Day36_Burst Baloons.py

# Burst Baloons                             Difficulty = Hard


# 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


class Solution:
    def maxCoins(self, nums: List[int]) -> int:
        nums = [1] + [x for x in nums if x] + [1]
        n = len(nums)
        dp = [[0] * n for _ in range(n)]
        for i in range(n-3, -1, -1):
          for j in range(i+2, n):
               temp = nums[i] * nums[j]
               dp[i][j] = max(temp * nums[k] + dp[i][k] + dp[k][j] for k in range(i+1, j))
        return dp[0][-1]