# Burst Balloons Problem

## Description

LeetCode Problem 312.

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:

``````1
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Input: nums = [3,1,5,8]
Output: 167
Explanation:
nums = [3,1,5,8] --> [3,5,8] --> [3,8] -->  --> []
coins =  3*1*5    +   3*5*8   +  1*3*8  + 1*8*1 = 167
``````

Example 2:

``````1
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Input: nums = [1,5]
Output: 10
``````

Constraints:

• n == nums.length
• 1 <= n <= 500
• 0 <= nums[i] <= 100

## Sample C++ Code

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class Solution {
public:
int maxCoins(vector<int>& nums) {
int n = nums.size();
nums.insert(nums.begin(), 1);
nums.push_back(1);
vector<vector<int>> dp(nums.size(), vector<int>(nums.size(), 0));
for (int len = 1; len <= n; ++len)
for (int left = 1; left <= n - len + 1; ++left) {
int right = left + len - 1;
for (int k = left; k <= right; ++k)
dp[left][right] = max(dp[left][right], nums[left-1]*nums[k]*nums[right+1] + dp[left][k-1] + dp[k+1][right]);
}
return dp[n];
}
};
``````