<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:
    def numEnclaves(self, grid: List[List[int]]) -> int:
        """
        0000
        0100
        0000
        1100
        1010
        0010
        0010
        0000
        """
        
        def outside(row, col):
            return not (0 <= row < height and 0 <= col < width)

        dirs = (1,0), (0,1), (-1, 0), (0, -1)

        def dfs(row, col) -> int:
            nonlocal is_on_border
            nonlocal visited

            if outside(row, col):
                is_on_border = True
                return 0

            if grid[row][col] == 0:
                return 0

            num = 0
            for dx, dy in dirs:
                r = row + dx
                c = col + dy
                if (r,c) not in visited:
                    visited.add((r,c))
                    num += dfs(r,c)

            return num + 1



        # for each cell in grid
        #	do res = DFS(cell)
        #	if not is_on_border:
        #		ans += res

        height = len(grid)
        width = len(grid[-1])
        ans = 0

        visited = set()
        for row in range(height):
            for col in range(width):
                if grid[row][col] == 1:
                    is_on_border = False
                    if (row, col) not in visited:
                        visited.add((row, col))
                        res = dfs(row, col)
                        if not is_on_border:
                            ans += res

        return ans

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