Implement algorithms with lists

Specify the task before the code

State the input domain, required output, treatment of empty input and whether order and repeats matter. A list is ordered and can repeat values. Positions in this lesson start at 1. A correct procedure must meet the whole specification, not just work on one convenient example

L = [6, −4, 6, 0, 9]. With positions starting at 1, what is L[3]?

Count, sum and filter are different updates

Visit every entry once. A count adds 1 for each passing entry; a sum adds the entry’s value; a filter appends that entry to a new list. Initialise the accumulator or output list once before the loop. Filtering retains the original order and all passing repeated entries

In L = [6, −4, 6, 0, 9], how many entries are at least 6?

For L = [6, −4, 6, 0, 9], what is the sum of entries at least 6?

Use all five entries. Select “x ≥ threshold”, “Append x to selected” and “No: initialise once”. The threshold is fixed at 5. Inspect the pseudocode and trace. Then try a shorter prefix and an empty list, and return to all five entries before answering

For the stated full-list settings, which output preserves order and repeats?

Construct a filter, ungraded

Write pseudocode returning every entry at least 6 from any finite numerical list, keeping order and repeats. Include empty input. Implement it in a calculator or program, and test [] and [6, −4, 6, 0, 9]. Explain why the output contains exactly the required entries. Independent construction and proof are ungraded

Model: initialise, visit, conditionally append

Set selected ← []. FOR EACH x IN L: IF x ≥ 6 THEN append x to selected; END IF; END FOR. Output selected after the loop. For L = [] and L = [6, −4, 6, 0, 9], the expected outputs are [] and [6, 6, 9], respectively. After each visit, selected contains exactly the qualifying entries from the visited prefix, in their original order. The empty prefix satisfies this statement, appending a passing entry preserves it, and a failing entry leaves it unchanged. After the finite list ends, the statement describes the required output

A count should include entries equal to 6. Which boundary condition is correct?

Test deliberately chosen boundary cases

Write expected outputs before running code. Include empty and one-entry lists, repeated values, negative values, and values just below, at and above a threshold. Test both branches of a decision. A repeated successful run of one input adds little evidence; a finite test set alone does not prove correctness for all inputs

Initialisation can silently exclude valid data

For a maximum over a nonempty list, initialise best to its first entry and compare the remaining entries. Starting at zero fails on an all-negative list. For empty input there is no maximum, so either reject it explicitly or return a stated “no maximum” result; do not silently invent zero

An incorrect maximum algorithm starts best = 0 for L = [−7, −2, −5] and changes best only when x > best. What does it output?

Implement a conditional sum, ungraded

For a nonnegative integer N, construct a program summing the odd integers from 1 through N. State the inclusive loop convention. Give tests for N = 0, 1, 2 and 5, and explain correctness and termination. Implement your pseudocode using the indexing and remainder syntax of your chosen tool. Independent code and proof are ungraded

Model: a finite loop and its invariant

Set total ← 0. FOR i FROM 1 TO N: IF i MOD 2 = 1 THEN total ← total + i; END IF; END FOR. Output total. Expected outputs at N = 0, 1, 2 and 5 are 0, 1, 1 and 9. After processing i, total is the sum of the odd integers in the processed prefix. The condition includes exactly those values and the update adds each once. A finite nonnegative N gives N iterations; N = 0 gives none. In a language whose upper range endpoint is excluded, adjust the bound to include N.