<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 shortestBridge(vector<vector<int>>& grid) {
        int minDistance = 1e6;
        int r = -1;
        int c = -1;
        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[0].size(); j++) {
                if (grid[i][j] == 1) {
                    r = i;
                    c = j;
                    break;
                }
            }
            if (r != -1) {
                break;
            }
        }

        deque<vector<int>> q;
        bool sawZero = false;
        unordered_set<string> set;
        q.push_back({r, c, 0});

        while(!q.empty()) {
            vector<int> v = q.front();
            q.pop_front();
            int curR = v[0];
            int curC = v[1];
            int d = v[2];
            if (set.find(to_string(curR) + "+" + to_string(curC)) != set.end()) {
                continue;
            }
            if (grid[curR][curC] == 0) {
                sawZero = true;
            }
            if (grid[curR][curC] == 1) {
                if (d > 0) {
                    return d - 1;
                }
            }
            set.insert(to_string(curR) + "+" + to_string(curC));
            if (curR - 1 >= 0) {
                if (grid[curR - 1][curC] == 0) {
                    q.push_back({curR - 1, curC, d + 1});
                }  else {
                    if (sawZero) {
                        q.push_back({curR - 1, curC, d + 1});
                    } else {
                        q.push_front({curR - 1, curC, d});
                    }
                } 
            } 
            if (curC - 1 >= 0) {
                if (grid[curR][curC - 1] == 0) {
                    q.push_back({curR, curC - 1, d + 1});
                }  else {
                    if (sawZero) {
                        q.push_back({curR, curC - 1, d + 1});
                    } else {
                        q.push_front({curR, curC - 1, d});
                    }
                } 
            } 
            if (curR + 1 < grid.size()) {
                if (grid[curR + 1][curC] == 0) {
                    q.push_back({curR + 1, curC, d + 1});
                }   else {
                    if (sawZero) {
                        q.push_back({curR + 1, curC, d + 1});
                    } else {
                        q.push_front({curR + 1, curC, d});
                    }
                } 
            } 
            if (curC + 1 < grid[0].size()) {
                if (grid[curR][curC + 1] == 0) {
                    q.push_back({curR, curC + 1, d + 1});
                }   else {
                    if (sawZero) {
                        q.push_back({curR, curC + 1, d + 1});
                    } else {
                        q.push_front({curR, curC + 1, d});
                    }
                } 
            } 
        }

        return -1;
    }
};
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