# 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 2 3 4 5 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:

 1 2 Input: nums = [1,5] Output: 10

Constraints:

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

## Sample C++ Code

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 class Solution { public: int maxCoins(vector& nums) { int n = nums.size(); nums.insert(nums.begin(), 1); nums.push_back(1); vector> dp(nums.size(), vector(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[1][n]; } };