Lecture Notes — Lecture 09: Aggregation Patterns

Companion to the lecture plan and the worked examples. Read the Definitions before class, the Explanation after it; the practice questions and the lecture quiz close the loop.

Definitions

• Running total — a variable updated inside a loop so its final value summarises the whole sequence.
• Count — a running total restricted to items meeting a condition.
• Min / Max / Argmax — the smallest/largest value; argmax is the position or key of the maximum.
• Streak — the number of consecutive items meeting a condition; state resets on a miss.
• Window (k-slice) — the sum/aggregate of k consecutive items; the window slides one step at a time.
• Two-pass thinking — first compute an intermediate aggregate (e.g. total), then answer the real question from it.
• Best-so-far — the pattern 'if candidate is better than best: best = candidate' - the core of argmax.

Explanation

Name the pattern before writing the loop. 'Which day had the most sales?' is argmax; 'how many rainy days' is count; 'longest run of goals met' is streak. The pattern decides the state variables - once named, the loop writes itself.

Argmax needs two variables. best value AND best position/key. Forgetting the second is the classic cs-034 slip: students report 420 but not where it happened.

Streaks reset, they do not stop. A miss zeroes the current streak but the best streak survives in a second variable. cs-035's zeros (3 | 0 | 0) make reset-vs-stop visible on three separate queries.

Windows slide, they do not restart. cs-036: window sum of [3,5,2,8,1,4] with k=3 goes 10, 15, 11, 13 - each step adds the entering item and subtracts the leaving one. Recomputing each sum from scratch is correct but hides the structure.

Two-pass honesty. cs-033's stats dict (total, avg, best, below) is one pass; the window question needed two passes. Saying which is which - and why - is the lecture's analysis habit.

Examples

The lecture's worked examples live in examples.md; the case studies this lecture builds on are worked in class from the projector. The case sequence with difficulties:

• cs-033 (Beginner)
• cs-034 (Foundational)
• cs-035 (Intermediate)
• cs-036 (Advanced)

Common misconceptions

• Recomputing totals inside the loop instead of maintaining them.
• Forgetting to reset streak state after a miss.
• Confusing max with argmax - the value versus its position.
• Sliding windows by recomputing each sum from scratch and calling it 'fine'.

Summary and key takeaways

1. Name the pattern (total/count/min/argmax/streak/window), then write the loop.
2. Argmax tracks the value AND its position.
3. Streaks reset on miss; the best streak lives in a second variable.
4. Windows slide by adding one and removing one.

Practice questions

• For sales [100, 210, 205, 420, 90]: report total, max, argmax, count above 200, and the best 2-day window.
• Goals [1,1,0,1,1,1,0,1]: current streak, longest streak, and where the longest streak ends.
• Rain [3,5,2,8,1,4], k=3: list every window sum by the slide method (add one, remove one).
• Pages [12,0,25,8,30], target 10: count below, sum above, and argue which pattern answers 'how unusual is 0?'.

Where this leads

Next lecture: Strings Under the Lens. The quiz below checks this lecture's essentials before we build on them.