Practice: Burst Balloons

Problem: https://leetcode.com/problems/burst-balloons/

Recognition reminder: you burst balloons one at a time, and bursting one earns coins equal to the product of it and its two current neighbors; you want the maximum total. The subproblem is a span of the array, named by its two endpoints, and the answer for a span builds from smaller spans inside it. Two endpoints naming the state is the tell for interval DP, a flavor of 2-D DP. The reframing that unlocks it (think about which balloon in a span is burst last, not first) is in the week README’s core concepts; do not look past that hint until you have wrestled with it.

Before you start (the five-beat rhythm)

  1. Your Pattern Card for this week is already written.
  2. Name the pattern aloud and write your approach as a plain-English comment before any code.
  3. Struggle floor: 25 minutes unaided. No hints, no AI, no Discuss tab.
  4. If stuck past the floor, ask the tutor for a hint. Six rungs, one per ask.
  5. Debrief in your commit message before moving to the next problem.

Your target

Fill these in yourself before you look at anyone else’s solution:

Target time complexity:  ____
Target space complexity: ____

This one has three nested loops in the natural solution: the two endpoints of the span, and the choice of which balloon inside it. Be able to say what each loop ranges over before you accept the complexity.

Where your code goes

Write your solution in your own work repo (see getting-started.md), not in this folder. This folder ships only the problem spec and a provided-example test (tests/test_provided.py) so you can check the given cases locally before you submit to LeetCode’s judge. The judge is the oracle; the tutor will not confirm your answer by reading it.

Debrief (paste into your commit message) 

1. What pattern did this turn out to be?
2. What was the trigger phrase or input shape that should have made me reach for it?
3. What was the time and space complexity, and what would dominate at scale?
4. What edge case would have broken my first attempt?
5. What would I do differently in three days when I see this cold?