52 lines
2.6 KiB
Markdown
52 lines
2.6 KiB
Markdown
# Binary Search
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Implement a binary search algorithm.
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Searching a sorted collection is a common task. A dictionary is a sorted
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list of word definitions. Given a word, one can find its definition. A
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telephone book is a sorted list of people's names, addresses, and
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telephone numbers. Knowing someone's name allows one to quickly find
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their telephone number and address.
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If the list to be searched contains more than a few items (a dozen, say)
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a binary search will require far fewer comparisons than a linear search,
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but it imposes the requirement that the list be sorted.
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In computer science, a binary search or half-interval search algorithm
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finds the position of a specified input value (the search "key") within
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an array sorted by key value.
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In each step, the algorithm compares the search key value with the key
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value of the middle element of the array.
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If the keys match, then a matching element has been found and the range of indices that equal the search key value are returned.
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Otherwise, if the search key is less than the middle element's key, then
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the algorithm repeats its action on the sub-array to the left of the
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middle element or, if the search key is greater, on the sub-array to the
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right.
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If the remaining array to be searched is empty, then the key cannot be
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found in the array and a special "not found" indication is returned. Search methods in Julia typically return an empty range located at the insertion point in this case.
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A binary search halves the number of items to check with each iteration,
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so locating an item (or determining its absence) takes logarithmic time.
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A binary search is a dichotomic divide and conquer search algorithm.
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**For simplification, you can assume that all elements of the list to be searched are unique.** Feel free to implement a solution that works on lists with non-unique elements as a bonus task.
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## Bonus task
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Implement keyword arguments `by`, `lt` and `rev` so that `by` specifies a transformation applied to all elements of the list, `lt` specifies a comparison and `rev` specifies if the list is ordered in reverse.
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## Source
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Wikipedia [http://en.wikipedia.org/wiki/Binary_search_algorithm](http://en.wikipedia.org/wiki/Binary_search_algorithm)
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Some phrases above and the bonus tasks are taken from the [Julia base documentation (MIT license)](https://docs.julialang.org/en/v1/base/sort/#Base.Sort.searchsorted) of `searchsorted`.
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## Version compatibility
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This exercise has been tested on Julia versions >=1.0.
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## Submitting Incomplete Solutions
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It's possible to submit an incomplete solution so you can see how others have completed the exercise.
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