A window maintains a contiguous range with an update rule for entering and leaving elements. Its shrinking rule must follow the constraint.
Before you start
You should know arrays, loops and basic complexity notation. Start with a small input you can trace by hand. State what each variable means and which invariant is maintained, then use that invariant to explain correctness before discussing performance or writing a more compact solution.
The practical goal is to reason through this situation: For bounded duplicate counts, expand right and shrink left until the invariant holds. Read the walkthrough first, then try the interview exercise before opening its answer. The important part is explaining the decision and its consequences, rather than remembering a definition alone.
Step-by-step walkthrough
Step 1: Define window validity
Track the exact property required for the contiguous range.
Step 2: Update both boundaries
Add entering values and remove leaving values consistently.
Step 3: Prove shrink decisions
Removing positive values reduces a sum; negative values break that monotonic assumption.
Worked scenario
For bounded duplicate counts, expand right and shrink left until the invariant holds.
For positive [2,1,3] and a maximum sum of 4, adding 3 makes the whole sum 6. Removing 2 restores 4. With negative values, removing an element may increase the sum, so that same reasoning cannot justify all decisions. State whether the goal is longest valid or shortest qualifying range.
Common mistake
A sum-based shrinking rule can fail when negative values destroy monotonicity.
Verify the behavior
Test boundary movement, repeated values and a negative-input counterexample where relevant.
Interview exercise
Explain why positive sums work.
Answer and reasoning
Removing positive elements cannot increase the sum, allowing a predictable shrink decision; negative inputs need different reasoning.
Continue learning
Compare the scenario with the Data Structures and Algorithms interview questions and test your understanding with the Data Structures and Algorithms MCQs. For terminology and implementation details, consult the reference material.