<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, int i, int j, int m, int n) {
        vector<int> position = {0,-1,0,1,0};

        for (int k = 0; k < position.size()-1; k++) {
            int x = i + position[k];
            int y = j + position[k+1];
            if (x >= 0 && x < m && y >= 0 && y < n && grid[x][y] == 1) {
                grid[x][y] = 0;
                dfs(grid, x, y, m, n);
            }
        }
    }
    int numEnclaves(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        for (int i=0;i<m;i++) {
            if (grid[i][0] == 1) {
                grid[i][0] = 0;
                dfs(grid, i, 0, m, n);
            }

            if (grid[i][n-1] == 1) {
                grid[i][n-1] = 0;
                dfs(grid, i, n-1, m, n);
            }
        }

        for (int i=0;i<n;i++) {
            if (grid[0][i] == 1) {
                grid[0][i] = 0;
                dfs(grid, 0, i, m, n);
            }

            if (grid[m-1][i] == 1) {
                grid[m-1][i] = 0;
                dfs(grid, m-1, i, m, n);
            }
        }

        int ans = 0;
        for (int i=0;i<m;i++) {
            for (int j=0;j<n;j++) {
                if (grid[i][j] == 1) {
                    ans++;
                }
            }
        }
        return ans;
    }
};

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