215. Burst Balloons

HardDynamic Programming

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 i-th 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.

Examples

Input: [3,1,5,8]

Output: 167

Explanation: Bursting in the order 1,5,3,8 yields 3*1*5 + 3*5*8 + 1*3*8 + 1*8*1 = 167.

Constraints

n == nums.length
1 <= n <= 300
0 <= nums[i] <= 100

Run checks all cases above. Submit evaluates all test cases.