<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:
    // 1 : horizontal
    // 2 : vertical
    int minimumMoves(vector<vector<int>>& g) {
        int n = g.size();
        queue<vector<int>> q; // head pos - direction
        vector<vector<vector<bool>>> vs(n, vector<vector<bool>>(n, vector<bool>(3, false)));
        int ans = 0;
        q.push({0, 1, 1});
        vs[0][1][1] = true;
        while (!q.empty()) {
            int sz = q.size();
            while (sz--) {
                int r = q.front()[0];
                int c = q.front()[1];
                int dir = q.front()[2];
                q.pop();
                if (r == n-1 && c == n-1 && dir == 1) return ans;
                if (dir == 1) { // horizontal
                    // go right
                    if (c + 1 < n && g[r][c+1] == 0 &&  !vs[r][c+1][1]) {
                        vs[r][c+1][1] = true;
                        q.push({r, c+1, 1});
                    }
                    // rotate clockwise
                    if (r + 1 < n && g[r+1][c-1] == 0 && g[r+1][c] == 0 && !vs[r + 1][c-1][2]) {
                        vs[r+1][c-1][2] = true;
                        q.push({r+1, c-1, 2});
                    }
                    // go down
                    if (r + 1 < n && g[r+1][c-1] == 0 && g[r+1][c] == 0 && !vs[r + 1][c][1]) {
                        vs[r+1][c][1] = true;
                        q.push({r+1, c, 1});
                    }                    
                } else { // vertical
                    // go down
                    if (r + 1 < n && g[r+1][c] == 0 && !vs[r+1][c][2]) {
                        vs[r+1][c][2] = true;
                        q.push({r+1, c, 2});
                    }
                    // rotate counterclockwise
                    if (c+1 < n && g[r][c+1] == 0 && g[r-1][c+1] ==0 && !vs[r-1][c+1][1]) {
                        vs[r-1][c+1][1] = true;
                        q.push({r-1, c+1, 1});
                    }
                    // go right
                    if (c+1 < n && g[r][c+1] == 0 && g[r-1][c+1] ==0 && !vs[r][c+1][2]) {
                        vs[r][c+1][2] = true;
                        q.push({r, c+1, 2});
                    }                    
                }

            }
            ans++;
        }
        return -1;;
    }
};
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