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