312. Burst Balloons

Hard

7.5K

190

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`

balloon, you will get ^{th}`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:167Explanation: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`

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