mirror of
https://codeberg.org/andyscott/exercism.git
synced 2024-11-13 23:00:47 -05:00
58 lines
2.5 KiB
Markdown
58 lines
2.5 KiB
Markdown
|
# Binary Search
|
||
|
|
|
||
|
|
Welcome to Binary Search on Exercism's Zig Track.
|
||
|
|
If you need help running the tests or submitting your code, check out `HELP.md`.
|
||
|
|
|
||
|
|
## Introduction
|
||
|
|
|
||
|
|
You have stumbled upon a group of mathematicians who are also singer-songwriters.
|
||
|
|
They have written a song for each of their favorite numbers, and, as you can imagine, they have a lot of favorite numbers (like [0][zero] or [73][seventy-three] or [6174][kaprekars-constant]).
|
||
|
|
|
||
|
|
You are curious to hear the song for your favorite number, but with so many songs to wade through, finding the right song could take a while.
|
||
|
|
Fortunately, they have organized their songs in a playlist sorted by the title — which is simply the number that the song is about.
|
||
|
|
|
||
|
|
You realize that you can use a binary search algorithm to quickly find a song given the title.
|
||
|
|
|
||
|
|
[zero]: https://en.wikipedia.org/wiki/0
|
||
|
|
[seventy-three]: https://en.wikipedia.org/wiki/73_(number)
|
||
|
|
[kaprekars-constant]: https://en.wikipedia.org/wiki/6174_(number)
|
||
|
|
|
||
|
|
## Instructions
|
||
|
|
|
||
|
|
Your task is to implement a binary search algorithm.
|
||
|
|
|
||
|
|
A binary search algorithm finds an item in a list by repeatedly splitting it in half, only keeping the half which contains the item we're looking for.
|
||
|
|
It allows us to quickly narrow down the possible locations of our item until we find it, or until we've eliminated all possible locations.
|
||
|
|
|
||
|
|
~~~~exercism/caution
|
||
|
|
Binary search only works when a list has been sorted.
|
||
|
|
~~~~
|
||
|
|
|
||
|
|
The algorithm looks like this:
|
||
|
|
|
||
|
|
- Find the middle element of a _sorted_ list and compare it with the item we're looking for.
|
||
|
|
- If the middle element is our item, then we're done!
|
||
|
|
- If the middle element is greater than our item, we can eliminate that element and all the elements **after** it.
|
||
|
|
- If the middle element is less than our item, we can eliminate that element and all the elements **before** it.
|
||
|
|
- If every element of the list has been eliminated then the item is not in the list.
|
||
|
|
- Otherwise, repeat the process on the part of the list that has not been eliminated.
|
||
|
|
|
||
|
|
Here's an example:
|
||
|
|
|
||
|
|
Let's say we're looking for the number 23 in the following sorted list: `[4, 8, 12, 16, 23, 28, 32]`.
|
||
|
|
|
||
|
|
- We start by comparing 23 with the middle element, 16.
|
||
|
|
- Since 23 is greater than 16, we can eliminate the left half of the list, leaving us with `[23, 28, 32]`.
|
||
|
|
- We then compare 23 with the new middle element, 28.
|
||
|
|
- Since 23 is less than 28, we can eliminate the right half of the list: `[23]`.
|
||
|
|
- We've found our item.
|
||
|
|
|
||
|
|
## Source
|
||
|
|
|
||
|
|
### Created by
|
||
|
|
|
||
|
|
- @massivelivefun
|
||
|
|
|
||
|
|
### Based on
|
||
|
|
|
||
|
|
Wikipedia - https://en.wikipedia.org/wiki/Binary_search_algorithm
|