<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 n,int i,int j,queue<vector<int>>&q){
        grid[i][j]=2;
        q.push({i,j,0});
        vector<vector<int>>dir={{-1,0},{0,1},{0,-1},{1,0}};
        for(auto &d:dir){
            int newi=i+d[0];
            int newj=j+d[1];
            if(newi>=0&&newi<n&&newj>=0&&newj<n&&grid[newi][newj]==1)dfs(grid,n,newi,newj,q);
        }
    }
    int shortestBridge(vector<vector<int>>& grid) {
        int n=grid.size();
        queue<vector<int>>q;
        bool x=false;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1) {
                    dfs(grid,n,i,j,q);
                    x=true;
                    break;
                }
                
            }
            if(x)break;
        }
        vector<vector<int>>dir={{-1,0},{0,1},{0,-1},{1,0}};
        while(!q.empty()){
            int i=q.front()[0];
            int j=q.front()[1];
            int dis=q.front()[2];
            q.pop();
            for(auto &d:dir){
                int newi=i+d[0];
                int newj=j+d[1];
                if(newi>=0&&newi<n&&newj>=0&&newj<n&&grid[newi][newj]==1)return dis;
                if(newi>=0&&newi<n&&newj>=0&&newj<n&&grid[newi][newj]==0){
                    grid[newi][newj]=2;
                    q.push({newi,newj,dis+1});
                }
            }
        }
        return 0;
    }
};
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