<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:
    vector<int> move{-1, 0, 1, 0, -1};

    bool isValidIndex(int n, int i, int j)
    {
        if(i < 0 || j < 0 || i >= n || j >= n)
            return false;
        return true;
    }

    void markIsland(vector<vector<int>>& grid, int start_i, int start_j, 
                    queue<pair<int, int>>& points)
    {
        int len = grid.size();
        queue<pair<int, int>> q;
        q.push(pair<int, int>{start_i, start_j});
        while(!q.empty())
        {
            auto [i, j] = q.front();
            q.pop();
            
            if(grid[i][j] == 2)
                continue;
    
            grid[i][j] = 2;

            for(int m = 0; m < move.size() - 1; ++m)
            {
                int cur_i = i + move[m];
                int cur_j = j + move[m + 1];

                if(!isValidIndex(grid.size(), cur_i, cur_j))
                    continue;
                
                if(grid[cur_i][cur_j] == 1)
                    q.push(pair<int, int>{cur_i, cur_j});
                
                if(grid[cur_i][cur_j] == 0)
                    points.push(pair<int, int>{cur_i, cur_j});
            }
        }
    }

    int shortestBridge(vector<vector<int>>& grid) {
        queue<pair<int, int>> points;
        int len = grid.size();
        for(int i = 0; i < len; ++i)
        {
            int j = 0;
            for(; j < len; ++j)
            {
                if(grid[i][j] == 1)
                {
                    markIsland(grid, i, j, points);
                    break;
                }
            }

            if(j < grid[0].size())
                break;
        }

        int res = 1;
        while(!points.empty())
        {
            for(int num = points.size(); num > 0; --num)
            {
                auto cur = points.front();
                points.pop();

                if(grid[cur.first][cur.second] == 2)
                    continue;
                grid[cur.first][cur.second] = 2;

                for(int m = 0; m < move.size() - 1; ++m)
                {
                    int cur_i = cur.first + move[m];
                    int cur_j = cur.second + move[m + 1];

                    if(!isValidIndex(grid.size(), cur_i, cur_j))
                        continue;
                
                    if(grid[cur_i][cur_j] == 1)
                        return res;
                
                    if(grid[cur_i][cur_j] == 0)
                        points.push(pair<int, int>{cur_i, cur_j});
                }
            }
            res++;
        }
        return res;
    }
};
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