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to Binary Search in the Clojure Track

Published at Jun 10 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
  "Returns the index of the middle item of coll. Retuns nil if coll is empty."
  (when-let [idx (and (seq coll) (-> coll count (/ 2) int))]

(defn search-for [q coll]
  (loop [coll coll
         offset 0]
    (let [middle-idx (middle coll)
          item (when middle-idx (nth coll middle-idx))
          found? (#{q} item)]
      (if (or (not item)
              (and (not found?) (-> coll rest seq not)))
        (throw (ex-info "not found" {:q q}))
        (if found?
          (+ offset middle-idx)
          (let [after? (not= (sort [q item]) [q item])]
            ;; It's easier to use > here to compare numbers. But i want this to work for strings and other comparable things. So i use sort.
             (if after? (drop middle-idx coll) (take middle-idx coll))
             (if after? (+ offset middle-idx) offset))))))))

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