A correct program is stronger when you can explain why it must work. A short proof also exposes bugs before the interviewer has to find them.
State the invariant
Describe what is true before and after every iteration or recursive call. For binary search, any existing target remains inside the current interval. For a sliding window, the stored counts match exactly the elements between its boundaries.
Connect the steps
Explain initialization, preservation, and termination. Show that the invariant is true initially, that each update keeps it true, and that the stopping condition converts it into the desired answer. This structure is concise and works for many algorithm families.
Address boundaries and complexity
Mention empty input, duplicates, missing answers, overflow, and maximum depth where relevant. Then derive time and space costs from the operations performed rather than reciting a label. Clear reasoning often matters as much as the final code.
Continue with the book
Explore the full treatment, worked examples, and exercises in Algorithmic Edge.
Adapted from Algorithmic Edge, published by Choral Software. Article text and original examples © 2026 Choral Software. All rights reserved.