Number of Islands
<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>
Depth-First Search; Breadth-First Search; Union Find; Array; Matrix
using System;
using System.Collections.Generic;
using System.Linq;

public class Solution {
    public int NumIslands(char[][] grid)
    {
        var queue = new Queue<Tuple<int, int>>();
        var lenI = grid.Length;
        var lenJ = lenI == 0 ? 0 : grid[0].Length;
        var paths = new int[,] { { 0, 1 }, { 1, 0 }, { 0, -1 }, { -1, 0 } };
        var result = 0;
        for (var i = 0; i < lenI; ++i)
        {
            for (var j = 0; j < lenJ; ++j)
            {
                if (grid[i][j] == '1')
                {
                    ++result;
                    grid[i][j] = '0';
                    queue.Enqueue(Tuple.Create(i, j));
                    while (queue.Any())
                    {
                        var position = queue.Dequeue();
                        for (var k = 0; k < 4; ++k)
                        {
                            var next = Tuple.Create(position.Item1 + paths[k, 0], position.Item2 + paths[k, 1]);
                            if (next.Item1 >= 0 && next.Item1 < lenI && next.Item2 >= 0 && next.Item2 < lenJ && grid[next.Item1][next.Item2] == '1')
                            {
                                grid[next.Item1][next.Item2] = '0';
                                queue.Enqueue(next);
                            }
                        }
                    }
                }
            }
        }
        return result;
    }
}