<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:
    int process(int r, int c, vector<vector<int>>& directions, vector<vector<int>>& grid) {
        grid[r][c] = -1;
        queue<vector<int>> q;
        q.push({ r, c });
        int count = 0;
        bool valid = false;
        while (!q.empty()) {
            vector<int> cell = q.front();
            q.pop();
            count++;
            for (auto& dir : directions) {
                int nr = cell[0] + dir[0];
                int nc = cell[1] + dir[1];
                if (nr >= 0 && nr < grid.size() && nc >= 0 && nc < grid[0].size()) {
                    if (grid[nr][nc] == 1) {
                        grid[nr][nc] = -1;
                        q.push({ nr, nc });
                    }
                } else {
                    valid = true;
                }
            }
        }
        if (valid) {
            return count;
        }
        return 0;
    }

    int numEnclaves(vector<vector<int>>& grid) {
        vector<vector<int>> directions = {{-1,0}, {0,1}, {1,0}, {0,-1}};
        int land = 0;
        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[0].size(); j++) {
                if (grid[i][j] == 1) {
                    land++;
                }
            }
        }
        int border = 0;
        for (int i = 0; i < grid.size(); i++) {
            if (grid[i][0] == 1) {
                border += process(i, 0, directions, grid);
            }
            if (grid[i][grid[0].size() - 1] == 1) {
                border += process(i, grid[0].size() - 1, directions, grid);
            }
        }
        for (int i = 0; i < grid[0].size(); i++) {
            if (grid[0][i] == 1) {
                border += process(0, i, directions, grid);
            }
            if (grid[grid.size() - 1][i] == 1) {
                border += process(grid.size() - 1, i, directions, grid);
            }
        }
        return land - border;
    }
};

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