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1130. Minimum Cost Tree From Leaf Values

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Description

Given an array arr of positive integers, consider all binary trees such that:

<li>Each node has either 0 or 2 children;</li>

<li>The values of <code>arr</code> correspond to the values of each&nbsp;<strong>leaf</strong> in an in-order traversal of the tree.&nbsp; <em>(Recall that a node is a leaf if and only if it has 0 children.)</em></li>

<li>The value&nbsp;of each non-leaf node is equal to the product of the largest leaf value in its left and right subtree respectively.</li>

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.

 

Example 1:

Input: arr = [6,2,4]

Output: 32

Explanation:

There are two possible trees.  The first has non-leaf node sum 36, and the second has non-leaf node sum 32.



    24            24

   /  \          /  \

  12   4        6    8

 /  \               / \

6    2             2   4

 

Constraints:

<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 (ie.&nbsp;it is less than <code>2^31</code>).</li>

Solutions

Python3

Java

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