<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 distance(int x1, int y1, int x2, int y2){
        return abs(x2-x1)+abs(y2-y1)-1;
    }
    int shortestBridge(vector<vector<int>>& grid) {
        int n=grid.size(),ans=INT_MAX;
        vector<vector<pair<int,int>>> island;
        vector<vector<bool>> is_island (n,vector<bool>(n,false));
        vector<vector<int>> directions={{0,1,0,-1},{1,0,-1,0}};
        vector<pair<int,int>> temp;
        bool flag=true;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1 && is_island[i][j]==false){
                    dfs(grid,island,i,j,n,temp,is_island,directions);
                    island.push_back(temp);
                    temp.clear();
                }
            }
        }
        for(int i=0;i<island[0].size();i++)
            for(int j=0;j<island[1].size();j++)
                ans = min(ans,distance(island[0][i].first,island[0][i].second,island[1][j].first,island[1][j].second));
        return ans;
    }
    void dfs(vector<vector<int>>& grid,vector<vector<pair<int,int>>> &island,int i, int j, int n,vector<pair<int,int>>&temp,
    vector<vector<bool>>&is_island,vector<vector<int>> directions){
        for(int k=0;k<4;k++){
            int new_i=i+directions[0][k];
            int new_j=j+directions[1][k];
            if(is_island[i][j]==false)
                temp.push_back({i,j});
            is_island[i][j]=true;
            if(new_i>=0 && new_i<n && new_j>=0 && new_j<n && grid[new_i][new_j]==1 && is_island[new_i][new_j]==false)
                dfs(grid,island,new_i,new_j,n,temp,is_island,directions);
        }
    }
};
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