README.md

312. Burst Balloons

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 <= 300
• 0 <= nums[i] <= 100

Solutions (Python)

1. Solution

from functools import cache


class Solution:
    def maxCoins(self, nums: List[int]) -> int:
        @cache
        def subarrayMaxCoins(i: int, j: int) -> int:
            if i >= j:
                return 0

            ret = 0

            for k in range(i, j):
                coins = nums[k]
                if i > 0:
                    coins *= nums[i - 1]
                if j < len(nums):
                    coins *= nums[j]
                coins += subarrayMaxCoins(i, k) + subarrayMaxCoins(k + 1, j)
                ret = max(ret, coins)

            return ret

        return subarrayMaxCoins(0, len(nums))