Cut Off Trees for Golf Event
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0600-0699/0675.Cut%20Off%20Trees%20for%20Golf%20Event/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0600-0699/0675.Cut%20Off%20Trees%20for%20Golf%20Event/images/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>
Breadth-First Search; Array; Matrix; Heap (Priority Queue)
var dirs = [][]int{{-1, 0}, {1, 0}, {0, -1}, {0, 1}}

type tree struct {
	height int
	pos    int
}

func cutOffTree(forest [][]int) int {
	row, col := len(forest), len(forest[0])

	bfs := func(start, end int) int {
		q := []int{start}
		vis := make(map[int]bool)
		vis[start] = true
		step := 0
		for n := len(q); n > 0; n = len(q) {
			for i := 0; i < n; i++ {
				state := q[0]
				q = q[1:]
				if state == end {
					return step
				}
				for k := 0; k < 4; k++ {
					x, y := state/col+dirs[k][0], state%col+dirs[k][1]
					nxt := x*col + y
					if x >= 0 && x < row && y >= 0 && y < col && forest[x][y] != 0 && !vis[nxt] {
						q = append(q, nxt)
						vis[nxt] = true
					}
				}
			}
			step++
		}
		return -1
	}

	var trees []tree
	for i := 0; i < row; i++ {
		for j := 0; j < col; j++ {
			if forest[i][j] > 1 {
				trees = append(trees, tree{forest[i][j], i*col + j})
			}
		}
	}
	sort.Slice(trees, func(i, j int) bool {
		return trees[i].height < trees[j].height
	})

	ans, start := 0, 0
	for _, t := range trees {
		end := t.pos
		step := bfs(start, end)
		if step == -1 {
			return -1
		}
		ans += step
		start = end
	}
	return ans
}