AlgoLounge

Burst Balloons

hard

You are given n balloons, indexed from 0 to n - 1. Each balloon is painted with a number on it represented by 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

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 = 15 + 120 + 24 + 8 = 167

Example 2:

  • Input: nums = [1,5]
  • Output: 10
  • Explanation:
    nums = [1,5] → [5] → []
    coins = 1*1*5 + 1*5*1 = 5 + 5 = 10

Constraints

  • n == nums.length
  • 1 <= n <= 300
  • 0 <= nums[i] <= 100
TypeScript
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List of test cases (12)
Case 1
nums = [3,1,5,8]
Case 2
nums = [1,5]
Case 3
nums = [1]
Case 4
nums = [2,4,8]
Case 5
nums = [5,10]
Case 6
nums = [9,76,64,21]
Case 7
nums = [7,9,8,0,2]
Case 8
nums = [1,2,3,4,5]
Case 9
nums = [100,1,1,100]
Case 10
nums = [6,2,7,4,3,5]
Case 11
nums = [50,60,70]
Case 12
nums = [15,25,35,45]