Problems: Algorithm Challenge

A number lab needs the prime at a requested position.

Specification: Define nth_prime(k) to return the k-th prime, where k is 1-indexed. Use a while counter over candidate numbers. Test each candidate with the inner loop for d in range(2, candidate):, and break when candidate % d == 0; the empty range makes 2 prime.

Worked sample:

nth_prime(1) -> 2
nth_prime(5) -> 11
nth_prime(10) -> 29

A display needs the digits of a non-negative number turned around.

Specification: Define reverse_digits(n) to reverse the digits of a non-negative integer arithmetically. Start rev at 0, then repeat rev = rev * 10 + n % 10 and n = n // 10 with a while loop. Return rev; make sure an input of 0 returns 0.

Worked sample:

reverse_digits(1234) -> 4321
reverse_digits(1200) -> 21
reverse_digits(0) -> 0

A scoreboard needs its three strongest results in order.

Specification: Define top_three(scores) for a list containing at least three values. Use sorted(scores) to make an ascending list, then read its last three values by index in reverse order — for example, if ordered = sorted(scores), then ordered[len(ordered) - 1] is the largest — and return them as a descending list. Do not use .copy() or [::-1].

Worked sample:

top_three([4,9,1,7,3]) -> [9,7,4]
top_three([5,5,2,8]) -> [8,5,5]
top_three([10,20,30]) -> [30,20,10]

Two sorted arrival lists need to become one sorted line.

Specification: Define merge_sorted(a, b) to merge two ascending lists into one ascending list. Use a two-index walk with while i < len(a) and j < len(b), append the smaller current value, and then drain each remaining list with its own while loop.

Worked sample:

merge_sorted([1,4,6],[2,3,5]) -> [1,2,3,4,5,6]
merge_sorted([],[2,9]) -> [2,9]
merge_sorted([3,8,9],[]) -> [3,8,9]

A catalog search should discard half of its remaining choices at every step.

Specification: Define binary_search(nums, target) for a sorted list of distinct values. Return the index of target, or -1 when it is absent. Use while lo <= hi and calculate mid = (lo + hi) // 2 on every pass.

Worked sample:

binary_search([1,3,5,7,9],7) -> 3
binary_search([1,3,5,7,9],4) -> -1
binary_search([2,4,6,8,10,12],2) -> 0

A text analyzer needs to count matches even when two matches overlap.

Specification: Define count_substring(text, part) to count overlapping, case-sensitive occurrences of part. Walk for i in range(len(text) - len(part) + 1): and compare text[i:i+len(part)] with part at every position.

Worked sample:

count_substring("cocoon","co") -> 2
count_substring("aaaa","aa") -> 3
count_substring("possession","ss") -> 2

A field notebook needs a reusable count of the words saved in a file.

Specification: Define word_counts_from_file(path) to READ a saved file of words and return their counts — the function itself only reads, it never writes. Open path with with open(path, "r"), loop with for line in f:, clean each word with .strip(), tally it in a dictionary with .get, and return the dictionary. For a self-contained test, first write the fixed words ["fern","moss","fern","larch","moss","fern"] one per line to path with an f-string (f.write(f"{word}\n")), then call the function. Use p7_words.txt for the sample.

Worked sample:

writing ["fern","moss","fern","larch","moss","fern"] to "p7_words.txt"
word_counts_from_file("p7_words.txt") -> {"fern":3,"moss":2,"larch":1}

A word report needs the single most frequent entry in a saved list.

Specification: Define most_common_word(path) to READ a saved file of words and return the single word with the highest count — the function only reads. Tally the words with .strip() and .get, then find the best by iterating with the single-variable form for key in counts: (do not use .items()). For a self-contained test, first write the fixed words ["kite","yoyo","kite","kite","yoyo"] one per f-string line to path, then call the function. Use p8_words.txt for the sample.

Worked sample:

writing ["kite","yoyo","kite","kite","yoyo"] to "p8_words.txt"
most_common_word("p8_words.txt") -> "kite"

A sorter needs to split numbers into even and odd groups without changing their order.

Specification: Define group_by_parity(nums) to return {"even": [...], "odd": [...]} while preserving the input order inside each list. Append n to the even list when n % 2 == 0, and otherwise append it to the odd list; 0 is even.

Worked sample:

group_by_parity([1,2,3,4]) -> {"even":[2,4],"odd":[1,3]}
group_by_parity([0,7,10]) -> {"even":[0,10],"odd":[7]}
group_by_parity([]) -> {"even":[],"odd":[]}

A live counter needs to remember every value and summarize the collection.

Specification: Define class RunningTally. Its __init__(self) starts an empty list attribute. add(self, value) appends the value and returns the number of stored values so far. total(self) returns sum(...), highest(self) returns max(...), and describe(self) returns the f-string f"{count} values, total {total}, highest {highest}". Call add at least once before highest or describe.

Worked sample:

t = RunningTally()
t.add(5) -> 1
t.add(9) -> 2
t.add(0) -> 3
t.total() -> 14
t.highest() -> 9
t.describe() -> "3 values, total 14, highest 9"

A data pipeline needs to turn saved values into saved running totals.

Specification: Define running_totals_to_file(in_path, out_path) to READ integers from in_path (one per line, with int(line.strip())), accumulate a running total, WRITE each running total as an f-string line to out_path, and return the list of running totals. The function reads its input file and writes its output file; it does not create the input. For a self-contained test, first write the fixed integers [5,3,2] one per f-string line to in_path, then call the function. Use p11_in.txt and p11_out.txt for the sample.

Worked sample:

writing [5,3,2] to "p11_in.txt"
running_totals_to_file("p11_in.txt", "p11_out.txt") -> [5,8,10]
p11_out.txt -> "5\n8\n10\n"