cut-off-trees-for-golf-event

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Algorithms

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:

<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>

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.

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).

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

Note: 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.

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

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

Example 3:

<pre>
Input: forest = [[2,3,4],[0,0,5],[8,7,6]]
Output: 6
Explanation: 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>

&nbsp;
Constraints:

<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;= 109</code></li>
	<li>Heights of all trees are distinct.</li>
</ul>

cutOffTree

Cut Off Trees for Golf Event

Breadth-First Search

Array

Matrix

Heap (Priority Queue)

你被请来给一个要举办高尔夫比赛的树林砍树。树林由一个 <code>m x n</code> 的矩阵表示， 在这个矩阵中：

<ul>
	<li><code>0</code> 表示障碍，无法触碰</li>
	<li><code>1</code> 表示地面，可以行走</li>
	<li><code>比 1 大的数</code> 表示有树的单元格，可以行走，数值表示树的高度</li>
</ul>

每一步，你都可以向上、下、左、右四个方向之一移动一个单位，如果你站的地方有一棵树，那么你可以决定是否要砍倒它。

你需要按照树的高度从低向高砍掉所有的树，每砍过一颗树，该单元格的值变为 <code>1</code>（即变为地面）。

你将从 <code>(0, 0)</code> 点开始工作，返回你砍完所有树需要走的最小步数。 如果你无法砍完所有的树，返回 <code>-1</code> 。

可以保证的是，没有两棵树的高度是相同的，并且你至少需要砍倒一棵树。

 

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/trees1.jpg" style="width: 242px; height: 242px;" />
<pre>
输入：forest = [[1,2,3],[0,0,4],[7,6,5]]
输出：6
解释：沿着上面的路径，你可以用 6 步，按从最矮到最高的顺序砍掉这些树。</pre>

示例 2：
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/trees2.jpg" style="width: 242px; height: 242px;" />
<pre>
输入：forest = [[1,2,3],[0,0,0],[7,6,5]]
输出：-1
解释：由于中间一行被障碍阻塞，无法访问最下面一行中的树。
</pre>

示例 3：

<pre>
输入：forest = [[2,3,4],[0,0,5],[8,7,6]]
输出：6
解释：可以按与示例 1 相同的路径来砍掉所有的树。
(0,0) 位置的树，可以直接砍去，不用算步数。
</pre>

 

提示：

<ul>
	<li><code>m == forest.length</code></li>
	<li><code>n == forest[i].length</code></li>
	<li><code>1 <= m, n <= 50</code></li>
	<li><code>0 <= forest[i][j] <= 109</code></li>
</ul>