<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 {
    int dr[4] = {0, 0, 1, -1};
    int dc[4] = {1, -1, 0, 0};

    void floodFill(vector<vector<int>> &grid, int r, int c, int state) {
        if (r < 0 || r >= grid.size() || c < 0 || c >= grid[0].size() || grid[r][c] != 1) {
            return;
        }

        grid[r][c] = state;

        for (int i = 0; i < 4; i++) {
            floodFill(grid, r + dr[i], c + dc[i], state);
        }
    }
public:
    int shortestBridge(vector<vector<int>>& grid) {
        int state = 2;

        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[0].size(); j++) {
                if (grid[i][j] == 1) {
                    floodFill(grid, i, j, state++);
                }
            }
        }

        queue<pair<int, int>> q;
        int level = 0, nodesInCurrLevel = 0, nodesInNextLevel = 0;
        vector<vector<bool>> vis(grid.size(), vector<bool>(grid[0].size(), false));

        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[0].size(); j++) {
                if (grid[i][j] == 2) {
                    q.push({i, j});
                    nodesInCurrLevel++;
                    vis[i][j] = true;
                }
            }
        }

        while (!q.empty()) {
            pair<int, int> curr = q.front();
            q.pop();
            nodesInCurrLevel--;

            if (grid[curr.first][curr.second] == 3) {
                return level-1;
            }

            for (int i = 0; i < 4; i++) {
                int r = curr.first + dr[i], c = curr.second + dc[i];

                if (r < 0 || c < 0 || r >= grid.size() || c >= grid[0].size() || vis[r][c] == true) {
                    continue;
                }

                q.push({r, c});
                vis[r][c] = true;
                nodesInNextLevel++;
            }

            if (nodesInCurrLevel == 0) {
                nodesInCurrLevel = nodesInNextLevel;
                nodesInNextLevel = 0;
                level++;
            }
        }

        return INT_MAX;
    }
};
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