Choose an order to burst balloons to maximize the accumulated product score.
A good solution should
- State the invariant or decision rule that makes the approach correct.
- Explain time and space costs in terms of input size and required output.
- Handle empty, minimal, duplicate, and boundary-shaped inputs.
Reasoning prompt
Choose the last balloon burst in an interval. This makes the remaining left and right subproblems independent.
Use the linked judge for the canonical challenge. The examples above are compact TRT checks; create additional tests around the boundary most likely to break your invariant.