Coding Grandmaster · project 3 of 46 · premium, free for now

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.

Learn

If the list is sorted you can do far better: look at the middle item. If it is too small, the target must be in the right half, so throw the left half away. Each look halves what is left, so even a million items need only about 20 looks.

Your task

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.

Stretch challenge

What is the largest number of steps for these 100 items? Why is it 7 and not 100?

← Searching one by one Two ways to sort →

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 →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

🧩 Play Number Sequences

Spot the pattern and type the next number. Add, multiply, squares, Fibonacci and more.

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FAQ

Halving the search: common questions

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