<p>You are given an <code>n x n</code> binary matrix <code>grid</code> where <code>1</code> represents land and <code>0</code> represents water.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>&#39;s not connected to any other <code>1</code>&#39;s. There are <strong>exactly two islands</strong> in <code>grid</code>.</p>

<p>You may change <code>0</code>&#39;s to <code>1</code>&#39;s to connect the two islands to form <strong>one island</strong>.</p>

<p>Return <em>the smallest number of </em><code>0</code><em>&#39;s you must flip to connect the two islands</em>.</p>

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

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

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

<pre>
<strong>Input:</strong> grid = [[0,1,0],[0,0,0],[0,0,1]]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>2 &lt;= n &lt;= 100</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
	<li>There are exactly two islands in <code>grid</code>.</li>
</ul>

class Solution {
 public:
  int shortestBridge(vector<vector<int>>& grid) {
    markGridTwo(grid);

    for (int color = 2;; ++color)
      for (int i = 0; i < grid.size(); ++i)
        for (int j = 0; j < grid[0].size(); ++j)
          if (grid[i][j] == color)
            if (expand(grid, i + 1, j, color) ||  //
                expand(grid, i - 1, j, color) ||  //
                expand(grid, i, j + 1, color) ||  //
                expand(grid, i, j - 1, color))
              return color - 2;
  }

 private:
  void markGridTwo(vector<vector<int>>& grid) {
    for (int i = 0; i < grid.size(); ++i)
      for (int j = 0; j < grid[0].size(); ++j)
        if (grid[i][j] == 1) {
          markGridTwo(grid, i, j);
          return;
        }
  }

  void markGridTwo(vector<vector<int>>& grid, int i, int j) {
    if (i < 0 || i == grid.size() || j < 0 || j == grid[0].size())
      return;
    if (grid[i][j] != 1)
      return;
    grid[i][j] = 2;
    markGridTwo(grid, i + 1, j);
    markGridTwo(grid, i - 1, j);
    markGridTwo(grid, i, j + 1);
    markGridTwo(grid, i, j - 1);
  }

  bool expand(vector<vector<int>>& grid, int i, int j, int color) {
    if (i < 0 || i == grid.size() || j < 0 || j == grid[0].size())
      return false;
    if (grid[i][j] == 0)
      grid[i][j] = color + 1;
    return grid[i][j] == 1;
  }
};
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