Burst Balloons — LeetCode 312 Python Solution

The problem

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.

Example

Input

nums = [3,1,5,8]

Output

167

Explanation

nums = [3,1,5,8] --> [3,5,8] --> [3,8] --> [8] --> []

Python solution

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

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 312. Burst Balloons is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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