[FEATURE REQUEST]Add "Burst Balloons" DP Problem

[Shiva953]

What would you like to Propose?

The "burst balloons" problem, which involves determining the optimal order of bursting balloons to maximize the total coins obtained by considering adjacent balloons and applying Dynamic Programming.

Issue details

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.

Additional Information

An example for the same would be :
Input - nums = [3,1,5,8]
Output - 167
Explanation:
nums = [3,1,5,8] --> [3,5,8] --> [3,8] --> [8] --> []
coins = 315 + 358 + 138 + 181 = 167