#+ANKI_DECK: study_deck_02
* TODO 0312. Burst Balloons :hard:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*0312. Burst Balloons][0312. Burst Balloons]]
:END:

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 ~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/.

*Example 1:*


#+begin_src
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
#+end_src


*Example 2:*


#+begin_src
Input: nums = [1,5]
Output: 10
#+end_src


*Constraints:*

 - ~n == nums.length~

 - ~1 <= n <= 300~

 - ~0 <= nums[i] <= 100~

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python
class Solution:
    def maxCoins(self, nums: List[int]) -> int:
#+end_src

** TODO C++
#+begin_src cpp
class Solution {
public:
    int maxCoins(vector<int>& nums) {
        
    }
};
#+end_src