burst-balloons

Burst Balloons

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You are given <code>n</code> balloons, indexed from <code>0</code> to <code>n - 1</code>. Each balloon is painted with a number on it represented by an array <code>nums</code>. You are asked to burst all the balloons.

If you burst the <code>ith</code> balloon, you will get <code>nums[i - 1] * nums[i] * nums[i + 1]</code> coins. If <code>i - 1</code> or <code>i + 1</code> goes out of bounds of the array, then treat it as if there is a balloon with a <code>1</code> painted on it.

Return the maximum coins you can collect by bursting the balloons wisely.

&nbsp;
Example 1:

<pre>
Input: nums = [3,1,5,8]
Output: 167
Explanation:
nums = [3,1,5,8] --&gt; [3,5,8] --&gt; [3,8] --&gt; [8] --&gt; []
coins = 3*1*5 + 3*5*8 + 1*3*8 + 1*8*1 = 167</pre>

Example 2:

<pre>
Input: nums = [1,5]
Output: 10
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 300</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 100</code></li>
</ul>

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