<p>Given an <code>m x n</code> 2D binary grid <code>grid</code> which represents a map of <code>&#39;1&#39;</code>s (land) and <code>&#39;0&#39;</code>s (water), return <em>the number of islands</em>.</p>

<p>An <strong>island</strong> is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [
  [&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;0&quot;],
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;],
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;0&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;]
]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;0&quot;,&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;1&quot;]
]
<strong>Output:</strong> 3
</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;= 300</code></li>
	<li><code>grid[i][j]</code> is <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

class Solution {
public:
    int numIslands(const vector<vector<char>>& grid) {
        const int R = grid.size();
        const int C = grid[0].size();

        auto cell = [&](int r, int c) -> char { return grid[r][c]; };

        int islands = 0;
        struct hash_func { size_t operator()(const std::pair<int, int>& p) const { return p.first ^ p.second; } };
        std::unordered_set<std::pair<int, int>, hash_func> visited;

        auto visit = [&](int r, int c, auto&& visit) {
          if (r < 0 || r >= R) return;
          if (c < 0 || c >= C) return;
          if (visited.contains({r, c})) return;
          if (cell(r, c) == '0') return;

          visited.emplace(r, c);
          visit(r-1, c, visit);
          visit(r+1, c, visit);
          visit(r, c-1, visit);
          visit(r, c+1, visit);
        };

        for (int r = 0; r < R; ++r)
        {
          for (int c = 0; c < C; ++c)
          {
            if (cell(r, c) == '0' || visited.contains({r, c}))
              continue;

            islands++;
            // mark all the parts of the island
            visit(r, c, visit);
            visited.emplace(r, c);
          }
        }

        return islands;
    }
};
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