<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:
    void dfs(vector<vector<int>>& grid, int x, int y, const int& N, queue<vector<int>>& q) {
        vector<vector<int>> delta {{1,0}, {0,1}, {-1,0}, {0,-1}};
        grid[x][y] = 2;
        q.push({x,y,2});
        for(auto &d : delta) {
            int i = x + d[0];
            int j = y + d[1];
            if(i < 0 || j < 0 || i >= N || j >= N || grid[i][j] != 1) continue;
            dfs(grid, i, j, N, q);
        }
    }

    int shortestBridge(vector<vector<int>>& grid) {
        const int n = grid.size();
        queue<vector<int>> q;
        bool flag = true;
        for(int i = 0; i < n; ++i)
            for(int j = 0; j < n; ++j) {
                if(flag && grid[i][j] == 1) {
                    flag = false;
                    dfs(grid, i, j, n, q);
                }
                if(grid[i][j] == 0) grid[i][j] = 1e9;
            }
        vector<vector<int>> delta {{1,0}, {0,1}, {-1,0}, {0,-1}};
        while(!q.empty()) {
            auto node = q.front();
            q.pop();
            for(auto &d : delta) {
                int i = node[0] + d[0];
                int j = node[1] + d[1];
                if(i < 0 || j < 0 || i >= n || j >= n) continue;
                if(grid[i][j] == 1) return node[2] - 2;
                if(grid[i][j] > node[2] + 1) {
                    grid[i][j] = node[2] + 1;
                    q.push({i, j, node[2] + 1});
                }
            }
        }
        return 0;
    }
};
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