<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>

#define WATER               0
#define LAND                1
#define DISCOVERED_LAND     2

class Solution {
public:

    /* =========================================================
     *
     * floodfill_count_enclaves():
     *
     * Run BFS floodfill to map the island. Return 1 if the island
     * does NOT touch any border of the grid
     *
     * ========================================================= */
    int floodfill_count_enclaves(vector<vector<int>>& grid, int m, int n, int x, int y) {

        int  num_enclaves = 0;
        bool touches_border = false;
        queue<pair<int,int>> bfs_queue;
        bfs_queue.push(make_pair(x, y));

        while (!bfs_queue.empty()) {

            int curr_x = bfs_queue.front().first;
            int curr_y = bfs_queue.front().second;
            grid[x][y] = DISCOVERED_LAND;
            bfs_queue.pop();

            /* If this square touches the border, disqualify the entire
             * island from having enclaves, but map the rest of the island */
            if ((!touches_border) &&
                (curr_x - 1 < 0) || (curr_x + 1 >= m) || 
                (curr_y - 1 < 0) || (curr_y + 1 >= n)) {
                touches_border = true;
                num_enclaves = 0;
            }

            if (!touches_border) num_enclaves++;

            /* Queue four directional in-bounds neighbors */
            if ((curr_x + 1 <  m) && (grid[curr_x + 1][curr_y] != WATER) && (grid[curr_x + 1][curr_y] != DISCOVERED_LAND)) { bfs_queue.push(make_pair(curr_x + 1, curr_y)); grid[curr_x + 1][curr_y] = DISCOVERED_LAND; };
            if ((curr_y + 1 <  n) && (grid[curr_x][curr_y + 1] != WATER) && (grid[curr_x][curr_y + 1] != DISCOVERED_LAND)) { bfs_queue.push(make_pair(curr_x, curr_y + 1)); grid[curr_x][curr_y + 1] = DISCOVERED_LAND; };
            if ((curr_x - 1 >= 0) && (grid[curr_x - 1][curr_y] != WATER) && (grid[curr_x - 1][curr_y] != DISCOVERED_LAND)) { bfs_queue.push(make_pair(curr_x - 1, curr_y)); grid[curr_x - 1][curr_y] = DISCOVERED_LAND; };
            if ((curr_y - 1 >= 0) && (grid[curr_x][curr_y - 1] != WATER) && (grid[curr_x][curr_y - 1] != DISCOVERED_LAND)) { bfs_queue.push(make_pair(curr_x, curr_y - 1)); grid[curr_x][curr_y - 1] = DISCOVERED_LAND; };
        }

        return num_enclaves;
    }

    /* =========================================================
     *
     * numEnclaves():
     *
     * ========================================================= */
    int numEnclaves(vector<vector<int>>& grid) {

        int m = grid.size();
        int n = grid[0].size();
        int num_enclaves = 0;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == LAND)
                    num_enclaves += floodfill_count_enclaves(grid, m, n, i, j);
            }
        }
        return num_enclaves;
    }
};
50977