Coding Grandmaster · project 5 of 46 · premium, free for now

The growth race

For each size in the list print one line like n=10 linear=10 nlogn=33 quadratic=100, where nlogn is int(n * math.log2(n)).

Learn

What matters most is how the step count grows with n. A linear algorithm takes about n steps, a quadratic one about n × n, and a clever one such as binary search or merge-style sorting sits in between at about n × log2(n). Doubling n doubles the first, quadruples the second, and does little more than double the third.

Your task

For each size in the list print one line like n=10 linear=10 nlogn=33 quadratic=100, where nlogn is int(n * math.log2(n)).

Stretch challenge

At which n does quadratic first exceed 100 times linear?

← Two ways to sort Remembering answers →

Python

Press Run to see what your program prints.

Keep going in Coding Grandmaster

How fast is it? Counting steps

Write pair_checks(n): two nested loops that count every pair (i, j) with i smaller than j among n items, and return the count. The program prints pair_checks(10).

Start →2

Searching one by one

Write find(items, target) that returns a pair (index, comparisons). If the target is missing, the index is -1 and the comparisons equal the length of the list.

Start →3

Halving the search

Write binary_search(items, target) for a sorted list. Return (index, steps) where steps counts how many middle items you looked at, or (-1, steps) if it is missing.

Start →4

Two ways to sort

Write bubble_sort(items) and selection_sort(items). Each returns (sorted_list, swaps) and must not change the list it was given. The program prints both results for the list.

Start →6

Remembering answers

Write fib_naive(n) returning (value, calls) and fib_memo(n, memo) returning the value while counting calls in memo["calls"]. Print the results for 20.

Start →

Practise the idea

🎯 Play Plinko Probability Lab

Drop balls through a peg board and see how gravity and chance shape the results.

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FAQ

The growth race: common questions

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