<p>In an&nbsp;<code>n*n</code>&nbsp;grid, there is a snake that spans 2 cells and starts moving from the top left corner at <code>(0, 0)</code> and <code>(0, 1)</code>. The grid has empty cells represented by zeros and blocked cells represented by ones. The snake wants to reach the lower right corner at&nbsp;<code>(n-1, n-2)</code>&nbsp;and&nbsp;<code>(n-1, n-1)</code>.</p>

<p>In one move the snake can:</p>

<ul>
	<li>Move one cell to the right&nbsp;if there are no blocked cells there. This move keeps the horizontal/vertical position of the snake as it is.</li>
	<li>Move down one cell&nbsp;if there are no blocked cells there. This move keeps the horizontal/vertical position of the snake as it is.</li>
	<li>Rotate clockwise if it&#39;s in a horizontal position and the two cells under it are both empty. In that case the snake moves from&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r, c+1)</code>&nbsp;to&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r+1, c)</code>.<br />
	<img alt="" src="https://assets.leetcode.com/uploads/2019/09/24/image-2.png" style="width: 300px; height: 134px;" /></li>
	<li>Rotate counterclockwise&nbsp;if it&#39;s in a vertical position and the two cells to its right are both empty. In that case the snake moves from&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r+1, c)</code>&nbsp;to&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r, c+1)</code>.<br />
	<img alt="" src="https://assets.leetcode.com/uploads/2019/09/24/image-1.png" style="width: 300px; height: 121px;" /></li>
</ul>

<p>Return the minimum number of moves to reach the target.</p>

<p>If there is no way to reach the target, return&nbsp;<code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/24/image.png" style="width: 400px; height: 439px;" /></strong></p>

<pre>
<strong>Input:</strong> grid = [[0,0,0,0,0,1],
               [1,1,0,0,1,0],
&nbsp;              [0,0,0,0,1,1],
&nbsp;              [0,0,1,0,1,0],
&nbsp;              [0,1,1,0,0,0],
&nbsp;              [0,1,1,0,0,0]]
<strong>Output:</strong> 11
<strong>Explanation:
</strong>One possible solution is [right, right, rotate clockwise, right, down, down, down, down, rotate counterclockwise, right, down].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,0,1,1,1,1],
&nbsp;              [0,0,0,0,1,1],
&nbsp;              [1,1,0,0,0,1],
&nbsp;              [1,1,1,0,0,1],
&nbsp;              [1,1,1,0,0,1],
&nbsp;              [1,1,1,0,0,0]]
<strong>Output:</strong> 9
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 100</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 1</code></li>
	<li>It is guaranteed that the snake starts at empty cells.</li>
</ul>

class Solution {
public:
    struct State {
        int x, y, horizontal;
        State(int _x, int _y, int _horizontal) : x(_x), y(_y), horizontal(_horizontal) {}
    };
    
    int minimumMoves(vector<vector<int>>& grid) {
        int n = grid.size();
        queue<State> q;
        vector<vector<vector<int>>> visited(n, vector<vector<int>>(n, vector<int>(2, 0)));
        
        q.push(State(0, 0, 1));
        visited[0][0][1] = 1;
        int moves = 0;
        
        while (!q.empty()) {
            int sz = q.size();
            for (int i = 0; i < sz; ++i) {
                State current = q.front();
                q.pop();
                
                int x = current.x, y = current.y, horizontal = current.horizontal;
                
                if (x == n-1 && y == n-2 && horizontal == 1) {
                    return moves;
                }
                
                if (horizontal == 1 && y + 2 < n && grid[x][y + 2] == 0 && !visited[x][y + 1][1]) {
                    q.push(State(x, y + 1, 1));
                    visited[x][y + 1][1] = 1;
                }
                if (horizontal == 0 && y + 1 < n && grid[x][y + 1] == 0 && grid[x + 1][y + 1] == 0 && !visited[x][y + 1][0]) {
                    q.push(State(x, y + 1, 0));
                    visited[x][y + 1][0] = 1;
                }
                
                if (horizontal == 1 && x + 1 < n && grid[x + 1][y] == 0 && grid[x + 1][y + 1] == 0 && !visited[x + 1][y][1]) {
                    q.push(State(x + 1, y, 1));
                    visited[x + 1][y][1] = 1;
                }
                if (horizontal == 0 && x + 2 < n && grid[x + 2][y] == 0 && !visited[x + 1][y][0]) {
                    q.push(State(x + 1, y, 0));
                    visited[x + 1][y][0] = 1;
                }
                
                if (horizontal == 1 && x + 1 < n && grid[x + 1][y] == 0 && grid[x + 1][y + 1] == 0 && !visited[x][y][0]) {
                    q.push(State(x, y, 0));
                    visited[x][y][0] = 1;
                }
                
                if (horizontal == 0 && y + 1 < n && grid[x][y + 1] == 0 && grid[x + 1][y + 1] == 0 && !visited[x][y][1]) {
                    q.push(State(x, y, 1));
                    visited[x][y][1] = 1;
                }
            }
            moves++;
        }
        
        return -1; 
    }
};
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