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computationalthinking-week2

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Reading compass

Now · Week map

Loop patterns combine walking data with filters (AND predicates) and aggregates (sum, max, count).

Week map

Loop over collection → neutral start value → accumulate → scan for max/min → filter with AND → empty input edge cases.

Accumulation notation

Sum accumulator → start 0 → total ← total + x.
Product accumulator → start 1 → prod ← prod * x.
Count accumulator → start 0 → increment when condition holds.
Max scan → start first item or sentinel → replace when x > best.

AND filter

All conditions must pass:

“positive and even” → x > 0 and x % 2 == 0.

Contrast OR (week 3 procedures): “positive or even” passes more items.

Mini-list: [3, -4, 6, 8, -2]. Positive and even → only 6, 8.

Max and min scans


text
best ← first item
for each x in data:
    if x > best:
        best ← x

Empty data: no first item — algorithm must guard or define error.

Mini-example: [5, 2, 9, 9, 1]. Max scan ends 9. For positive max only: ignore nonpositive, start best at first positive or None.

Pattern families

Easy — Sum or count list

Sum all elements.
Count how many equal a target.
Product of list (start 1).

Medium — Max with AND filter

Largest among entries meeting two tests.
Count items where both predicates true.
Sum only negatives in list.

Hard — Compound loop logic

Multiple accumulators in one pass (sum and count together).
Empty list: max undefined; count returns 0.
Index loop vs for-each — same totals if bounds correct.

Worked mini-examples

Example 1 — Sum.

Data [10, 20, 5]. total=0 → 10 → 30 → 35.

Example 2 — AND count.

Data [2, 3, 4, 5, 6]. Count even and >3:

4 yes, 6 yes → count 2.

Example 3 — Filtered max.

Data [-1, 8, 3, 12, 5]. Max among positive:

Candidates 8,3,12,5 → max 12.

Example 4 — Empty.

Data []. Sum loop leaves total=0. Max scan without guard — undefined; safe design returns sentinel or “no data”.

Example 5 — Dual accumulator.

Data [1,2,3,4]. Track sum and count of evens in one pass:

Evens 2,4 → sum 6, count 2.

Traps

Product accumulator starting at 0 (always 0).
OR filter when problem says “all conditions”.
Max of empty without check.
Off-by-one manual index: 0..len-1 not 0..len.
Updating max before checking filter — polluted by ineligible items.

Diagnostic (try yourself)

List [7, -2, 4, 0, 11]. What is the sum of positive entries only?
Same list: how many entries are both positive and less than 10?
List [3, 9, 1, 9, 2]. What is the maximum value? If we only consider values ≥ 5, what is the max?
Why does product accumulation start at 1, not 0?
One pass: for [5, 10, 15, 20], find sum and count of multiples of 5.