<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>

int dr[] = {0, 1, 0, -1};
int dc[] = {1, 0, -1, 0};
class Solution {
public:
    int n, m, ans = INT_MAX;
    bool isValid(int r, int c){
        if(r < 0 || r >= n || c < 0 || c >= m) return false;
        return true;
    }

    void firstIsland(vector<vector<int>>& grid, int r, int c){
        grid[r][c] = 2;
        for(int i = 0;i < 4;i++){
            if(isValid(r + dr[i], c + dc[i]) && grid[r + dr[i]][c + dc[i]] == 1){
                firstIsland(grid, r + dr[i], c + dc[i]);
            }
        }
    }

    int shortestBridge(vector<vector<int>>& grid) {
        n = grid.size(), m = grid[0].size();
        map<pair<int, int>, int> mp;
        queue<pair<int, int>> q;
        for(int i = 0;i < n;i++){
            int flag = 0;
            for(int j = 0;j < m;j++){
                if(grid[i][j] == 1){
                    firstIsland(grid, i, j);
                    flag = 1;
                    break;
                }
            }
            if(flag) break;
        }

        for(int i = 0;i < n;i++){
            for(int j = 0;j < m;j++){
                if(grid[i][j] == 1){
                    q.push({i, j});
                    mp[{i, j}]++;
                }
            }
        }

        int ans = 0;
        while(!q.empty()){
            int s = q.size();
            while(s--){
                int r = q.front().first;
                int c = q.front().second;
                q.pop();
                if(grid[r][c] == 2) return ans - 1;
                for(int i = 0;i < 4;i++){
                    if(isValid(r + dr[i], c + dc[i]) && !mp.count({r + dr[i], c + dc[i]})){
                        mp[{r + dr[i], c + dc[i]}]++;
                        q.push({r + dr[i], c + dc[i]});
                    }
                }
            }
            ans++;
        }

        return -1;
    }
};

auto init = []()
{ 
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    return 'c';
}();
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