Lecture 09 — Aggregation Patterns

Learning objectives

• Implement running totals, min/max, and counting loops
• Combine aggregation with filtering
• Initialise accumulators correctly

Case-based lecture: you attempt, we discuss, then we reveal.

The plan

• Four cases: cs-033, cs-142, cs-034, cs-035, cs-036
• Each: 5-minute attempt → discussion → reveal → prompt
• Worked examples in between — ask anything
• Break mid-lecture · exit question at the end

Key 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.

The reading log: one pass, four aggregates

Expected: {'total': 75, 'avg': 15.0, 'best': 30, 'below': 2}

Cost: O(n) time, O(1) space - four aggregates for the price of one loop.

Stockroom spikes: argmax with witnesses

Expected: [1, 3]

Cost: O(n) time, O(1) extra space (output excluded).

The longest streak: reset vs stop

Expected: best 3 | end-current 0 in the reference's variant | all-miss 0

Cost: O(n) time, O(1) space - the two-variable discipline is the whole lesson.

Rainfall windows: the slide

pages = [12, 0, 25, 8, 30]
target = 10
total = sum(pages)
best = max(pages)
below = sum(1 for p in pages if p < target)
print(total, total / len(pages), best, below)

Expected: sums [10, 15, 11, 13]; maxima [5, 8, 8, 8] (the reference's question)

Cost: O(n) slide vs O(n*k) recomputed - the analysis teaser for Block III.

• **Input:** pages [12, 0, 25, 8, 30], target 10
• **Output:** total 75, average 15.0, best 30, below-target days 3 (0, 8, and... recount: 0,8 yes; 12 no; careful)
• Solve for the worked instance first. Then ask what would change if one
• number, name, or condition were replaced by something stranger.

Pseudocode, flowchart or Python. State one assumption. Compare with your neighbour at minute 4.

cs-033 — discuss

• What did the deciding quantity turn out to be?
• Which assumption shaped your answer?
• After the solution is revealed, the class spends five minutes on this prompt: **"Which accumulator was hardest to get right, and what test would have caught the mistake?"**

Instructor: the reveal, the reasoning section and common wrong turns are in the instructor distribution for cs-033 — not embedded in this deck.

• **Input:** the eleven slips
• **Output:** Zoe 4, Amir 3, Bea 2, Cal 2 — winner Zoe 36.4%,
• runner-up Amir 27.3% — one honest sentence
• Solve for the worked instance first. Then ask what would change if one

Pseudocode, flowchart or Python. State one assumption. Compare with your neighbour at minute 4.

cs-142 — discuss

• What did the deciding quantity turn out to be?
• Which assumption shaped your answer?
• After the solution is revealed, the class spends five minutes on this prompt: **"The committee chair asks you to announce 'Zoe wins by a landslide.' Redraft the sentence so it stays true with the same numbers."**

Instructor: the reveal, the reasoning section and common wrong turns are in the instructor distribution for cs-142 — not embedded in this deck.

• **Input:** sales [100, 210, 205, 420, 90]
• **Output:** spike days: index 1 (210 > 2x100) and index 3 (420 > 2x205); not index 2 (205 < 2x210)
• Solve for the worked instance first. Then ask what would change if one
• number, name, or condition were replaced by something stranger.

Pseudocode, flowchart or Python. State one assumption. Compare with your neighbour at minute 4.

cs-034 — discuss

• What did the deciding quantity turn out to be?
• Which assumption shaped your answer?
• After the solution is revealed, the class spends five minutes on this prompt: **"Where exactly would this solution break first if the input grew to a million items — and would anything break at all?"**

Instructor: the reveal, the reasoning section and common wrong turns are in the instructor distribution for cs-034 — not embedded in this deck.

• **Input:** goals met: [1, 1, 0, 1, 1, 1, 0, 1]
• **Output:** current best streak 3 (days 4-6); final streak at end is 1 - do not confuse the two
• Solve for the worked instance first. Then ask what would change if one
• number, name, or condition were replaced by something stranger.

Pseudocode, flowchart or Python. State one assumption. Compare with your neighbour at minute 4.

cs-035 — discuss

• What did the deciding quantity turn out to be?
• Which assumption shaped your answer?
• After the solution is revealed, the class spends five minutes on this prompt: **"Which accumulator was hardest to get right, and what test would have caught the mistake?"**

Instructor: the reveal, the reasoning section and common wrong turns are in the instructor distribution for cs-035 — not embedded in this deck.

• **Input:** rain [3, 5, 2, 8, 1, 4], window k = 3
• **Output:** window maxima: 5, 8, 8, 8 (windows [3,5,2], [5,2,8], [2,8,1]... recheck: [2,8,1] -> 8, [8,1,4] -> 8)
• Solve for the worked instance first. Then ask what would change if one
• number, name, or condition were replaced by something stranger.

Pseudocode, flowchart or Python. State one assumption. Compare with your neighbour at minute 4.

cs-036 — discuss

• What did the deciding quantity turn out to be?
• Which assumption shaped your answer?
• After the solution is revealed, the class spends five minutes on this prompt: **"Where exactly would this solution break first if the input grew to a million items — and would anything break at all?"**

Instructor: the reveal, the reasoning section and common wrong turns are in the instructor distribution for cs-036 — not embedded in this deck.

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 & exit question

• Named technique today: Aggregation Patterns
• Four cases attempted — methods before answers

Exit question (choose one, 60 seconds)

1. Name the aggregation pattern for 'which day had the most sales'.
2. Why reset streak state?
3. What is two-pass thinking and when does it pay?