<p>On an <code>2 x 3</code> board, there are five tiles labeled from <code>1</code> to <code>5</code>, and an empty square represented by <code>0</code>. A <strong>move</strong> consists of choosing <code>0</code> and a 4-directionally adjacent number and swapping it.</p>

<p>The state of the board is solved if and only if the board is <code>[[1,2,3],[4,5,0]]</code>.</p>

<p>Given the puzzle board <code>board</code>, return <em>the least number of moves required so that the state of the board is solved</em>. If it is impossible for the state of the board to be solved, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide1-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[4,0,5]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Swap the 0 and the 5 in one move.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide2-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[5,4,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> No number of moves will make the board solved.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide3-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[4,1,2],[5,0,3]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> 5 is the smallest number of moves that solves the board.
An example path:
After move 0: [[4,1,2],[5,0,3]]
After move 1: [[4,1,2],[0,5,3]]
After move 2: [[0,1,2],[4,5,3]]
After move 3: [[1,0,2],[4,5,3]]
After move 4: [[1,2,0],[4,5,3]]
After move 5: [[1,2,3],[4,5,0]]
</pre>

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

<ul>
	<li><code>board.length == 2</code></li>
	<li><code>board[i].length == 3</code></li>
	<li><code>0 &lt;= board[i][j] &lt;= 5</code></li>
	<li>Each value <code>board[i][j]</code> is <strong>unique</strong>.</li>
</ul>

class Solution {

struct Node
{
    Node(size_t v, size_t d, size_t z) : value(v), depth(d), zero_index(z) {}
    size_t value;
    size_t depth;
    size_t zero_index;
};

public:
    int slidingPuzzle(vector<vector<int>>& board) {
        size_t compressed = 0;
        size_t zero_index = 0;
        for (size_t i = 0; i < 6; ++i)
        {
            int n = board[i / 3][i % 3];
            if (n == 0)
            {
                zero_index = i;
            }
            compressed += n * pow(10, 5 - i);
        }

        size_t target = 123450;
        if (compressed == target)
        {
            return 0;
        }

        std::cout << "zero is at " << zero_index << ", " << compressed << std::endl;
        std::cout << index(compressed, zero_index);

        to_visit.emplace(Node(compressed, 0, zero_index));

        while (!to_visit.empty())
        {
            Node node = to_visit.front();
            to_visit.pop();
            visited.insert(node.value);
            if (node.value == target)
            {
                return node.depth;
            }

            if (node.zero_index % 3 != 0)
            {
                // can swap left
                Node left_swap_node = swap(node, node.zero_index - 1);
                if (!visited.count(left_swap_node.value))
                {
                    to_visit.emplace(std::move(left_swap_node));
                }
            }

            if (node.zero_index % 3 != 2)
            {
                // can swap right
                Node right_swap_node = swap(node, node.zero_index + 1);
                if (!visited.count(right_swap_node.value))
                {
                    to_visit.emplace(std::move(right_swap_node));
                }
            }

            if (node.zero_index / 3 > 0)
            {
                // can swap left
                Node left_swap_node = swap(node, node.zero_index - 3);
                if (!visited.count(left_swap_node.value))
                {
                    to_visit.emplace(std::move(left_swap_node));
                }
            }
            else
            {
                // can swap left
                Node left_swap_node = swap(node, node.zero_index + 3);
                if (!visited.count(left_swap_node.value))
                {
                    to_visit.emplace(std::move(left_swap_node));
                }
            }
        }


        return -1;
    }

private:

    std::unordered_set<size_t> visited;
    std::queue<Node> to_visit;


    Node swap(const Node& current, size_t target_index)
    {
        size_t pow10 = pow(10, 5 - target_index);
        size_t zero_pow10 = pow(10, 5 - current.zero_index);
        size_t val_at_index = index(current.value, target_index);
        size_t new_value = current.value - val_at_index * pow10 + val_at_index * zero_pow10;

        return Node(new_value, current.depth + 1, target_index);
    }

    size_t index(size_t num, size_t index)
    {
        size_t pow10 = pow(10, 5 - index);
        return (num / pow10) % (10);
    }


};
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