Burst Balloons
Problem Statement
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
Code
Python Code
class Solution(object):
def maxCoins(self, nums):
nums = [1] + nums + [1] # add the dummy head and tail, both are left till end and DO NOT burst them.
dp = [[0] * len(nums) for _ in nums]
def search(i, j):
if j - i < 2: return 0
if dp[i][j] > 0: return dp[i][j]
for k in range(i + 1, j):
dp[i][j] = max(dp[i][j], search(i, k) + search(k, j) + nums[i] * nums[k] * nums[j])
return dp[i][j]
return search(0, len(nums) - 1)