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Add iterative and recursive linear searches (#30)
 * Create linear_search.nim * Update linear_search.nim * Delete sorting directory * Update linear_search.nim Adding time and space complexity * Update linear_search.nim Support search in types other than int, such as char and string * Update searchings/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update searchings/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Rename linear_search.nim to linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim Adding runnableExamples * Remove comment about imports Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com> * Remove system import Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com> * Update searches/linear_search.nim Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com> * Update searches/linear_search.nim Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com> * Update searches/linear_search.nim Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com> * Update searches/linear_search.nim Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com> * Update searches/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update searches/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim Shortening line 38 using type: OptNat = Option[Natural] * Update linear_search.nim * Update searches/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update searches/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update linear_search.nim * Update searches/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update linear_search.nim * Update searches/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> * Update DIRECTORY.md * Update searches/linear_search.nim Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> --------- Co-authored-by: dlesnoff <54949944+dlesnoff@users.noreply.github.com> Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com>
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‎DIRECTORY.md‎

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## Strings
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* [Check Anagram](strings/check_anagram.nim)
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## Searches
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* [Linear Search](searches/linear_search.nim)

‎searches/linear_search.nim‎

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## Linear Search
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## =============
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## Linear search is the simplest but least efficient searching algorithm
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## to search for an element in an array.
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## It examines each element until it finds a match,
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## starting at the beginning of the data set toward the end.
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## The search ends when the element is located or when the end of the array is reached.
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## https://en.wikipedia.org/wiki/Linear_search
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##
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## Time Complexity: O(n) where n is the length of the array.
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## Space Complexity in for-loop linear search: O(1)
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## Space Complexity in recursive linear search: O(n)
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## Notice that recursive algorithms are nice to write and provide elegant implementations,
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## but they are impeded by call stack management. Whatever the problem we face,
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## there will be as much memory requirement as the number of stack frames.
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## Therefore the recursive linear search is less efficient than the for-loop-based one.
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runnableExamples:
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var arr1 = [0, 3, 1, 4, 5, 6]
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doAssert linearSearch(arr1, 5) == some(Natural(4))
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doAssert recursiveLinearSearch(arr1, 5) == some(Natural(4))
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var arr2 = ['0', 'c', 'a', 'u', '5', '7']
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doAssert linearSearch(arr2, '5') == some(Natural(4))
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doAssert recursiveLinearSearch(arr2, '5') == some(Natural(4))
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var arr3 = [0, 3, 1, 4, 5, 6]
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doAssert linearSearch(arr3, 7) == none(Natural)
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doAssert recursiveLinearSearch(arr3, 7) == none(Natural)
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import std/options
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type
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Nat = Natural
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OptNat = Option[Natural]
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func linearSearch*[T](arr: openArray[T], key: T): OptNat =
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# key is the value we are searching for in the array.
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for i, val in arr.pairs():
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if val == key:
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return some(Natural(i))
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none(Natural) # `key` not found
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func recursiveLinearSearch*[T](arr: openArray[T], key: T, idx: Nat = arr.low.Nat): OptNat=
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# Recursion is another method for linear search.
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# Recursive calls replace the for loop.
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# `none(Natural)` is returned when the array is traversed completely
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# and no key is matched, or when `arr` is empty.
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if idx > arr.high:
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return none(Natural)
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if arr[idx] == key:
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return some(idx)
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recursiveLinearSearch(arr, key, idx + 1)
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when isMainModule:
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import unittest
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template checkLinearSearch[T](arr: openArray[T], key: T, expectedIdx: OptNat): untyped =
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check linearSearch(arr, key) == expectedIdx
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check recursiveLinearSearch(arr, key) == expectedIdx
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suite "Linear search":
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test "Search in an empty array":
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var arr: array[0, int]
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checkLinearSearch(arr, 5, none(Natural))
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test "Search in an int array matching with a valid value":
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var arr = [0, 3, 1, 4, 5, 6]
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checkLinearSearch(arr, 5, some(Natural(4)))
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test "Search in an int array for a missing value":
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var arr = [0, 3, 1, 4, 5, 6]
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checkLinearSearch(arr, 7, none(Natural))
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test "Search in a char array matching with a char matching value":
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var arr = ['0', 'c', 'a', 'u', '5', '7']
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checkLinearSearch(arr, '5', some(Natural(4)))
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test "Search in a string array matching with a string matching value":
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var arr = ["0", "c", "a", "u", "5", "7"]
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checkLinearSearch(arr, "5", some(Natural(4)))
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test "Search in an int array with a valid key at the end":
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var arr = [1, 5, 3, 6, 5, 7]
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checkLinearSearch(arr, 7, some(Natural(5)))

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