Week 4 revision and practice
Try each question before opening the explained answer. Use the labs to test your reasoning, then explain why the method works, what it counts and which assumptions it needs.
Try it yourself
Six distinct cards: how many unordered pairs? Show two ways to calculate it.
Show explained answer
6 × 5 ÷ 2 = 15, or 5 + 4 + 3 + 2 + 1 = 15. Remove self-pairs and keep each reversed pair only once.
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A nine-card dataset splits into bins of 4, 3 and 2. How many within-bin pair checks remain?
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6 + 3 + 1 = 10, compared with 36 unbinned checks. Add nine placement visits separately when describing the work.
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A date bin uses the exact birthday key. How can you count matching pairs without comparing every pair in the bin?
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As each new card arrives, add the number of earlier cards with that same key to PairCount, then increase that key’s count. In a group of three matching dates the additions are 0, 1 and 2, totalling 3. This is a stated extension using per-key counts.
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A class has two January birthdays, both January 8, and two March birthdays, both March 8. How many matching pairs?
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Two: one January pair and one March pair. Do not compare the two months merely because their day numbers agree.
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Every bill in a two-bill customer bin comes from the same shop. Does that meet the lecture’s definition?
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Yes. At least two observed bills and one distinct shop meet it. This does not predict unobserved visits.
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A developer bins bills by BillAmount to find customer loyalty. Is that enough?
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No. Loyalty is about all visits of one customer and their shops, not spending size. Group by customer.
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After checking an outer row X, the code returns X to the unprocessed table. What can go wrong?
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X may be selected again, causing repeated pairs or even nontermination. Processed outer rows must stay separate unless the algorithm has another explicit progress mechanism.
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What happens to the full result when the score-card order is reversed?
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Exact complete birthday and city/Maths pair sets remain the same. Early-stop work and the first pair encountered can change.
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Does two nested loops always imply n squared visits?
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No. A loop over disjoint bins followed by a scan of each bin’s own contents visits each record once overall. Count the actual visits. All pairs within one size-n group does grow quadratically.
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Why is the total-band partner finder not guaranteed to be optimal?
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It ignores some cross-band pairs, uses a chosen subject-strength heuristic, and lists candidates without solving an exclusive global assignment objective.
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For a 4-by-3 cross-group search, how many candidate pairs are checked?
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4 × 3 = 12. These are pairs across two separate groups; do not divide this product by 2.
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In a pronoun search, does restoring the total number of cards satisfy an exact restoration contract?
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No. Their values, original order and marked position must also survive. The same count can hide a scrambled paragraph.
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Why is a correct candidate at position 40 insufficient to prove the rule generally correct?
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A few successful examples do not rule out counterexamples. Positions 55 and 61 expose failures of the nearest explicit name rule.
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A condition is A OR B, but the body increases both a noun counter and a verb counter. What should you inspect?
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Which condition should control each update. Shared entry into the body does not mean both categories apply; separate conditional updates are needed.
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For reluctant, what is true after processing seven letters?
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The prefix relucta contains 3 vowels and 4 consonants. Their sum is 7. The next letter position is 8.
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What happens if a word procedure swaps its return values but the caller still expects (vowels, consonants)?
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The caller interprets the counts incorrectly. Return order is part of the interface contract, just like parameter order.
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A score record is valid but two month labels have different spellings. Is a type check alone enough?
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No. Meaningful comparison also needs consistent representation or normalization. Jul and July denote the same month.
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Which lesson from this week helps in every algorithm trace?
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State exactly what the variables mean, what one step processes, how progress happens, when it stops, and what the procedure promises to preserve.