0312. Burst Balloons

https://leetcode.com/problems/burst-balloons

Description

You are given n balloons, indexed from 0 to n - 1. Each balloon is painted with a number on it represented by an array nums. You are asked to burst all the balloons.

If you burst the ith balloon, you will get nums[i - 1] * nums[i] * nums[i + 1] coins. If i - 1 or i + 1 goes out of bounds of the array, then treat it as if there is a balloon with a 1 painted on it.

Return the maximum coins you can collect by bursting the balloons wisely.

Example 1:

**Input:** nums = [3,1,5,8]
**Output:** 167
**Explanation:**
nums = [3,1,5,8] --> [3,5,8] --> [3,8] --> [8] --> []
coins =  3*1*5    +   3*5*8   +  1*3*8  + 1*8*1 = 167

Example 2:

**Input:** nums = [1,5]
**Output:** 10

Constraints:

• n == nums.length

• 1 <= n <= 500

• 0 <= nums[i] <= 100

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