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Loops and invariants

Loops and invariants

1.[2p]

How many times does the body of for (let i = 3; i < 12; i += 2) run?

CorrectNot quite: 5

2.[3p]

What is a loop invariant?

Correct
The answer is: A claim about the state that holds before the loop, is preserved by every pass, and is strong enough at the end to give the wanted result
The answer is: A claim about the state that holds before the loop, is preserved by every pass, and is strong enough at the end to give the wanted result
The answer is: A claim about the state that holds before the loop, is preserved by every pass, and is strong enough at the end to give the wanted result

3.[2p]

Put the three parts of a loop in the order the machine reaches them for the first time.

  1. The update

  2. The initialisation

  3. The condition

Show the answer

c, a, b

4.[3p]

for (let x = 0; x < 1; x += 0.1) steps++; How many times does the body run?

CorrectNot quite: 11

5.[2p]

The Collatz loop has been checked by computer for every starting value below about 2.95×1020 without exception, which counts as a proof that it always terminates.

The answer is: False
Correct

6.[3p]

Which of these are reasons for the for (let i = 0; i < n; i++) convention?

Select all that apply

Correct
Correct
Correct
The answer is: The number of passes is `n`, readable off the header with no arithmetic, Two adjacent half open ranges join with no gap and no overlap, It matches array indices, where the first element is at 0 and the last at `n - 1`

7.[2p]

How many trial divisions does for (let d = 2; d * d <= n; d++) perform for n = 97?

CorrectNot quite: 8

8.[3p]

Match each term to what it means.

  • Invariant

  • Variant

  • Accumulator

  • Fencepost error

  • Infinite loop

  • a name declared outside the loop and updated inside it

  • a claim the body preserves on every pass

  • counting the gaps when you meant the boundaries

  • a whole number that strictly decreases and cannot go below zero

  • a condition that never becomes false because the state stops changing

Show the answer

Invariant: a claim the body preserves on every pass Variant: a whole number that strictly decreases and cannot go below zero Accumulator: a name declared outside the loop and updated inside it Fencepost error: counting the gaps when you meant the boundaries Infinite loop: a condition that never becomes false because the state stops changing

9.[2p]

A program neither crashes nor prints anything and never returns. What is the most likely cause?

Correct
The answer is: A loop whose state is not being changed, so its condition never becomes false
The answer is: A loop whose state is not being changed, so its condition never becomes false
The answer is: A loop whose state is not being changed, so its condition never becomes false