<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 shortestBridge = INT_MAX;

        pair<int, int> entry = paintOneIsland(grid);

        vector<vector<int>> costMatrix(grid.size(), vector<int>(grid[0].size(), INT_MAX));

        queue<tuple<int, int, int>> q;

        q.push(make_tuple(get<0>(entry), get<1>(entry), 0));

        while(!q.empty()) {
            tuple<int, int, int> entry = q.front();
            q.pop();

            int row = get<0>(entry);
            int column = get<1>(entry);
            int cost = get<2>(entry);


            if(row < 0 || row >= grid.size() || column < 0 || column >= grid.size()) {
                // out of bounds
                continue;
            }

            if(grid[row][column] == 1) {
                cout << row << ", " << column << endl;
                shortestBridge = min(shortestBridge, cost);
                costMatrix[row][column] = min(costMatrix[row][column], cost);
                continue;
            }

            if(cost >= costMatrix[row][column]) {
                // We already have a better way to reach here
                continue;
            }

            costMatrix[row][column] = cost;

            int nextCost = 0;

            if(grid[row][column] == 0) {
                nextCost = cost + 1;
            } 

            q.push(make_tuple(row + 1, column, nextCost));
            q.push(make_tuple(row - 1, column, nextCost));
            q.push(make_tuple(row, column + 1, nextCost));
            q.push(make_tuple(row, column - 1, nextCost));
        }

        return shortestBridge;
    }

    pair<int, int> paintOneIsland(vector<vector<int>>& grid){
        for(int i = 0; i < grid.size(); i++) {
            for(int j = 0; j < grid[0].size(); j++) {
                if(grid[i][j] == 1) {
                    paint(grid, i, j);
                    return make_pair(i, j);
                }
            }
        }

        return make_pair(-1, -1);
    }

    void paint(vector<vector<int>>& grid, int row, int column) {
        if(row < 0 || row >= grid.size() || column < 0 || column >= grid[0].size()) {
            return;
        }

        if(grid[row][column] == 2 || grid[row][column] == 0) {
            return;
        }

        grid[row][column] = 2;

        paint(grid, row + 1, column);
        paint(grid, row - 1, column);
        paint(grid, row, column + 1);
        paint(grid, row, column - 1);
    }
};
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