<p>You are asked to cut off all the trees in a forest for a golf event. The forest is represented as an <code>m x n</code> matrix. In this matrix:</p>

<ul>
	<li><code>0</code> means the cell cannot be walked through.</li>
	<li><code>1</code> represents an empty cell that can be walked through.</li>
	<li>A number greater than <code>1</code> represents a tree in a cell that can be walked through, and this number is the tree&#39;s height.</li>
</ul>

<p>In one step, you can walk in any of the four directions: north, east, south, and west. If you are standing in a cell with a tree, you can choose whether to cut it off.</p>

<p>You must cut off the trees in order from shortest to tallest. When you cut off a tree, the value at its cell becomes <code>1</code> (an empty cell).</p>

<p>Starting from the point <code>(0, 0)</code>, return <em>the minimum steps you need to walk to cut off all the trees</em>. If you cannot cut off all the trees, return <code>-1</code>.</p>

<p><strong>Note:</strong> The input is generated such that no two trees have the same height, and there is at least one tree needs to be cut off.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/trees1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> forest = [[1,2,3],[0,0,4],[7,6,5]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> Following the path above allows you to cut off the trees from shortest to tallest in 6 steps.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/trees2.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> forest = [[1,2,3],[0,0,0],[7,6,5]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> The trees in the bottom row cannot be accessed as the middle row is blocked.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> forest = [[2,3,4],[0,0,5],[8,7,6]]
<strong>Output:</strong> 6
<b>Explanation:</b> You can follow the same path as Example 1 to cut off all the trees.
Note that you can cut off the first tree at (0, 0) before making any steps.
</pre>

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

<ul>
	<li><code>m == forest.length</code></li>
	<li><code>n == forest[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>0 &lt;= forest[i][j] &lt;= 10<sup>9</sup></code></li>
	<li>Heights of all trees are <strong>distinct</strong>.</li>
</ul>

class Solution:
    def cutOffTree(self, forest: List[List[int]]) -> int:
        forest.append([0] * len(forest[0]))
        for row in forest: row.append(0)
        def bfs(end, start):
            if end == start: return 0
            visited, queue = set(), {start}
            visited.add(start)
            step = 0
            while queue:
                s = set()
                step += 1
                for p in queue:                    
                    for dr, dc in ((-1, 0), (1, 0), (0, 1), (0, -1)):
                        r, c = p[0] + dr, p[1] + dc
                        if not forest[r][c] or (r, c) in visited: continue
                        if (r, c) == end: return step
                        visited.add((r, c))
                        s.add((r, c))
                queue = s

        trees = [(height, r, c) for r, row in enumerate(forest) for c, height in enumerate(row) if forest[r][c] > 1]
        # check
        queue = [(0, 0)]
        reached = set()
        reached.add((0, 0))
        while queue:
            r, c = queue.pop()
            for dr, dc in ((-1, 0), (1, 0), (0, -1), (0, 1)):
                row, col = r + dr, c + dc
                if forest[row][col] and (row, col) not in reached:
                    queue.append((row, col))
                    reached.add((row,col))
        if not all([(i, j) in reached for (height, i, j) in trees]): return -1
        trees.sort()
        return sum([bfs((I,J),(i,j)) for (_, i, j), (_, I, J) in zip([(0, 0, 0)] + trees, trees)])
                
            
        
        
17600