Coding Grandmaster · project 1 of 46 · premium, free for now

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).

Learn

Two programs can give the same answer and still differ hugely in speed. Programmers measure speed by counting how many basic steps the program takes, and then watching how that number grows when the input gets bigger. The easiest way to see it is to add a counter inside the loops.

Your task

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).

Stretch challenge

Find a formula for the answer using n. Test it on 10 and 100.

← All lessons Searching one by one →

Python

Press Run to see what your program prints.

Keep going in Coding Grandmaster

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 →5

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)).

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.

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Practise the idea

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Estimate big sums without a calculator and see how close you get.

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FAQ

How fast is it? Counting steps: common questions

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