Burst Balloons

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Problem

Given n balloons with values, bursting a balloon earns coins equal to the product of its two current neighbors' values (using 1 for a missing out-of-bounds neighbor); once burst, its former neighbors become adjacent. Return the maximum coins obtainable by bursting all the balloons.

Examples

Example 1

Input:nums = [3,1,5,8]

Output:167

Constraints

1 <= nums.length <= 300

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How to approach it: the 2-D Dynamic Programming pattern

The same DP idea as 1-D, but the state depends on two indices — often two positions in a grid, or a position in each of two sequences being compared.

Look for this pattern when

You're comparing two sequences (finding a longest common subsequence, edit distance).
You're computing paths or optimal values across a 2-D grid.

Read the full 2-D Dynamic Programming guide →

Video walkthroughs

Original problem on LeetCode ↗