minimum-cost-tree-from-leaf-values

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Algorithms

Given an array <code>arr</code> of positive integers, consider all binary trees such that:

<ul>
	<li>Each node has either <code>0</code> or <code>2</code> children;</li>
	<li>The values of <code>arr</code> correspond to the values of each leaf in an in-order traversal of the tree.</li>
	<li>The value of each non-leaf node is equal to the product of the largest leaf value in its left and right subtree, respectively.</li>
</ul>

Among all possible binary trees considered, return the smallest possible sum of the values of each non-leaf node. It is guaranteed this sum fits into a 32-bit integer.

A node is a leaf if and only if it has zero children.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree1.jpg" style="width: 500px; height: 169px;" />
<pre>
Input: arr = [6,2,4]
Output: 32
Explanation: There are two possible trees shown.
The first has a non-leaf node sum 36, and the second has non-leaf node sum 32.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree2.jpg" style="width: 224px; height: 145px;" />
<pre>
Input: arr = [4,11]
Output: 44
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= arr.length &lt;= 40</code></li>
	<li><code>1 &lt;= arr[i] &lt;= 15</code></li>
	<li>It is guaranteed that the answer fits into a 32-bit signed integer (i.e., it is less than 231).</li>
</ul>

mctFromLeafValues

Minimum Cost Tree From Leaf Values

Stack

Greedy

Array

Dynamic Programming

Monotonic Stack

给你一个正整数数组&nbsp;<code>arr</code>，考虑所有满足以下条件的二叉树：

<ul>
	<li>每个节点都有 <code>0</code> 个或是 <code>2</code> 个子节点。</li>
	<li>数组&nbsp;<code>arr</code>&nbsp;中的值与树的中序遍历中每个叶节点的值一一对应。</li>
	<li>每个非叶节点的值等于其左子树和右子树中叶节点的最大值的乘积。</li>
</ul>

在所有这样的二叉树中，返回每个非叶节点的值的最小可能总和。这个和的值是一个&nbsp;32 位整数。

如果一个节点有 0 个子节点，那么该节点为叶节点。

&nbsp;

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree1.jpg" style="width: 500px; height: 169px;" />
<pre>
输入：arr = [6,2,4]
输出：32
解释：有两种可能的树，第一种的非叶节点的总和为 36 ，第二种非叶节点的总和为 32 。 
</pre>

示例 2：
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree2.jpg" style="width: 224px; height: 145px;" />
<pre>
输入：arr = [4,11]
输出：44
</pre>

&nbsp;

提示：

<ul>
	<li><code>2 &lt;= arr.length &lt;= 40</code></li>
	<li><code>1 &lt;= arr[i] &lt;= 15</code></li>
	<li>答案保证是一个 32 位带符号整数，即小于&nbsp;<code>231</code> 。</li>
</ul>