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mergesort

mergesort is one of the earlier sorting algorithms. It was developed and characterized by none other than von Neumann. It's a great example of a divide-and-conquer algorithm, and it's quite fun to write in Clojure.

So that's the task: implement mergesort.

You can find descriptions of mergesort by searching. But remember, it's easy in Clojure because recursion is the norm.

Note: Make sure it works on large lists. Try it on a list of 1 million numbers.

Bonus:

  1. Have it use compare to work on more than numbers.
  2. Have it take a key to sort by.
  3. Use clojure.reducers to implement a parallel version.
(defn merge [l1 l2]
(lazy-seq
(cond
(empty? l1)
l2
(empty? l2)
l1
(< (first l1) (first l2))
(cons (first l1) (merge (rest l1) l2))
:else
(cons (first l2) (merge l1 (rest l2))))))
(defn mergesort* [v]
(case (count v)
0 ()
1 (seq v)
;; else
(let [half (quot (count v) 2)]
(merge (mergesort* (subvec v 0 half))
(mergesort* (subvec v half))))))
(defn mergesort [ls]
(seq (mergesort* (vec ls))))
(ns clj-challenge.merge-sort
"Sorts numbers using the Merge Sort algorithm"
(:require [clojure.set :as clj-set]
[clojure.string :as cs]))
(defn do-merge
"Merges two sorted sequences - `left` and `right`. The sequences are
destructured as e.g.
x - the first element
xs - the rest of the elements
lt - the whole left sequence
If either first element is `nil` then we can safely append them to the result.
Otherwise, we still have elements, and so we append the smaller of the two onto
the result of a recursive call with the rest of the elements from that sequence
and the other sequence."
[left right]
(loop [[x & xs :as lt] left
[y & ys :as rt] right
result []]
(cond
(or (nil? x) (nil? y)) (concat result lt rt)
(< x y) (recur xs rt (conj result x))
:else (recur lt ys (conj result y)))))
(defn merge-sort [arg]
(let [cnt (count arg)
mid (/ cnt 2)
left (take mid arg)
right (drop mid arg)]
(if (= 1 cnt)
arg
(do-merge (merge-sort left) (merge-sort right)))))
;;
;; A few REPL expressions to try things out
;;
(comment
(def data1 [1 9 2 8 3 7 4 6 5])
(def data2 [1 9 2 8 3 7 4 6 5 10])
(merge-sort data1)
(merge-sort data2)
(do-merge [1 4 4 5] [2 3 7 9])
(do-merge [1] [2 5])
;; Make sure there's no StackOverflow
(do-merge (range 1000000) (range 1000000 2000000))
(merge-sort (take 1000000 (map rand-int (repeat 1000000)))))
(ns scratchpad.pftv.334
(:require [clojure.string :as str]
[clojure.test :refer :all]
[clojure.core.reducers :as r]))
(defn combine [compare-fn left right]
(loop [a left
b right
result []]
(cond
(empty? a) (concat result b)
(empty? b) (concat result a)
:else
(if (neg? (compare-fn (first a) (first b)))
(recur (rest a) b (conj result (first a)))
(recur a (rest b) (conj result (first b)))))))
(defn mergesort [compare-fn lst]
;; list of 0 or 1 is sorted.
(if (<= (count lst) 1)
lst
;; split in middle recursively and combine results
(let [mid (int (/ (count lst) 2))
[left right] (split-at mid lst)]
(combine compare-fn
(mergesort compare-fn left)
(mergesort compare-fn right)))))
(deftest test-combine
(is (= (combine compare [5 6] [1 7]) [1 5 6 7]))
(is (= (combine compare [4] [1 2 3]) [1 2 3 4]))
(is (= (combine compare [1 2 3] [4]) [1 2 3 4]))
(is (= (combine compare (range 500000 1000000) (range 0 500000)) (range 0 1000000))))
(deftest test-mergesort
(is (= (mergesort compare [8 1 5 1 5 2 3]) [1 1 2 3 5 5 8]))
(is (= (mergesort compare (reverse (range 0 1000000))) (range 1000000))))
(run-tests)
(ns miner.mergesort)
;; https://purelyfunctional.tv/issues/purelyfunctional-tv-newsletter-334-tip-can-you-fill-in-the-blanks/
;; mergesort
;; https://en.wikipedia.org/wiki/Merge_sort
;;
;; Bonus:
;; Have it use compare to work on more than numbers.
;; Have it take a key to sort by.
;; Use clojure.reducers to implement a parallel version.
(defn mergesort
([coll] (mergesort identity coll))
([fkey coll]
(if (empty? coll)
coll
(let [merge2 (fn [as bs]
(loop [as as bs bs res []]
(cond (empty? as) (into res bs)
(empty? bs) (into res as)
:else (let [a (first as)
b (first bs)]
(if (pos? (compare (fkey a) (fkey b)))
(recur as (rest bs) (conj res b))
(recur (rest as) bs (conj res a)))))))]
(loop [runs (mapv list coll)]
(if (= (count runs) 1)
(peek runs)
(recur (loop [[a b & cs] runs res []]
(cond (nil? a) res
(nil? b) (conj res a)
:else (recur cs (conj res (merge2 a b))))))))))))
(defn partition-while
"Returns a lazy sequence of partitions with each partition containing a run of elements for
which `pred2` returns true when applied to the previous element and the current input. The
first input goes into the first partition without calling `pred2`. Returns a stateful
transducer when no collection is provided."
([pred2]
(fn [rf]
(let [a (java.util.ArrayList.)]
(fn
([] (rf))
([result]
(let [result (if (.isEmpty a)
result
(let [v (vec (.toArray a))]
;;clear first!
(.clear a)
(unreduced (rf result v))))]
(rf result)))
([result input]
(if (or (.isEmpty a) (pred2 (.get a (dec (.size a))) input))
(do
(.add a input)
result)
(let [v (vec (.toArray a))]
(.clear a)
(let [ret (rf result v)]
(when-not (reduced? ret)
(.add a input))
ret))))))))
([pred2 coll]
(sequence (partition-while pred2) coll)))
;; slightly faster with some transducers
(defn xmergesort
([coll] (xmergesort identity coll))
([fkey coll]
(if (empty? coll)
coll
(let [merge2 (fn
([as] as)
([as bs]
(loop [as as bs bs res []]
(cond (empty? as) (into res bs)
(empty? bs) (into res as)
:else (let [a (first as)
b (first bs)]
(if (pos? (compare (fkey a) (fkey b)))
(recur as (rest bs) (conj res b))
(recur (rest as) bs (conj res a))))))))
lte (fn [a b] (not (pos? (compare (fkey a) (fkey b)))))]
(loop [runs (into [] (partition-while lte) coll)]
(if (= (count runs) 1)
(peek runs)
(recur (into [] (comp (partition-all 2) (map #(apply merge2 %))) runs))))))))
;; My reducers version wasn't faster so I didn't include it.
(defn smoke-sort []
(let [xs (repeatedly (long 1e6) #(rand-int 10000))]
(assert (= (sort xs) (mergesort xs) (xmergesort xs))))
(let [amaps (shuffle (map #(hash-map :a % :b (- %)) (range 1000)))]
(assert (= (sort-by :a amaps) (mergesort :a amaps) (xmergesort :a amaps)))
(assert (= (sort-by :b amaps) (mergesort :b amaps) (xmergesort :b amaps))))
true)
(ns mergesort.mergesort
(:require [cljs.test :refer-macros [deftest is run-tests]]))
(defn merge
"Merge two sorted lists to a sorted list."
[xs ys]
(cond
(empty? xs) ys
(empty? ys) xs
(<= (first xs) (first ys))
(cons (first xs) (merge (rest xs) ys))
(<= (first ys) (first xs))
(cons (first ys) (merge xs (rest ys)))))
(defn mergesort
"Mergesort algorithm. Hey, von Neuman!"
[xs]
(if (empty? (rest xs))
xs
(let [left (take (/ (count xs) 2) xs)
right (drop (/ (count xs) 2) xs)]
(merge (mergesort left) (mergesort right)))))
;;; tests
(deftest merge-test
(is (= (merge [] []) []))
(is (= (merge [1] []) [1]))
(is (= (merge [] [1]) [1]))
(is (= (merge [] [1 2]) [1 2]))
(is (= (merge [1 2] [3 4]) [1 2 3 4]))
(is (= (merge [1 4] [2 3]) [1 2 3 4]))
)
(deftest mergesort-test
(is (= (mergesort []) []))
(is (= (mergesort [1]) [1]))
(is (= (mergesort [2 1]) [1 2]))
(is (= (mergesort [1 2]) [1 2]))
(is (= (mergesort [3 2 1]) [1 2 3]))
(is (= (mergesort [1 2 1]) [1 1 2]))
#_(is (= (mergesort [3 2 2 3 77 1 5 83]) [1 2 2 3 3 5 77 83]))
)
(run-tests)
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