<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 dirs[5] = {0, 1, 0, -1, 0};

    void change(vector<vector<int>> &grid, int i, int j, vector<pair<int,int>> &q){

        if (i < 0 || j < 0 || i >= grid.size() || j >= grid[i].size() || grid[i][j] != 1)
            return ;

        q.push_back({i, j});
        grid[i][j] = 2;
        change(grid, i + 1, j, q);
        change(grid, i, j + 1, q);
        change(grid, i - 1, j, q);
        change(grid, i, j - 1, q);

    }

    int shortestBridge(vector<vector<int>>& grid) {
        
        vector<pair<int,int>> q;
        for (int i = 0; i < grid.size(); ++i){
            for (int j = 0; q.size() == 0 && j < grid[i].size(); ++j){
                change(grid, i, j, q);
            }
        }

        while (!q.empty()){

            vector<pair<int,int>> q1;
            for (auto [i, j]: q){
                for (int d = 0; d < 4; ++d){
                    int x = i + dirs[d];
                    int y = j + dirs[d+1];

                    if (min(x, y) >= 0 && max(x, y) < grid.size()){
                        if (grid[x][y] == 1){
                            return grid[i][j] - 2;
                        }
                        if (grid[x][y] == 0){
                            q1.push_back({x, y});
                            grid[x][y] = grid[i][j] + 1;
                        }
                    } 
                }
            }
            swap(q, q1);
        }

        return 0;
    }
};
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