Common sorted list

Common sorted list is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Sorting Algorithm
This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or:

O(n logn) sorts

Heap sort | Merge sort | Patience sort | Quick sort

O(n log²n) sorts
Shell Sort

O(n²) sorts
Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort

other sorts
Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort

Given an integer array nums, the goal is create common sorted list with unique elements.

Example

nums = [5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9]

output = [1,3,4,5,7,8,9]

11l

F csl(nums)
   Set[Int] r
   L(num) nums
      r.update(num)
   R sorted(Array(r))
 
print(csl([[5, 1, 3, 8, 9, 4, 8, 7], [3, 5, 9, 8, 4], [1, 3, 7, 9]]))

Output:

[1, 3, 4, 5, 7, 8, 9]

Ada

with Ada.Text_Io;
with Ada.Containers.Vectors;
 
procedure Sorted is
 
   package Integer_Vectors is
     new Ada.Containers.Vectors (Index_Type   => Positive,
                                 Element_Type => Integer);
   use Integer_Vectors;
 
   package Vector_Sorting is
     new Integer_Vectors.Generic_Sorting;
   use Vector_Sorting;
 
   procedure Unique (Vec : in out Vector) is
      Res : Vector;
   begin
      for E of Vec loop
         if Res.Is_Empty or else Res.Last_Element /= E then
            Res.Append (E);
         end if;
      end loop;
      Vec := Res;
   end Unique;
 
   procedure Put (Vec : Vector) is
      use Ada.Text_Io;
   begin
      Put ("[");
      for E of Vec loop
         Put (E'Image);  Put (" ");
      end loop;
      Put ("]");
      New_Line;
   end Put;
 
   A : constant Vector := 5 & 1 & 3 & 8 & 9 & 4 & 8 & 7;
   B : constant Vector := 3 & 5 & 9 & 8 & 4;
   C : constant Vector := 1 & 3 & 7 & 9;
   R : Vector          := A & B & C;
begin
   Sort (R);
   Unique (R);
   Put (R);
end Sorted;

Output:

[ 1  3  4  5  7  8  9 ]

APL

Works with: Dyalog APL

csl ← (⊂∘⍋⌷⊢)∪∘∊

Output:

      csl (5 1 3 8 9 4 8 7)(3 5 9 8 4)(1 3 7 9)
1 3 4 5 7 8 9

AppleScript

use AppleScript version "2.4" -- OS X 10.10 (Yosemite) or later
use framework "Foundation"
 
local nums, output
 
set nums to current application's class "NSArray"'s arrayWithArray:({{5, 1, 3, 8, 9, 4, 8, 7}, {3, 5, 9, 8, 4}, {1, 3, 7, 9}})
set output to (nums's valueForKeyPath:("@distinctUnionOfArrays.self"))'s sortedArrayUsingSelector:("compare:")
return output as list

Output:

{1, 3, 4, 5, 7, 8, 9}

Or, as a composition of slightly more commonly-used generic functions (given that distinctUnionOfArrays is a relatively specialised function, while concat/flatten and nub/distinct are more atomic, and more frequently reached for):

use AppleScript version "2.4"
use framework "Foundation"
 
 
------------------- COMMON SORTED ARRAY ------------------
on run
    sort(nub(concat({¬
        {5, 1, 3, 8, 9, 4, 8, 7}, ¬
        {3, 5, 9, 8, 4}, ¬
        {1, 3, 7, 9}})))
end run
 
 
-------------------- GENERIC FUNCTIONS -------------------
 
-- concat :: [[a]] -> [a]
on concat(xs)
    ((current application's NSArray's arrayWithArray:xs)'s ¬
        valueForKeyPath:"@unionOfArrays.self") as list
end concat
 
 
-- nub :: [a] -> [a]
on nub(xs)
    ((current application's NSArray's arrayWithArray:xs)'s ¬
        valueForKeyPath:"@distinctUnionOfObjects.self") as list
end nub
 
 
-- sort :: Ord a => [a] -> [a]
on sort(xs)
    ((current application's NSArray's arrayWithArray:xs)'s ¬
        sortedArrayUsingSelector:"compare:") as list
end sort

Output:

{1, 3, 4, 5, 7, 8, 9}

AutoHotkey

Common_sorted_list(nums){
    elements := [], output := []
    for i, num in nums
        for j, d in num
            elements[d] := true
    for val, bool in elements
        output.push(val)
    return output
}

Examples:

nums := [[5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9]]
output := Common_sorted_list(nums)
return

Output:

[1, 3, 4, 5, 6, 7, 9]

AWK

 
# syntax: GAWK -f COMMON_SORTED_LIST.AWK
BEGIN {
    PROCINFO["sorted_in"] = "@ind_num_asc"
    nums = "[5,1,3,8,9,4,8,7],[3,5,9,8,4],[1,3,7,9]"
    printf("%s : ",nums)
    n = split(nums,arr1,"],?") - 1
    for (i=1; i<=n; i++) {
      gsub(/[\[\]]/,"",arr1[i])
      split(arr1[i],arr2,",")
      for (j in arr2) {
        arr3[arr2[j]]++
      }
    }
    for (j in arr3) {
      printf("%s ",j)
    }
    printf("\n")
    exit(0)
}
 

Output:

[5,1,3,8,9,4,8,7],[3,5,9,8,4],[1,3,7,9] : 1 3 4 5 7 8 9

C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
 
#define COUNTOF(a) (sizeof(a)/sizeof(a[0]))
 
void fatal(const char* message) {
    fprintf(stderr, "%s\n", message);
    exit(1);
}
 
void* xmalloc(size_t n) {
    void* ptr = malloc(n);
    if (ptr == NULL)
        fatal("Out of memory");
    return ptr;
}
 
int icompare(const void* p1, const void* p2) {
    const int* ip1 = p1;
    const int* ip2 = p2;
    return (*ip1 < *ip2) ? -1 : ((*ip1 > *ip2) ? 1 : 0);
}
 
size_t unique(int* array, size_t len) {
    size_t out_index = 0;
    int prev;
    for (size_t i = 0; i < len; ++i) {
        if (i == 0 || prev != array[i])
            array[out_index++] = array[i];
        prev = array[i];
    }
    return out_index;
}
 
int* common_sorted_list(const int** arrays, const size_t* lengths, size_t count, size_t* size) {
    size_t len = 0;
    for (size_t i = 0; i < count; ++i)
        len += lengths[i];
    int* array = xmalloc(len * sizeof(int));
    for (size_t i = 0, offset = 0; i < count; ++i) {
        memcpy(array + offset, arrays[i], lengths[i] * sizeof(int));
        offset += lengths[i];
    }
    qsort(array, len, sizeof(int), icompare);
    *size = unique(array, len);
    return array;
}
 
void print(const int* array, size_t len) {
    printf("[");
    for (size_t i = 0; i < len; ++i) {
        if (i > 0)
            printf(", ");
        printf("%d", array[i]);
    }
    printf("]\n");
}
 
int main() {
    const int a[] = {5, 1, 3, 8, 9, 4, 8, 7};
    const int b[] = {3, 5, 9, 8, 4};
    const int c[] = {1, 3, 7, 9};
    size_t len = 0;
    const int* arrays[] = {a, b, c};
    size_t lengths[] = {COUNTOF(a), COUNTOF(b), COUNTOF(c)};
    int* sorted = common_sorted_list(arrays, lengths, COUNTOF(arrays), &len);
    print(sorted, len);
    free(sorted);
    return 0;
}

Output:

[1, 3, 4, 5, 7, 8, 9]

C++

#include <iostream>
#include <vector>
#include <set>
#include <algorithm>
 
template<typename T>
std::vector<T> common_sorted_list(const std::vector<std::vector<T>>& ll) {
    std::set<T> resultset;
    std::vector<T> result;
    for (auto& list : ll)
        for (auto& item : list)
            resultset.insert(item);
    for (auto& item : resultset)
        result.push_back(item);
 
    std::sort(result.begin(), result.end());
    return result;
}
 
int main() {
    std::vector<int> a = {5,1,3,8,9,4,8,7};
    std::vector<int> b = {3,5,9,8,4};
    std::vector<int> c = {1,3,7,9};
    std::vector<std::vector<int>> nums = {a, b, c};
 
    auto csl = common_sorted_list(nums);
    for (auto n : csl) std::cout << n << " ";
    std::cout << std::endl;
 
    return 0;
}

Output:

1 3 4 5 7 8 9

Excel

LAMBDA

Binding the name COMMONSORTED to the following lambda expression in the Name Manager of the Excel WorkBook:

(See LAMBDA: The ultimate Excel worksheet function)

Works with: Office 365 betas 2021

COMMONSORTED
=LAMBDA(grid,
    SORT(
        UNIQUE(
            CONCATCOLS(grid)
        )
    )
)

and also assuming the following generic bindings in the Name Manager for the WorkBook:

CONCATCOLS
=LAMBDA(cols,
    LET(
        nRows, ROWS(cols),
        ixs, SEQUENCE(
            COLUMNS(cols) * nRows, 1,
            1, 1
        ),
 
        FILTERP(
            LAMBDA(x, 0 < LEN("" & x))
        )(
            INDEX(cols,
                LET(
                    r, MOD(ixs, nRows),
 
                    IF(0 = r, nRows, r)
                ),
                1 + QUOTIENT(ixs - 1, nRows)
            )
        )
    )
)
 
 
FILTERP
=LAMBDA(p,
    LAMBDA(xs,
        FILTER(xs, p(xs))
    )
)

The formula in cell B2 defines a dynamic array of values, additionally populating further cells in column B.

Output:

	fx	=COMMONSORTED(C2:E9)
	A	B	C	D	E
1		Common sorted
2		1	5	3	1
3		3	1	5	3
4		4	3	9	7
5		5	8	8	9
6		7	9	4
7		8	4
8		9	8
9			7

F#

 
// Common sorted list. Nigel Galloway: February 25th., 2021
let nums=[|[5;1;3;8;9;4;8;7];[3;5;9;8;4];[1;3;7;9]|]
printfn "%A" (nums|>Array.reduce(fun n g->[email protected])|>List.distinct|>List.sort)
 

Output:

[1; 3; 4; 5; 7; 8; 9]

Factor

Note: in older versions of Factor, union-all is called combine.

Works with: Factor version 0.99 2021-02-05

USING: formatting kernel sets sorting ;
 
{ { 5 1 3 8 9 4 8 7 } { 3 5 9 8 4 } { 1 3 7 9 } }
dup union-all natural-sort
"Sorted union of %u is:\n%u\n" printf

Output:

Sorted union of { { 5 1 3 8 9 4 8 7 } { 3 5 9 8 4 } { 1 3 7 9 } } is:
{ 1 3 4 5 7 8 9 }

Go

Translation of: Wren

package main
 
import (
    "fmt"
    "sort"
)
 
func distinctSortedUnion(ll [][]int) []int {
    var res []int
    for _, l := range ll {
        res = append(res, l...)
    }
    set := make(map[int]bool)
    for _, e := range res {
        set[e] = true
    }
    res = res[:0]
    for key := range set {
        res = append(res, key)
    }
    sort.Ints(res)
    return res
}
 
func main() {
    ll := [][]int{{5, 1, 3, 8, 9, 4, 8, 7}, {3, 5, 9, 8, 4}, {1, 3, 7, 9}}
    fmt.Println("Distinct sorted union of", ll, "is:")
    fmt.Println(distinctSortedUnion(ll))
}

Output:

Distinct sorted union of [[5 1 3 8 9 4 8 7] [3 5 9 8 4] [1 3 7 9]] is:
[1 3 4 5 7 8 9]

Haskell

import Data.List (nub, sort)
 
-------------------- COMMON SORTED LIST ------------------
 
commonSorted :: Ord a => [[a]] -> [a]
commonSorted = sort . nub . concat
 
--------------------------- TEST -------------------------
main :: IO ()
main =
  print $
    commonSorted
      [ [5, 1, 3, 8, 9, 4, 8, 7],
        [3, 5, 9, 8, 4],
        [1, 3, 7, 9]
      ]

Output:

[1,3,4,5,7,8,9]

J

csl =: /:[email protected][email protected];

Output:

   nums =: 5 1 3 8 9 4 8 7;3 5 9 8 4;1 3 7 9
   csl nums
1 3 4 5 7 8 9

JavaScript

(() => {
    "use strict";
 
    // --------------- COMMON SORTED LIST ----------------
 
    // commonSorted :: Ord a => [[a]] -> [a]
    const commonSorted = xs =>
        sort(nub(concat(xs)));
 
 
    // ---------------------- TEST -----------------------
    const main = () =>
        commonSorted([
            [5, 1, 3, 8, 9, 4, 8, 7],
            [3, 5, 9, 8, 4],
            [1, 3, 7, 9]
        ]);
 
 
    // --------------------- GENERIC ---------------------
 
    // concat :: [[a]] -> [a]
    const concat = xs => [].concat(...xs);
 
 
    // nub :: [a] -> [a]
    const nub = xs => [...new Set(xs)];
 
 
    // sort :: Ord a => [a] -> [a]
    const sort = xs =>
        // An (ascending) sorted copy of xs.
        xs.slice().sort();
 
    return main();
})();

Output:

[1, 3, 4, 5, 7, 8, 9]

jq

Works with: jq

Works with gojq, the Go implementation of jq

Assuming the input is a single array of arrays, we can simply chain the `add` and `unique` filters:

jq -nc '[[5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9]] | add | unique'

Output:

[1,3,4,5,7,8,9]

If the arrays are presented individually in an external stream, we could use the `-s` command-line option.

Alternatively, here's a stream-oriented version of `add` that could be used:

def add(s): reduce s as $x (null; . + $x);

For example:

jq -nc '
    def add(s): reduce s as $x (null; . + $x);
    add(inputs) | unique' <<< '[5,1,3,8,9,4,8,7] [3,5,9,8,4] [1,3,7,9]'

Julia

 
julia> sort(union([5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9]))
7-element Array{Int64,1}:
 1
 3
 4
 5
 7
 8
 9
 
julia> sort(union([2, 3, 4], split("3.14 is not an integer", r"\s+")), lt=(x, y) -> "$x" < "$y")
8-element Array{Any,1}:
 2
 3
  "3.14"
 4
  "an"
  "integer"
  "is"
  "not"
 
 

Mathematica/Wolfram Language

Union[{5, 1, 3, 8, 9, 4, 8, 7}, {3, 5, 9, 8, 4}, {1, 3, 7, 9}]

Output:

{1, 3, 4, 5, 7, 8, 9}

Nim

We could use a HashSet or an IntSet to deduplicate. We have rather chosen to use the procedure deduplicate from module sequtils applied to the sorted list.

import algorithm, sequtils
 
proc commonSortedList(list: openArray[seq[int]]): seq[int] =
  sorted(concat(list)).deduplicate(true)
 
echo commonSortedList([@[5,1,3,8,9,4,8,7], @[3,5,9,8,4], @[1,3,7,9]])

Output:

@[1, 3, 4, 5, 7, 8, 9]

Perl

@c{@$_}++ for [5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9];
print join ' ', sort keys %c;
@c{@$_}++ for [qw<not all is integer ? is not ! 4.2>];
print join ' ', sort keys %c;

Output:

1 3 4 5 7 8 9
! 1 3 4 4.2 5 7 8 9 ? all integer is not

Phix

Library: Phix/basics

?unique(join({{5,1,3,8,9,4,8,7}, {3,5,9,8,4}, {1,3,7,9}, split("not everything is an integer")},{}))

Note the join(x,{}): the 2nd param is needed to prevent it putting 32 (ie the acsii code for a space) in the output.

Output:

(Unexpectedly rather Yoda-esque)

{1,3,4,5,7,8,9,"an","everything","integer","is","not"}

Python

'''Common sorted list'''
 
from itertools import chain
 
 
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
    '''Sorted union of lists'''
 
    print(
        sorted(nub(concat([
            [5, 1, 3, 8, 9, 4, 8, 7],
            [3, 5, 9, 8, 4],
            [1, 3, 7, 9]
        ])))
    )
 
 
# ----------------------- GENERIC ------------------------
 
# concat :: [[a]] -> [a]
# concat :: [String] -> String
def concat(xs):
    '''The concatenation of all the elements in a list.
    '''
    return list(chain(*xs))
 
 
# nub :: [a] -> [a]
def nub(xs):
    '''A list containing the same elements as xs,
       without duplicates, in the order of their
       first occurrence.
    '''
    return list(dict.fromkeys(xs))
 
 
# MAIN ---
if __name__ == '__main__':
    main()

Output:

[1, 3, 4, 5, 7, 8, 9]

Quackery

uniquewith is defined at Remove duplicate elements#Quackery.

  ' [ [ 5 1 3 8 9 4 8 7 ]
      [ 3 5 9 8 4 ]
      [ 1 3 7 9 ] ]
 
  [] swap witheach [ witheach join ]
  uniquewith > echo

Output:

[ 1 3 4 5 7 8 9 ]

Raku

put sort keys [∪] [5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9];
put sort keys [∪] [5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9], [<not everything is an integer so why not avoid special cases # ~ 23 4.2>];

Output:

1 3 4 5 7 8 9
# 1 3 4 4.2 5 7 8 9 23 an avoid cases everything integer is not so special why ~

REXX

/*REXX pgm creates and displays a  common sorted list  of a specified collection of sets*/
parse arg a                                      /*obtain optional arguments from the CL*/
if a='' | a=","  then a= '[5,1,3,8,9,4,8,7]  [3,5,9,8,4]  [1,3,7,9]'     /*default sets.*/
x= translate(a, ,'],[')                          /*extract elements from collection sets*/
se= words(x)
#= 0;            $=                              /*#: number of unique elements; $: list*/
$=                                               /*the list of common elements (so far).*/
    do j=1  for se;  _= word(x, j)               /*traipse through all elements in sets.*/
    if wordpos(_, $)>0  then iterate             /*Is element in the new list? Yes, skip*/
    $= $ _;   #= # + 1;    @.#= _                /*add to list; bump counter; assign──►@*/
    end   /*j*/
$=
call eSort #                                     /*use any short (small)  exchange sort.*/
                 do k=1  for #;   $= $  @.k      /*rebuild the $ list, it's been sorted.*/
                 end   /*k*/
 
say 'the list of sorted common elements in all sets: ' "["translate(space($), ',', " ")']'
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
eSort: procedure expose @.; arg h 1 z; do while h>1; h= h%2; do i=1  for z-h; j= i; k= h+i
        do while @.k<@.j; [email protected].j; @.[email protected].k; @.k=t; if h>=j then leave; j=j-h; k=k-h; end;end
        end;     return                          /*this sort was used 'cause of brevity.*/

output   when using the default inputs:

the list of sorted common elements in all sets:  [1,3,4,5,7,8,9]

Ring

 
nums = [[5,1,3,8,9,4,8,7],[3,5,9,8,4],[1,3,7,9]]
sumNums = []
 
for n = 1 to len(nums)
    for m = 1 to len(nums[n])
        add(sumNums,nums[n][m])
    next
next
 
sumNums = sort(sumNums)
for n = len(sumNums) to 2 step -1
    if sumNums[n] = sumNums[n-1]
       del(sumNums,n)
    ok
next
 
sumNums = sort(sumNums)
 
see "common sorted list elements are: "
showArray(sumNums)
 
func showArray(array)
     txt = ""
     see "["
     for n = 1 to len(array)
         txt = txt + array[n] + ","
     next
     txt = left(txt,len(txt)-1)
     txt = txt + "]"
     see txt
 

Output:

common sorted list elements are: [1,3,4,5,7,8,9]

Ruby

nums = [5,1,3,8,9,4,8,7], [3,5,9,8,4], [1,3,7,9]
p nums.inject(:+).sort.uniq  
 

Output:

[1, 3, 4, 5, 7, 8, 9]

Wren

Library: Wren-seq

Library: Wren-sort

import "/seq" for Lst
import "/sort" for Sort
 
var distinctSortedUnion = Fn.new { |ll| 
    var res = ll.reduce([]) { |acc, l| acc + l }
    res = Lst.distinct(res)
    Sort.insertion(res)
    return res
}
 
var ll = [[5, 1, 3, 8, 9, 4, 8, 7], [3, 5, 9, 8, 4], [1, 3, 7, 9]]
System.print("Distinct sorted union of %(ll) is:")
System.print(distinctSortedUnion.call(ll))

Output:

Distinct sorted union of [[5, 1, 3, 8, 9, 4, 8, 7], [3, 5, 9, 8, 4], [1, 3, 7, 9]] is:
[1, 3, 4, 5, 7, 8, 9]