);
        traverseBoundary(grid, visited, n - 1, n, 0, m);
        traverseBoundary(grid, visited, 0, n, m - 1, m);
        for(int i = 0; i < n; i++){
            for(int j = 0; j < m; j++){
                if(grid[i][j] == 1 && visited[i][j] == false){
                    ans++;
                }
            }
        }
        return ans;
    }
};
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