<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) {
        int rows = grid.size();
        int cols = grid[0].size();
        queue<pair<int,int>> q;

        for (int row = 0; row < rows; ++row) {
            if (!q.empty()) { break; }
            
            for (int col = 0; col < cols; ++col) {
                if (grid[row][col] == 1) {
                    mapIsland(grid, row, col, rows, cols, q);
                    break;
                }
            }
        }

        char dirs[]{-1, 0, 1, 0, -1};
        int len = 0;
        int row = 0;
        int col = 0;
        int newRow = 0;
        int newCol = 0;

        while (!q.empty()) {
            int sz = q.size();
            ++len;

            while (sz--) {
                tie(row, col) = q.front();
                q.pop();

                for (int i = 0; i < 4; ++i) {
                    newRow = row + dirs[i];
                    newCol = col + dirs[i+1];

                    if (newRow >= 0 && newRow < rows && newCol >= 0 && newCol < cols) {
                        int& val = grid[newRow][newCol];

                        if (val == 1) { return len-1; }
                        if (val == 0) {
                            val = 2;
                            q.emplace(newRow, newCol);
                        }
                    }
                }
            }
        }

        return len;
    }
private:
    void mapIsland(vector<vector<int>>& grid, int row, int col, int rows, int cols, queue<pair<int,int>>& q) {
        q.emplace(row, col);
        grid[row][col] = 2;
        char dirs[]{-1, 0, 1, 0, -1};

        for (int i = 0; i < 4; ++i) {
            int newRow = row + dirs[i];
            int newCol = col + dirs[i+1];

            if (newRow >= 0 && newRow < rows && newCol >= 0 && newCol < cols) {
                if (grid[newRow][newCol] == 1) {
                    mapIsland(grid, newRow, newCol, rows, cols, q);
                }
            }
        }
    }
};
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