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fabjan's solution

to Binary Search in the Clojure Track

Published at Feb 26 2021 · 0 comments
Test suite

Implement a binary search algorithm.

Searching a sorted collection is a common task. A dictionary is a sorted list of word definitions. Given a word, one can find its definition. A telephone book is a sorted list of people's names, addresses, and telephone numbers. Knowing someone's name allows one to quickly find their telephone number and address.

If the list to be searched contains more than a few items (a dozen, say) a binary search will require far fewer comparisons than a linear search, but it imposes the requirement that the list be sorted.

In computer science, a binary search or half-interval search algorithm finds the position of a specified input value (the search "key") within an array sorted by key value.

In each step, the algorithm compares the search key value with the key value of the middle element of the array.

If the keys match, then a matching element has been found and its index, or position, is returned.

Otherwise, if the search key is less than the middle element's key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the search key is greater, on the sub-array to the right.

If the remaining array to be searched is empty, then the key cannot be found in the array and a special "not found" indication is returned.

A binary search halves the number of items to check with each iteration, so locating an item (or determining its absence) takes logarithmic time. A binary search is a dichotomic divide and conquer search algorithm.


Wikipedia http://en.wikipedia.org/wiki/Binary_search_algorithm

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(ns binary-search-test
  (:require [clojure.test :refer [deftest is]]

(def short-vector [1, 3, 4, 6, 8, 9, 11])

(def large-vector [1, 3, 5, 8, 13, 21, 34, 55, 89])

(def even-length-vector [1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377])

(deftest it-finds-position-of-middle-item
  (is (= 3 (binary-search/middle short-vector))))

(deftest searches-a-singleton
  (is (= 0 (binary-search/search-for 4 [4]))))

(deftest it-finds-position-of-search-data
  (is (= 5 (binary-search/search-for 9 short-vector))))

(deftest it-finds-position-in-a-larger-list
  (is (= 1 (binary-search/search-for 3 large-vector))))

(deftest it-finds-position-in-a-larger-list-again
  (is (= 7 (binary-search/search-for 55 large-vector))))

(deftest it-finds-correct-position-in-a-list-with-an-even-number-of-elements
  (is (= 5 (binary-search/search-for 21 even-length-vector))))

(deftest it-finds-correct-position-in-a-list-with-an-even-number-of-elements-again
  (is (= 6 (binary-search/search-for 34 even-length-vector))))

(deftest it-works-on-lists
  (is (= 7 (binary-search/search-for 7 (range 10)))))

(deftest it-works-on-lists-again
  (is (= 4 (binary-search/search-for 3 '(-3 -2 0 1 3 4)))))

(deftest throws-exception-when-element-not-found
  (is (thrown-with-msg? Throwable #"not found"
                        (binary-search/search-for 20 short-vector))))
(ns binary-search)

(defn middle [v]
  (quot (count v) 2))

(defn search-for
  ([needle haystack]
   (search-for needle haystack 0 (middle haystack) (count haystack)))
  ([needle haystack l i u]
   (if (and (<= l i) (< i u))
     (let [cmp (compare needle (nth haystack i))]
         (zero? cmp) i
         (pos? cmp) (search-for needle haystack (inc i) (- u (quot (- u i) 2)) u)
         (neg? cmp) (search-for needle haystack l (- i (quot (- i l) 2) 1) i)))
     (throw (Exception. "not found")))))

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fabjan's Reflection

I was apparently not smart enough to think of adding the mid point to the index when searching higher, so instead of using take, drop and middle I'm always using the original collection and bumping the upper and lower bounds for the search so can't use the `middle` function.