Order by pair comparisons

From Rosetta Code
Revision as of 21:36, 29 November 2021 by rosettacode>Amarok (Added solution for Action!)
Task
Order by pair comparisons
You are encouraged to solve this task according to the task description, using any language you may know.

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

Assume we have a set of items that can be sorted into an order by the user.

The user is presented with pairs of items from the set in no order, the user states which item is less than, equal to, or greater than the other (with respect to their relative positions if fully ordered).

Write a function that given items that the user can order, asks the user to give the result of comparing two items at a time and uses the comparison results to eventually return the items in order.

Try and minimise the comparisons the user is asked for.

Show on this page, the function ordering the colours of the rainbow: 

   violet red green indigo blue yellow orange

The correct ordering being: 

   red orange yellow green blue indigo violet

Note:

  • Asking for/receiving user comparisons is a part of the task.
  • Code inputs should not assume an ordering.
  • The seven colours can form twenty-one different pairs.
  • A routine that does not ask the user "too many" comparison questions should be used.



Action!

<lang Action!>DEFINE PTR="CARD"

PROC PrintArray(PTR ARRAY a BYTE size) 

 BYTE i

 Put('[)
 FOR i=0 TO size-1
 DO
   IF i>0 THEN Put(' ) FI
   Print(a(i))
 OD
 Put(']) PutE()

RETURN

BYTE FUNC IsBefore(CHAR ARRAY a,b) 

 DEFINE NO_KEY="255"
 DEFINE KEY_Y="43"
 DEFINE KEY_N="35"
 BYTE CH=$02FC ;Internal hardware value for last key pressed
 BYTE k

 PrintF("Is %S before %S (y/n)? ",a,b)
 CH=NO_KEY ;Flush the keyboard
 DO
   k=CH
 UNTIL k=KEY_Y OR k=KEY_N
 OD
 CH=NO_KEY ;Flush the keyboard
 IF k=KEY_Y THEN
   PrintE("yes")
   RETURN (1)
 FI
 PrintE("no")

RETURN (0)

PROC InteractiveInsertionSort(PTR ARRAY a BYTE size) 

 INT i,j
 PTR value

 FOR i=1 TO size-1
 DO
   value=a(i)
   j=i-1
   WHILE j>=0 AND IsBefore(value,a(j))=1
   DO
     a(j+1)=a(j)
     j==-1
   OD
   a(j+1)=value
 OD

RETURN

PROC Main() 

 DEFINE COUNT="7"
 PTR ARRAY arr(COUNT)

 arr(0)="violet" arr(1)="red"
 arr(2)="green"  arr(3)="indigo"
 arr(4)="blue"   arr(5)="yellow"
 arr(6)="orange"

 Print("Shuffled array: ")
 PrintArray(arr,COUNT) PutE()

 InteractiveInsertionSort(arr,COUNT)
 PutE() Print("Sorted array: ")
 PrintArray(arr,COUNT)

RETURN</lang>

Output:

Screenshot from Atari 8-bit computer 

Shuffled array: [violet red green indigo blue yellow orange]

Is red before violet (y/n)? yes
Is green before violet (y/n)? yes
Is green before red (y/n)? no
Is indigo before violet (y/n)? yes
Is indigo before green (y/n)? no
Is blue before violet (y/n)? yes
Is blue before indigo (y/n)? yes
Is blue before green (y/n)? no
Is yellow before violet (y/n)? yes
Is yellow before indigo (y/n)? yes
Is yellow before blue (y/n)? yes
Is yellow before green (y/n)? yes
Is yellow before red (y/n)? no
Is orange before violet (y/n)? yes
Is orange before indigo (y/n)? yes
Is orange before blue (y/n)? yes
Is orange before green (y/n)? yes
Is orange before yellow (y/n)? yes
Is orange before red (y/n)? no

Sorted array: [red orange yellow green blue indigo violet]

Arturo

<lang rebol>lst: ["violet" "red" "green" "indigo" "blue" "yellow" "orange"] count: 0

findSpot: function [l,e][ 

   if empty? l -> return 0

   loop.with:'i l 'item [
       answer: input ~"Is |item| greater than |e| [y/n]? "
       if answer="y" -> return i
   ]
   return dec size l

]

sortedLst: new []

loop lst 'element -> 

   insert 'sortedLst findSpot sortedLst element element

print "" print ["sorted =>" sortedLst]</lang>

Output:
Is violet greater than red [y/n]? y
Is red greater than green [y/n]? y
Is green greater than indigo [y/n]? y
Is indigo greater than blue [y/n]? n
Is green greater than blue [y/n]? n
Is red greater than blue [y/n]? y
Is indigo greater than yellow [y/n]? n
Is green greater than yellow [y/n]? y
Is indigo greater than orange [y/n]? n
Is yellow greater than orange [y/n]? y

sorted => [indigo orange yellow green blue red violet]

AutoHotkey

<lang AutoHotkey>data := ["Violet", "Red", "Green", "Indigo", "Blue", "Yellow", "Orange"] result := [], num := 0, Questions :=""

for i, Color1 in data{ 

   found :=false
   if !result.count(){
       result.Push(Color1)
       continue
   }
   
   for j, Color2 in result	{
       if (color1 = color2)
           continue
       MsgBox, 262180,, % (Q := "Q" ++num " is " Color1 " > " Color2 "?")
       ifMsgBox, Yes 
           Questions .= Q "`t`tYES`n"
       else {
           Questions .= Q "`t`tNO`n"
           result.InsertAt(j, Color1)
           found := true
           break
       }
   }
   if !found
       result.Push(Color1)

} for i, color in result 

   output .= color ", "

MsgBox % Questions "`nSorted Output :`n" Trim(output, ", ") return</lang>

Output:
Q1 is Red > Violet?		NO
Q2 is Green > Red?		YES
Q3 is Green > Violet?		NO
Q4 is Indigo > Red?		YES
Q5 is Indigo > Green?		YES
Q6 is Indigo > Violet?		NO
Q7 is Blue > Red?		YES
Q8 is Blue > Green?		YES
Q9 is Blue > Indigo?		NO
Q10 is Yellow > Red?		YES
Q11 is Yellow > Green?		NO
Q12 is Orange > Red?		YES
Q13 is Orange > Yellow?		NO

Sorted Output :
Red, Orange, Yellow, Green, Blue, Indigo, Violet

C

Using qsort; not very efficient <lang c>#include <stdio.h>

  1. include <string.h>
  2. include <stdlib.h>

int interactiveCompare(const void *x1, const void *x2) { 

 const char *s1 = *(const char * const *)x1;
 const char *s2 = *(const char * const *)x2;
 static int count = 0;
 printf("(%d) Is %s <, ==, or > %s? Answer -1, 0, or 1: ", ++count, s1, s2);
 int response;
 scanf("%d", &response);
 return response;

}

void printOrder(const char *items[], int len) { 

 printf("{ ");
 for (int i = 0; i < len; ++i) printf("%s ", items[i]);
 printf("}\n");

}

int main(void) { 

 const char *items[] =
   {
     "violet", "red", "green", "indigo", "blue", "yellow", "orange"
   };

 qsort(items, sizeof(items)/sizeof(*items), sizeof(*items), interactiveCompare);
 printOrder(items, sizeof(items)/sizeof(*items));
 return 0;

}</lang>

Output:
(1) Is violet <, ==, or > red? Answer -1, 0, or 1: 1
(2) Is violet <, ==, or > green? Answer -1, 0, or 1: 1
(3) Is red <, ==, or > green? Answer -1, 0, or 1: -1
(4) Is violet <, ==, or > indigo? Answer -1, 0, or 1: 1
(5) Is green <, ==, or > indigo? Answer -1, 0, or 1: -1
(6) Is violet <, ==, or > blue? Answer -1, 0, or 1: 1
(7) Is indigo <, ==, or > blue? Answer -1, 0, or 1: 1
(8) Is green <, ==, or > blue? Answer -1, 0, or 1: -1
(9) Is violet <, ==, or > yellow? Answer -1, 0, or 1: 1
(10) Is indigo <, ==, or > yellow? Answer -1, 0, or 1: 1
(11) Is blue <, ==, or > yellow? Answer -1, 0, or 1: 1
(12) Is green <, ==, or > yellow? Answer -1, 0, or 1: 1
(13) Is red <, ==, or > yellow? Answer -1, 0, or 1: -1
(14) Is violet <, ==, or > orange? Answer -1, 0, or 1: 1
(15) Is indigo <, ==, or > orange? Answer -1, 0, or 1: 1
(16) Is blue <, ==, or > orange? Answer -1, 0, or 1: 1
(17) Is green <, ==, or > orange? Answer -1, 0, or 1: 1
(18) Is yellow <, ==, or > orange? Answer -1, 0, or 1: 1
(19) Is red <, ==, or > orange? Answer -1, 0, or 1: -1
{ red orange yellow green blue indigo violet }

C++

C++: Binary search insertion sort

<lang cpp>#include <algorithm>

  1. include <iostream>
  2. include <vector>

using namespace std;

bool InteractiveCompare(const string& s1, const string& s2) { 

   if(s1 == s2) return false;  // don't ask to compare items that are the same
   static int count = 0;
   string response;
   cout << "(" << ++count << ") Is " << s1 << " < " << s2 << "? ";
   getline(cin, response);
   return !response.empty() && response.front() == 'y';

}

void PrintOrder(const vector<string>& items) { 

   cout << "{ ";
   for(auto& item : items) cout << item << " ";
   cout << "}\n";

}

int main() { 

   const vector<string> items
   {
       "violet", "red", "green", "indigo", "blue", "yellow", "orange"
   };
   
   vector<string> sortedItems;
   
   // Use a binary insertion sort to order the items.  It should ask for
   // close to the minimum number of questions required
   for(auto& item : items)
   {
       cout << "Inserting '" << item << "' into ";
       PrintOrder(sortedItems);
       // lower_bound performs the binary search using InteractiveCompare to
       // rank the items
       auto spotToInsert = lower_bound(sortedItems.begin(),
                                       sortedItems.end(), item, InteractiveCompare);
       sortedItems.insert(spotToInsert, item);
   }
   PrintOrder(sortedItems);
   return 0;

}</lang>

Output:
Inserting 'violet' into { }
Inserting 'red' into { violet }
(1) Is violet < red? n
Inserting 'green' into { red violet }
(2) Is violet < green? n
(3) Is red < green? y
Inserting 'indigo' into { red green violet }
(4) Is green < indigo? y
(5) Is violet < indigo? n
Inserting 'blue' into { red green indigo violet }
(6) Is indigo < blue? n
(7) Is green < blue? y
Inserting 'yellow' into { red green blue indigo violet }
(8) Is blue < yellow? n
(9) Is green < yellow? n
(10) Is red < yellow? y
Inserting 'orange' into { red yellow green blue indigo violet }
(11) Is blue < orange? n
(12) Is yellow < orange? n
(13) Is red < orange? y
{ red orange yellow green blue indigo violet }

C++: STL sort with custom comparator

<lang cpp>#include <algorithm>

  1. include <iostream>
  2. include <vector>

using namespace std;

bool InteractiveCompare(const string& s1, const string& s2) { 

   if(s1 == s2) return false;  // don't ask to compare items that are the same
   static int count = 0;
   string response;
   cout << "(" << ++count << ") Is " << s1 << " < " << s2 << "? ";
   getline(cin, response);
   return !response.empty() && response.front() == 'y';

}

void PrintOrder(const vector<string>& items) { 

   cout << "{ ";
   for(auto& item : items) cout << item << " ";
   cout << "}\n";

}

int main() { 

   vector<string> items
   {
       "violet", "red", "green", "indigo", "blue", "yellow", "orange"
   };
   
   sort(items.begin(), items.end(), InteractiveCompare);
   PrintOrder(items);
   return 0;

}</lang>

Output:
(1) Is indigo < violet? y
(2) Is orange < indigo? y
(3) Is orange < indigo? y
(4) Is red < indigo? y
(5) Is green < indigo? y
(6) Is yellow < indigo? y
(7) Is blue < indigo? y
(8) Is blue < indigo? y
(9) Is red < orange? y
(10) Is green < red? n
(11) Is green < orange? n
(12) Is yellow < green? y
(13) Is yellow < orange? n
(14) Is blue < green? n
{ red orange yellow green blue indigo violet }

Commodore BASIC

<lang basic>100 REM SORT BY COMPARISON 110 DIM IN$(6), OU$(6) 120 FOR I=0 TO 6:READ IN$(I): NEXT I 130 DATA VIOLET,RED,GREEN,INDIGO,BLUE,YELLOW,ORANGE 140 OU$(0)=IN$(0):N=1 150 FOR I=1 TO 6 160 : IN$=IN$(I) 180 : GOSUB 390 190 : FOR J=0 TO N-1 200 : OU$ = OU$(J) 210 : GOSUB 340 220 : IF R>=0 THEN 280 230 : FOR K=N TO J+1 STEP -1 240 : OU$(K) = OU$(K-1) 250 : NEXT K 260 : OU$(J) = IN$ 270 : GOTO 300 280 : NEXT J 290 : OU$(N) = IN$ 300 : N=N+1 310 NEXT I 320 GOSUB 390 330 END 340 PRINT "IS "IN$" < "OU$"? (Y/N)"; 350 GET K$: IF K$<>"Y" AND K$<>"N" THEN 350 360 PRINT K$ 370 R = K$="Y" 380 RETURN 390 PRINT "("; 400 IF N=1 THEN 420 410 FOR Q=0 TO N-2:PRINT OU$(Q)",";:NEXT Q 420 PRINT OU$(N-1)")" 430 RETURN</lang>

Output:
IS RED < VIOLET? (Y/N)Y
IS GREEN < RED? (Y/N)N
IS GREEN < VIOLET? (Y/N)Y
IS INDIGO < RED? (Y/N)N
IS INDIGO < GREEN? (Y/N)N
IS INDIGO < VIOLET? (Y/N)Y
IS BLUE < RED? (Y/N)N
IS BLUE < GREEN? (Y/N)N
IS BLUE < INDIGO? (Y/N)Y
IS YELLOW < RED? (Y/N)N
IS YELLOW < GREEN? (Y/N)Y
IS ORANGE < RED? (Y/N)N
IS ORANGE < YELLOW? (Y/N)Y
(RED,ORANGE,YELLOW,GREEN,BLUE,INDIGO,VIOLET)

F#

This task uses Factorial base numbers indexing permutations of a collection (F#) <lang fsharp> // Order by pair comparisons. Nigel Galloway: April 23rd., 2021 let clrs=let n=System.Random() in lN2p [|for g in 7..-1..2->n.Next(g)|] [|"Red";"Orange";"Yellow";"Green";"Blue";"Indigo";"Violet"|] let rec fG n g=printfn "Is %s less than %s" n g; match System.Console.ReadLine() with "Yes"-> -1|"No"->1 |_->printfn "Enter Yes or No"; fG n g let mutable z=0 in printfn "%A sorted to %A using %d questions" clrs (clrs|>Array.sortWith(fun n g->z<-z+1; fG n g)) z </lang>

Output:

Possible interaction: 

Is Indigo less than Orange
Yes
Is Blue less than Orange
Yes
Is Blue less than Indigo
No
Is Yellow less than Orange
Yes
Is Yellow less than Blue
No
Is Red less than Orange
Yes
Is Red less than Yellow
Yes
Is Red less than Blue
Yes
Is Red less than Indigo
Yes
Is Green less than Orange
Yes
Is Green less than Yellow
Yes
Is Green less than Blue
Yes
Is Green less than Indigo
Yes
Is Green less than Red
No
Is Violet less than Orange
Yes
Is Violet less than Yellow
Yes
Is Violet less than Blue
Yes
Is Violet less than Indigo
Yes
Is Violet less than Green
Yes
Is Violet less than Red
Yes
[|"Orange"; "Indigo"; "Blue"; "Yellow"; "Red"; "Green"; "Violet"|] sorted to [|"Violet"; "Red"; "Green"; "Indigo"; "Blue"; "Yellow"; "Orange"|] using 20 questions

Factor

Asking the user for an ordering specifier inside a custom comparator:

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: formatting io kernel math.order prettyprint qw sorting ;

qw{ violet red green indigo blue yellow orange } [ "Is %s > %s? (y/n) " printf readln "y" = +gt+ +lt+ ? ] sort .</lang>

Output:
Is violet > red? (y/n) y
Is green > indigo? (y/n) n
Is blue > yellow? (y/n) y
Is red > green? (y/n) n
Is violet > green? (y/n) y
Is violet > indigo? (y/n) y
Is yellow > orange? (y/n) y
Is red > orange? (y/n) n
Is green > orange? (y/n) y
Is green > yellow? (y/n) y
Is green > blue? (y/n) n
Is indigo > blue? (y/n) y
{ "red" "orange" "yellow" "green" "blue" "indigo" "violet" }


FreeBASIC

Translation of: Commodore BASIC

<lang freebasic> Dim Shared As Byte r, n = 1 Dim Shared As String IN1, OU1 Dim Shared As String IN(6), OU(6) Dim As Byte i, j, k For i = 0 To 6 : Read IN(i) : Next i Data "violet", "red", "green", "indigo", "blue", "yellow", "orange" OU(0) = IN(0)

Sub PrintOrder 

   Print : Print "{";
   If n = 1 Then Print OU(n-1);")" : Exit Sub
   For q As Byte = 0 To n-2
       Print OU(q);", ";
   Next q        
   Print OU(n-1);"}"

End Sub

Sub InteractiveCompare 

   Dim As String*1 T
   Print "Es "; IN1; " < "; OU1; "? (S/N) ";
   Do: T = Inkey$: Loop Until T <> ""
   If Instr("snSN", T) Then Print Ucase(T)
   r = T = "S"

End Sub

For i = 1 To 6 

   IN1 = IN(i) 
   For j = 0 To n-1
       OU1 = OU(j)
       InteractiveCompare
       If r < 0 Then
           For k = n To j+1 Step -1
               OU(k) = OU(k-1)
           Next k
           OU(j) = IN1
           n += 1
           Exit For, For
       End If
   Next j
   OU(n) = IN1
   n += 1

Next i PrintOrder Sleep </lang>


Go

Go: Binary search insertion sort

<lang go>package main

import ( 

   "fmt"
   "sort"
   "strings"

)

var count int = 0

func interactiveCompare(s1, s2 string) bool { 

   count++
   fmt.Printf("(%d) Is %s < %s? ", count, s1, s2)
   var response string
   _, err := fmt.Scanln(&response)
   return err == nil && strings.HasPrefix(response, "y")

}

func main() { 

   items := []string{"violet", "red", "green", "indigo", "blue", "yellow", "orange"}
   
   var sortedItems []string
   
   // Use a binary insertion sort to order the items.  It should ask for
   // close to the minimum number of questions required
   for _, item := range items {
       fmt.Printf("Inserting '%s' into %s\n", item, sortedItems)
       // sort.Search performs the binary search using interactiveCompare to
       // rank the items
       spotToInsert := sort.Search(len(sortedItems), func(i int) bool {
           return interactiveCompare(item, sortedItems[i])
       })
       sortedItems = append(sortedItems[:spotToInsert],
                            append([]string{item}, sortedItems[spotToInsert:]...)...)
   }
   fmt.Println(sortedItems)

}</lang>

Output:
Inserting 'violet' into []
Inserting 'red' into [violet]
(1) Is red < violet? y
Inserting 'green' into [red violet]
(2) Is green < violet? y
(3) Is green < red? n
Inserting 'indigo' into [red green violet]
(4) Is indigo < green? n
(5) Is indigo < violet? y
Inserting 'blue' into [red green indigo violet]
(6) Is blue < indigo? y
(7) Is blue < green? n
Inserting 'yellow' into [red green blue indigo violet]
(8) Is yellow < blue? y
(9) Is yellow < green? y
(10) Is yellow < red? n
Inserting 'orange' into [red yellow green blue indigo violet]
(11) Is orange < blue? y
(12) Is orange < yellow? y
(13) Is orange < red? n
[red orange yellow green blue indigo violet]

Go: Standard sort with custom comparator

<lang go>package main

import ( 

   "fmt"
   "sort"
   "strings"

)

var count int = 0

type sortable []string func (s sortable) Len() int { return len(s) } func (s sortable) Swap(i, j int) { s[i], s[j] = s[j], s[i] } func (s sortable) Less(i, j int) bool { 

   s1, s2 := s[i], s[j]
   count++
   fmt.Printf("(%d) Is %s < %s? ", count, s1, s2)
   var response string
   _, err := fmt.Scanln(&response)
   return err == nil && strings.HasPrefix(response, "y")

}

func main() { 

   items := sortable{"violet", "red", "green", "indigo", "blue", "yellow", "orange"}
   sort.Sort(items)
   fmt.Println(items)

}</lang>

Output:
(1) Is orange < violet? y
(2) Is red < orange? y
(3) Is green < orange? n
(4) Is indigo < green? n
(5) Is blue < indigo? y
(6) Is blue < green? n
(7) Is yellow < indigo? y
(8) Is yellow < blue? y
(9) Is yellow < green? y
(10) Is yellow < orange? n
(11) Is violet < indigo? n
[red orange yellow green blue indigo violet]

Haskell

Injection of interaction with user is not straight-forward in pure functional language. In Haskell we use monads in order to abstract the computation flow and side effects. Fortunately the monadlist library [[1]] contains monadic variants of most popular list operations so that it becomes easy to implement our favorite sorting algorithms.

<lang haskell>import Control.Monad import Control.Monad.ListM (sortByM, insertByM, partitionM, minimumByM) import Data.Bool (bool) import Data.Monoid import Data.List

isortM, msortM, tsortM :: Monad m => (a -> a -> m Ordering) -> [a] -> m [a]

-- merge sort from the Control.Monad.ListM library msortM = sortByM

-- insertion sort isortM cmp = foldM (flip (insertByM cmp)) []

-- tree sort aka qsort (which is not) tsortM cmp = go 

 where
   go [] = pure []
   go (h:t) = do (l, g) <- partitionM (fmap (LT /=) . cmp h) t
                 go l <+> pure [h] <+> go g
   (<+>) = liftM2 (++)</lang>

Now we can sort lists with effects. For example, we may count number of comparisons, using writer monad: 

*Main> let countComparisons cmp a b = (Sum 1, a `cmp` b)
*Main> msortM (countComparisons compare) [2,6,3,5,9,1,5]
(Sum {getSum = 15},[1,2,3,5,5,6,9])

*Main> isortM (countComparisons compare) [2,6,3,5,9,1,5]
(Sum {getSum = 15},[1,2,3,5,5,6,9])

*Main> tsortM (countComparisons compare) [2,6,3,5,9,1,5]
(Sum {getSum = 13},[1,2,3,5,5,6,9])

Or use a "database" as a reference for sorting, using reader monad 

let fromList a b l = elemIndex a l `compare` elemIndex b l
*Main> msortM fromList [2,1,3,2,4,4,5,11,2,3,2,3] [1..]
[1,2,2,2,2,3,3,3,4,4,5,11]

Or even generate all possible permutations of a list making comparisons ambiguous: 

*Main> isortM (\_ _ -> [LT, GT]) [1,2,3]
[[1,2,3],[1,3,2],[3,1,2],[2,1,3],[2,3,1],[3,2,1]]

We are ready to ask user to compare entries for us: <lang haskell>ask a b = do 

 putStr $ show a ++ " ≤ " ++ show b ++ " ? [y/n]  "
 bool GT LT . ("y" ==) <$> getLine

colors = ["Violet", "Red", "Green", "Indigo", "Blue", "Yellow", "Orange"]</lang> 

*Main> isortM ask colors
"Red" ≤ "Violet" ? [y/n]  y
"Green" ≤ "Red" ? [y/n]  n
"Green" ≤ "Violet" ? [y/n]  y
"Indigo" ≤ "Red" ? [y/n]  n
"Indigo" ≤ "Green" ? [y/n]  n
"Indigo" ≤ "Violet" ? [y/n]  y
"Blue" ≤ "Red" ? [y/n]  n
"Blue" ≤ "Green" ? [y/n]  n
"Blue" ≤ "Indigo" ? [y/n]  y
"Yellow" ≤ "Red" ? [y/n]  n
"Yellow" ≤ "Green" ? [y/n]  y
"Orange" ≤ "Red" ? [y/n]  n
"Orange" ≤ "Yellow" ? [y/n]  y
["Red","Orange","Yellow","Green","Blue","Indigo","Violet"]

*Main> msortM ask colors
"Violet" ≤ "Red" ? [y/n]  n
"Red" ≤ "Green" ? [y/n]  y
"Green" ≤ "Indigo" ? [y/n]  y
"Indigo" ≤ "Blue" ? [y/n]  n
"Blue" ≤ "Yellow" ? [y/n]  n
"Yellow" ≤ "Orange" ? [y/n]  n
"Red" ≤ "Green" ? [y/n]  y
"Violet" ≤ "Green" ? [y/n]  n
"Violet" ≤ "Indigo" ? [y/n]  n
"Red" ≤ "Orange" ? [y/n]  y
"Green" ≤ "Orange" ? [y/n]  n
"Green" ≤ "Yellow" ? [y/n]  n
"Green" ≤ "Blue" ? [y/n]  y
"Indigo" ≤ "Blue" ? [y/n]  n
["Red","Orange","Yellow","Green","Blue","Indigo","Violet"]

*Main> tsortM ask colors
"Violet" ≤ "Red" ? [y/n]  n
"Violet" ≤ "Green" ? [y/n]  n
"Violet" ≤ "Indigo" ? [y/n]  n
"Violet" ≤ "Blue" ? [y/n]  n
"Violet" ≤ "Yellow" ? [y/n]  n
"Violet" ≤ "Orange" ? [y/n]  n
"Red" ≤ "Green" ? [y/n]  y
"Red" ≤ "Indigo" ? [y/n]  y
"Red" ≤ "Blue" ? [y/n]  y
"Red" ≤ "Yellow" ? [y/n]  y
"Red" ≤ "Orange" ? [y/n]  y
"Green" ≤ "Indigo" ? [y/n]  y
"Green" ≤ "Blue" ? [y/n]  y
"Green" ≤ "Yellow" ? [y/n]  n
"Green" ≤ "Orange" ? [y/n]  n
"Yellow" ≤ "Orange" ? [y/n]  n
"Indigo" ≤ "Blue" ? [y/n]  n
["Red","Orange","Yellow","Green","Blue","Indigo","Violet"]

It seems that insertion sort with 13 comparisons is the best one, and tree sort which needed 17 questions is the worst. But efficiency of sorting depends on the order of given list. Simple statistics could be made to compare these three methods for all possible permutations of seven elements.

<lang haskell>test method = do 

 mapM_ showHist $ hist res
 putStrLn $ "Median number of comparisons: " ++ show (median res)
 putStrLn $ "Mean number of comparisons: " ++ show (mean res)
 where
   res = getSum . fst . method cmp <$> permutations [1..7]
   cmp a b = (Sum 1, compare a b)
   median lst = sort lst !! (length lst `div` 2)
   mean lst = sum (fromIntegral <$> lst) / genericLength lst
   hist lst = (\x -> (head x, length x)) <$> group (sort lst)
   showHist (n, l) = putStrLn line
     where
       line = show n ++ "\t" ++ bar ++ " " ++ show perc ++ "%"
       bar = replicate (max perc 1) '*'
       perc = (100 * l) `div` product [1..7]</lang>

Comparing these three methods gives that for random inputs tree sort is the best choice. 

*Main> test msortM
6	* 0%
7	* 0%
8	* 0%
9	* 0%
10	* 1%
11	*** 3%
12	******* 7%
13	******** 8%
14	**************** 16%
15	************************ 24%
16	************************ 24%
17	************ 12%
Median number of comparisons: 15
Mean number of comparisons: 14.693055555555556

*Main> test isortM
6	* 0%
7	* 0%
8	* 0%
9	* 1%
10	*** 3%
11	***** 5%
12	******** 8%
13	********** 10%
14	************ 12%
15	************* 13%
16	************* 13%
17	*********** 11%
18	******** 8%
19	***** 5%
20	*** 3%
21	* 1%
Median number of comparisons: 15
Mean number of comparisons: 14.907142857142857

*Main> test tsortM
10	* 1%
11	******************** 20%
12	******************** 20%
13	***************** 17%
14	******** 8%
15	************* 13%
16	***** 5%
17	****** 6%
18	** 2%
19	* 1%
20	* 0%
21	* 1%
Median number of comparisons: 13
Mean number of comparisons: 13.485714285714286

Java

Java: Binary search insertion sort

<lang java>import java.util.*;

public class SortComp1 { 

   public static void main(String[] args) {
       List<String> items = Arrays.asList("violet", "red", "green", "indigo", "blue", "yellow", "orange");
       List<String> sortedItems = new ArrayList<>();
       Comparator<String> interactiveCompare = new Comparator<String>() {
               int count = 0;
               Scanner s = new Scanner(System.in);
               public int compare(String s1, String s2) {
                   System.out.printf("(%d) Is %s <, =, or > %s. Answer -1, 0, or 1: ", ++count, s1, s2);
                   return s.nextInt();
               }
           };
       for (String item : items) {
           System.out.printf("Inserting '%s' into %s\n", item, sortedItems);
           int spotToInsert = Collections.binarySearch(sortedItems, item, interactiveCompare);
           // when item does not equal an element in sortedItems,
           // it returns bitwise complement of insertion point
           if (spotToInsert < 0) spotToInsert = ~spotToInsert;
           sortedItems.add(spotToInsert, item);
       }
       System.out.println(sortedItems);
   }

}</lang>

Output:
Inserting 'violet' into []
Inserting 'red' into [violet]
(1) Is violet <, =, or > red. Answer -1, 0, or 1: 1
Inserting 'green' into [red, violet]
(2) Is red <, =, or > green. Answer -1, 0, or 1: -1
(3) Is violet <, =, or > green. Answer -1, 0, or 1: 1
Inserting 'indigo' into [red, green, violet]
(4) Is green <, =, or > indigo. Answer -1, 0, or 1: -1
(5) Is violet <, =, or > indigo. Answer -1, 0, or 1: 1
Inserting 'blue' into [red, green, indigo, violet]
(6) Is green <, =, or > blue. Answer -1, 0, or 1: -1
(7) Is indigo <, =, or > blue. Answer -1, 0, or 1: 1
Inserting 'yellow' into [red, green, blue, indigo, violet]
(8) Is blue <, =, or > yellow. Answer -1, 0, or 1: 1
(9) Is red <, =, or > yellow. Answer -1, 0, or 1: -1
(10) Is green <, =, or > yellow. Answer -1, 0, or 1: 1
Inserting 'orange' into [red, yellow, green, blue, indigo, violet]
(11) Is green <, =, or > orange. Answer -1, 0, or 1: 1
(12) Is red <, =, or > orange. Answer -1, 0, or 1: -1
(13) Is yellow <, =, or > orange. Answer -1, 0, or 1: 1
[red, orange, yellow, green, blue, indigo, violet]

Java: Standard sort with custom comparator

<lang java>import java.util.*;

public class OrderByPair { 

   public static void main(String[] args) {
       List<String> items = Arrays.asList("violet", "red", "green", "indigo", "blue", "yellow", "orange");
       Collections.sort(items, new Comparator<String>() {
               int count = 0;
               Scanner s = new Scanner(System.in);
               public int compare(String s1, String s2) {
                   System.out.printf("(%d) Is %s <, =, or > %s. Answer -1, 0, or 1: ", ++count, s1, s2);
                   return s.nextInt();
               }
           });
       System.out.println(items);
   }

}</lang>

Output:
(1) Is red <, =, or > violet. Answer -1, 0, or 1: -1
(2) Is green <, =, or > red. Answer -1, 0, or 1: 1
(3) Is green <, =, or > violet. Answer -1, 0, or 1: -1
(4) Is green <, =, or > red. Answer -1, 0, or 1: 1
(5) Is indigo <, =, or > green. Answer -1, 0, or 1: 1
(6) Is indigo <, =, or > violet. Answer -1, 0, or 1: -1
(7) Is blue <, =, or > indigo. Answer -1, 0, or 1: -1
(8) Is blue <, =, or > green. Answer -1, 0, or 1: 1
(9) Is yellow <, =, or > blue. Answer -1, 0, or 1: -1
(10) Is yellow <, =, or > green. Answer -1, 0, or 1: -1
(11) Is yellow <, =, or > red. Answer -1, 0, or 1: 1
(12) Is orange <, =, or > blue. Answer -1, 0, or 1: -1
(13) Is orange <, =, or > yellow. Answer -1, 0, or 1: 1
(14) Is orange <, =, or > green. Answer -1, 0, or 1: 1
[red, yellow, green, orange, blue, indigo, violet]

jq

Translation of: Wren
Works with: jq

Works with gojq, the Go implementation of jq

In order for a jq program to interact with a user, prompts must be directed to stderr, which currently means that the prompt string will be printed with quotation marks. <lang jq>def inputOption($prompt; $options): 

 def r:
   $prompt | stderr
   | input as $in
     | if $in|test($options) then $in else r end;
 r;
  1. Inserts item $x in the array input, which is kept sorted as per user input
  2. assuming it is already sorted. $q is the prompt number.
  3. Input: [$q; $a]
  4. Output: [$qPrime, $aPrime]

def insortRight($x): 

 . as [$q, $a]
 | { lo: 0, hi: ($a|length), $q }
 | until( .lo >= .hi; 
       ( ((.lo + .hi)/2)|floor) as $mid
       | .q += 1
       | "\(.q): Is \($x) less than \($a[$mid])? y/n: " as $prompt
       | (inputOption($prompt; "[yn]") == "y") as $less 
       | if ($less) then .hi = $mid
         else .lo = $mid + 1
         end) 
  # insert at position .lo
  | [ .q, ($a[: .lo] + [x] + $a[.lo :]) ];

def order: 

 reduce .[] as $item ( [0, []]; insortRight($item) )
 | .[1];

["violet red green indigo blue yellow orange"|splits(" ")] | order as $ordered | ("\nThe colors of the rainbow, in sorted order, are:", 

   $ordered )</lang>

Recommended Invocation Options: -nRrc

Sample Transcript 

"1: Is red less than violet? y/n: "y
y
"2: Is green less than violet? y/n: "y
y
"3: Is green less than red? y/n: "n
n
"4: Is indigo less than green? y/n: "n
n
"5: Is indigo less than violet? y/n: "y
y
"6: Is blue less than indigo? y/n: "y
y
"7: Is blue less than green? y/n: "n
n
"8: Is yellow less than blue? y/n: "y
y
"9: Is yellow less than green? y/n: "y
y
"10: Is yellow less than red? y/n: "n
n
"11: Is orange less than blue? y/n: "y
y
"12: Is orange less than yellow? y/n: "y
y
"13: Is orange less than red? y/n: "n
n

The colors of the rainbow, in sorted order, are:
["red","orange","yellow","green","blue","indigo","violet"]


Julia

<lang julia>const nrequests = [0] const ordering = Dict("violet" => 7, "red" => 1, "green" => 4, "indigo" => 6, "blue" => 5, 

                     "yellow" => 3, "orange" => 2)

function tellmeifgt(x, y) 

   nrequests[1] += 1
   while true
       print("Is $x greater than $y?  (Y/N) =>  ")
       s = strip(readline())
       if length(s) > 0
           (s[1] == 'Y' || s[1] == 'y') && return true
           (s[1] == 'N' || s[1] == 'n') && return false
       end
   end

end

function orderbypair!(a::Vector) 

   incr = div(length(a), 2)
   while incr > 0
       for i in incr+1:length(a)
           j = i
           tmp = a[i]
           while j > incr && tellmeifgt(a[j - incr], tmp)
               a[j] = a[j-incr]
               j -= incr
           end
           a[j] = tmp
       end
       if incr == 2
           incr = 1
       else
           incr = floor(Int, incr * 5.0 / 11)
       end
   end
   return a

end

const words = String.(split("violet red green indigo blue yellow orange", r"\s+")) println("Unsorted: $words") println("Sorted: $(orderbypair!(words)). Total requests: $(nrequests[1]).")

</lang>

Output:
Is violet greater than indigo?  (Y/N) =>  y
Is red greater than blue?  (Y/N) =>  n
Is green greater than yellow?  (Y/N) =>  y
Is violet greater than orange?  (Y/N) =>  y
Is indigo greater than orange?  (Y/N) =>  y
Is orange greater than red?  (Y/N) =>  y
Is orange greater than yellow?  (Y/N) =>  n
Is yellow greater than indigo?  (Y/N) =>  n
Is indigo greater than blue?  (Y/N) =>  y
Is yellow greater than blue?  (Y/N) =>  n
Is indigo greater than green?  (Y/N) =>  y
Is blue greater than green?  (Y/N) =>  y
Is yellow greater than green?  (Y/N) =>  n
Is indigo greater than violet?  (Y/N) =>  n
Sorted: ["red", "orange", "yellow", "green", "blue", "indigo", "violet"]. Total requests: 14.

Mathematica / Wolfram Language

<lang Mathematica>ClearAll[HumanOrderCheck] HumanOrderCheck[opt1_,opt2_]:=ChoiceDialog[Row@{"Is {",opt1,", ", opt2, "} ordered?"},{"Yes"->True,"No"->False}] Sort[{"violet","red","green","indigo","blue","yellow","orange"},HumanOrderCheck]</lang>

Output:

After some Yes/No clicks you should get: 

{"red", "orange", "yellow", "green", "blue", "indigo", "violet"}

Nim

Using a list filled by binary insertion and a custom comparison function. <lang Nim>import algorithm, strformat, strutils

let list = ["violet", "red", "green", "indigo", "blue", "yellow", "orange"]

var count = 0

proc comp(x, y: string): int = 

 if x == y: return 0
 inc count
 while true:
   stdout.write &"{count:>2}) Is {x} less than {y} (y/n)? "
   let answer = stdin.readLine()[0]
   case answer
   of 'y': return -1
   of 'n': return 1
   else: echo "Incorrect answer."

var sortedList: seq[string]

for elem in list: 

 sortedList.insert(elem, sortedList.upperBound(elem, comp))

echo "Sorted list: ", sortedList.join(", ")</lang>

Output:
 1) Is violet less than red (y/n)? n
 2) Is violet less than green (y/n)? n
 3) Is red less than green (y/n)? n
 4) Is red less than indigo (y/n)? n
 5) Is green less than indigo (y/n)? y
 6) Is red less than blue (y/n)? n
 7) Is indigo less than blue (y/n)? n
 8) Is green less than blue (y/n)? n
 9) Is indigo less than yellow (y/n)? y
10) Is violet less than yellow (y/n)? y
11) Is red less than orange (y/n)? n
12) Is green less than orange (y/n)? y
13) Is indigo less than orange (y/n)? y
Sorted list: blue, green, indigo, orange, red, violet, yellow

OCaml

Standard sort with custom comparator

List: <lang ocaml>let () = 

 let count = ref 0 in
 let mycmp s1 s2 = (
   incr count;
   Printf.printf "(%d) Is %s <, ==, or > %s? Answer -1, 0, or 1: " (!count) s1 s2;
   read_int ()
 ) in
 let items = ["violet"; "red"; "green"; "indigo"; "blue"; "yellow"; "orange"] in
 let sorted = List.sort mycmp items in
 List.iter (Printf.printf "%s ") sorted;
 print_newline ()</lang>
Output:
(1) Is violet <, ==, or > red? Answer -1, 0, or 1: 1
(2) Is red <, ==, or > green? Answer -1, 0, or 1: -1
(3) Is violet <, ==, or > green? Answer -1, 0, or 1: 1
(4) Is indigo <, ==, or > blue? Answer -1, 0, or 1: 1
(5) Is yellow <, ==, or > orange? Answer -1, 0, or 1: 1
(6) Is blue <, ==, or > orange? Answer -1, 0, or 1: 1
(7) Is blue <, ==, or > yellow? Answer -1, 0, or 1: 1
(8) Is violet <, ==, or > indigo? Answer -1, 0, or 1: 1
(9) Is green <, ==, or > indigo? Answer -1, 0, or 1: -1
(10) Is green <, ==, or > blue? Answer -1, 0, or 1: -1
(11) Is green <, ==, or > yellow? Answer -1, 0, or 1: 1
(12) Is red <, ==, or > yellow? Answer -1, 0, or 1: -1
(13) Is red <, ==, or > orange? Answer -1, 0, or 1: -1
red orange yellow green blue indigo violet

Array: <lang ocaml>let () = 

 let count = ref 0 in
 let mycmp s1 s2 = (
   incr count;
   Printf.printf "(%d) Is %s <, ==, or > %s? Answer -1, 0, or 1: " (!count) s1 s2;
   read_int ()
 ) in
 let items = [|"violet"; "red"; "green"; "indigo"; "blue"; "yellow"; "orange"|] in
 Array.sort mycmp items;
 Array.iter (Printf.printf "%s ") items;
 print_newline ()</lang>
Output:
(1) Is blue <, ==, or > yellow? Answer -1, 0, or 1: 1
(2) Is blue <, ==, or > orange? Answer -1, 0, or 1: 1
(3) Is blue <, ==, or > red? Answer -1, 0, or 1: 1
(4) Is blue <, ==, or > green? Answer -1, 0, or 1: 1
(5) Is blue <, ==, or > indigo? Answer -1, 0, or 1: -1
(6) Is indigo <, ==, or > violet? Answer -1, 0, or 1: -1
(7) Is blue <, ==, or > green? Answer -1, 0, or 1: 1
(8) Is blue <, ==, or > indigo? Answer -1, 0, or 1: -1
(9) Is indigo <, ==, or > orange? Answer -1, 0, or 1: 1
(10) Is blue <, ==, or > green? Answer -1, 0, or 1: 1
(11) Is blue <, ==, or > orange? Answer -1, 0, or 1: 1
(12) Is red <, ==, or > yellow? Answer -1, 0, or 1: -1
(13) Is blue <, ==, or > yellow? Answer -1, 0, or 1: 1
(14) Is yellow <, ==, or > green? Answer -1, 0, or 1: -1
(15) Is green <, ==, or > orange? Answer -1, 0, or 1: 1
(16) Is green <, ==, or > red? Answer -1, 0, or 1: 1
(17) Is yellow <, ==, or > red? Answer -1, 0, or 1: 1
(18) Is yellow <, ==, or > orange? Answer -1, 0, or 1: 1
(19) Is orange <, ==, or > red? Answer -1, 0, or 1: 1
red orange yellow green blue indigo violet

Perl

<lang perl>#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Order_by_pair_comparisons use warnings;

sub ask 

 {
 while( 1 )
   {
   print "Compare $a to $b [<,=,>]: ";
   <STDIN> =~ /[<=>]/ and return +{qw( < -1 = 0 > 1 )}->{$&};
   }
 }

my @sorted = sort ask qw( violet red green indigo blue yellow orange ); print "sorted: @sorted\n";</lang>

Output:
Compare violet to red [<,=,>]: >
Compare green to indigo [<,=,>]: <
Compare blue to yellow [<,=,>]: >
Compare red to green [<,=,>]: <
Compare green to violet [<,=,>]: <
Compare violet to indigo [<,=,>]: ?
Compare violet to indigo [<,=,>]: >
Compare yellow to orange [<,=,>]: >
Compare red to orange [<,=,>]: <
Compare orange to green [<,=,>]: <
Compare green to yellow [<,=,>]: >
Compare green to blue [<,=,>]: <
Compare indigo to blue [<,=,>]: >
sorted: red orange yellow green blue indigo violet


Phix

The number of questions asked is entirely dependent on how the initial order marries in with the sorting algorithm.
This needs just 6 questions to handle an already in-order or only first two items swapped list.
I picked an initial ordering that requires a fairly easy to remember set of answers: 4Y then alternate.
The builtin sort(s) use an initial gap of 10%, ultimately balancing #comparisons against cache hits, which leads to a wider range of #questions, as said best case 6, worst case 21. A better match to the narrower range of Python (I think 10..14) could probably be made using a copy of custom_sort (it is only 52 lines) with an initial 50% gap. 

integer qn = 0
function ask(string a, b)
    qn += 1
    printf(1,"%d: Is %s < %s (Y/N)?:",{qn,a,b})
    integer ch = upper(wait_key())
    printf(1,"%s\n",ch)
    return iff(ch='Y'?-1:1)
end function

?custom_sort(ask,split("violet orange red yellow green blue indigo"))
Output:
1: Is orange < violet (Y/N)?:Y
2: Is red < violet (Y/N)?:Y
3: Is red < orange (Y/N)?:Y
4: Is yellow < violet (Y/N)?:Y
5: Is yellow < orange (Y/N)?:N
6: Is green < violet (Y/N)?:Y
7: Is green < yellow (Y/N)?:N
8: Is blue < violet (Y/N)?:Y
9: Is blue < green (Y/N)?:N
10: Is indigo < violet (Y/N)?:Y
11: Is indigo < blue (Y/N)?:N
{"red","orange","yellow","green","blue","indigo","violet"}

Python

Python: Binary insertion

Uses binary search to insert successive items into a growing ordered list. Comparisons are asked for.

<lang python>def _insort_right(a, x, q): 

   """
   Insert item x in list a, and keep it sorted assuming a is sorted.
   If x is already in a, insert it to the right of the rightmost x.
   """

   lo, hi = 0, len(a)
   while lo < hi:
       mid = (lo+hi)//2
       q += 1
       less = input(f"{q:2}: IS {x:>6} LESS-THAN {a[mid]:>6} ? y/n: ").strip().lower() == 'y'
       if less: hi = mid
       else: lo = mid+1
   a.insert(lo, x)
   return q

def order(items): 

   ordered, q = [], 0
   for item in items:
       q = _insort_right(ordered, item, q)
   return ordered, q

if __name__ == '__main__': 

   items = 'violet red green indigo blue yellow orange'.split()
   ans, questions = order(items)
   print('\n' + ' '.join(ans))</lang>
Output:
 1: IS    red LESS-THAN violet ? y/n: y

 2: IS  green LESS-THAN violet ? y/n: y

 3: IS  green LESS-THAN    red ? y/n: n

 4: IS indigo LESS-THAN  green ? y/n: n

 5: IS indigo LESS-THAN violet ? y/n: y

 6: IS   blue LESS-THAN indigo ? y/n: y

 7: IS   blue LESS-THAN  green ? y/n: n

 8: IS yellow LESS-THAN   blue ? y/n: y

 9: IS yellow LESS-THAN  green ? y/n: y

10: IS yellow LESS-THAN    red ? y/n: n

11: IS orange LESS-THAN   blue ? y/n: y

12: IS orange LESS-THAN yellow ? y/n: y

13: IS orange LESS-THAN    red ? y/n: n

red orange yellow green blue indigo violet

Python: Sort with custom comparator

This uses a custom comparator together with functools.cmp_to_key to sort the previous order in fourteen questions.

<lang python>from functools import cmp_to_key

def user_cmp(a, b): 

   return int(input(f"IS {a:>6} <, ==, or > {b:>6}  answer -1, 0 or 1:"))

if __name__ == '__main__': 

   items = 'violet red green indigo blue yellow orange'.split()
   ans = sorted(items, key=cmp_to_key(user_cmp))
   print('\n' + ' '.join(ans))</lang>
Output:
IS    red <, ==, or > violet  answer -1, 0 or 1:-1

IS  green <, ==, or >    red  answer -1, 0 or 1:1

IS  green <, ==, or > violet  answer -1, 0 or 1:-1

IS  green <, ==, or >    red  answer -1, 0 or 1:1

IS indigo <, ==, or >  green  answer -1, 0 or 1:1

IS indigo <, ==, or > violet  answer -1, 0 or 1:-1

IS   blue <, ==, or > indigo  answer -1, 0 or 1:-1

IS   blue <, ==, or >  green  answer -1, 0 or 1:1

IS yellow <, ==, or >   blue  answer -1, 0 or 1:-1

IS yellow <, ==, or >  green  answer -1, 0 or 1:-1

IS yellow <, ==, or >    red  answer -1, 0 or 1:1

IS orange <, ==, or >   blue  answer -1, 0 or 1:-1

IS orange <, ==, or > yellow  answer -1, 0 or 1:-1

IS orange <, ==, or >    red  answer -1, 0 or 1:1

red orange yellow green blue indigo violet

Quackery

sortwith sorts by insertion sort by default, of by merge sort falling back to insertion sort for nests of fewer than 16 items if the Quackery extensions are loaded. In either instance, as this is sorting a nest of seven items, it will be by insertion sort.

<lang Quackery> [ $ "Is " swap join 

  $ " before " join
  swap join 
  $ "? (y/n) " join
  input $ "y" = ]       is askuser

$ "red orange yellow green blue indigo violet" say "Correct order --> " dup echo$ cr cr nest$ shuffle dup witheach [ echo$ sp ] cr cr sortwith askuser cr witheach [ echo$ sp ] cr</lang>

Output:
Correct order --> red orange yellow green blue indigo violet

green blue orange indigo yellow violet red 

Is blue before green? (y/n) n
Is orange before green? (y/n) y
Is indigo before orange? (y/n) n
Is indigo before green? (y/n) n
Is indigo before blue? (y/n) n
Is yellow before orange? (y/n) n
Is yellow before green? (y/n) y
Is violet before orange? (y/n) n
Is violet before yellow? (y/n) n
Is violet before green? (y/n) n
Is violet before blue? (y/n) n
Is violet before indigo? (y/n) n
Is red before orange? (y/n) y

red orange yellow green blue indigo violet

Raku

Raku's sort (like most languages) can take a custom "comparator" routine. Since the calls to the comparator are minimized, and the info that the user provides is analogous to the required return values of the comparator, we just need to embed the prompt directly in the comparator.

<lang perl6>my $ask_count = 0; sub by_asking ( $a, $b ) { 

   $ask_count++;
   constant $fmt = '%2d. Is %-6s [ less than | greater than | equal to ] %-6s? ( < = > ) ';
   constant %o = '<' => Order::Less,
                 '=' => Order::Same,
                 '>' => Order::More;

   loop {
       my $input = prompt sprintf $fmt, $ask_count, $a, $b;
       return $_ with %o{ $input.trim };
       say "Invalid input '$input'";
   }

}

my @colors = <violet red green indigo blue yellow orange>; my @sorted = @colors.sort: &by_asking; say (:@sorted);

die if @sorted».substr(0,1).join ne 'roygbiv'; my $expected_ask_count = @colors.elems * log(@colors.elems); warn "Too many questions? ({:$ask_count} > {:$expected_ask_count})" if $ask_count > $expected_ask_count;</lang>

Output:
 1. Is violet [ less than | greater than | equal to ] red   ? ( < = > ) >
 2. Is green  [ less than | greater than | equal to ] indigo? ( < = > ) <
 3. Is blue   [ less than | greater than | equal to ] yellow? ( < = > ) >
 4. Is red    [ less than | greater than | equal to ] green ? ( < = > ) <
 5. Is violet [ less than | greater than | equal to ] green ? ( < = > ) >
 6. Is violet [ less than | greater than | equal to ] indigo? ( < = > ) >
 7. Is yellow [ less than | greater than | equal to ] orange? ( < = > ) >
 8. Is red    [ less than | greater than | equal to ] orange? ( < = > ) <
 9. Is green  [ less than | greater than | equal to ] orange? ( < = > ) >
10. Is green  [ less than | greater than | equal to ] yellow? ( < = > ) >
11. Is green  [ less than | greater than | equal to ] blue  ? ( < = > ) <
12. Is indigo [ less than | greater than | equal to ] blue  ? ( < = > ) >
sorted => [red orange yellow green blue indigo violet]

REXX

Translation of: Python


Extra code was added to the REXX program to handle incorrectly formatted answers.

Also note that lists in REXX start with unity, not zero. <lang rexx>/*REXX pgm orders some items based on (correct) answers from a carbon─based life form. */ colors= 'violet red green indigo blue yellow orange' 

                                       q= 0;    #= 0;    $=
          do j=1  for words(colors);   q= inSort( word(colors, j), q)
          end   /*j*/                           /*poise questions the CBLF about order.*/

say 

          do i=1  for #;   say '   query'   right(i, length(#) )":"   !.i
          end   /*i*/                           /* [↑] show the list of queries to CBLF*/

say say 'final ordering: ' $ exit 0 /*──────────────────────────────────────────────────────────────────────────────────────*/ getAns: #= # + 1; _= copies('─', 8); y_n= ' Answer y/n' 

             do try=0  until ansU='Y'  |  ansU='N'
             if try>0  then say _ '(***error***)  incorrect answer.'
             ask= _  ' is '   center(x,6)   " less than "   center(word($, mid+1),6)  '?'
             say ask   y_n;  parse pull ans 1 ansU;   ansU= space(ans);   upper ansU
             end   /*until*/;      !.#= ask   '  '    ans;                return

/*──────────────────────────────────────────────────────────────────────────────────────*/ inSort: parse arg x, q; hi= words($); lo= 0 

             do q=q-1  while lo<hi;              mid= (lo+hi) % 2
             call getAns;  if ansU=='Y'  then hi= mid
                                         else lo= mid + 1
             end   /*q*/
       $= subword($, 1, lo)  x  subword($, lo+1);      return q</lang>
output   (only showing the results and eliding the querying/answering):
   query  1: ────────  is   red    less than  violet ?    y
   query  2: ────────  is  green   less than  violet ?    y
   query  3: ────────  is  green   less than   red   ?    n
   query  4: ────────  is  indigo  less than  green  ?    n
   query  5: ────────  is  indigo  less than  violet ?    y
   query  6: ────────  is   blue   less than  indigo ?    y
   query  7: ────────  is   blue   less than  green  ?    n
   query  8: ────────  is  yellow  less than   blue  ?    y
   query  9: ────────  is  yellow  less than  green  ?    y
   query 10: ────────  is  yellow  less than   red   ?    n
   query 11: ────────  is  orange  less than   blue  ?    y
   query 12: ────────  is  orange  less than  yellow ?    y
   query 13: ────────  is  orange  less than   red   ?    n

final ordering:  red orange yellow green blue indigo violet

Ruby

Ruby: Binary search insertion sort

<lang ruby>items = ["violet", "red", "green", "indigo", "blue", "yellow", "orange"] count = 0 sortedItems = [] items.each {|item| 

 puts "Inserting '#{item}' into #{sortedItems}"
 spotToInsert = sortedItems.bsearch_index{|x|
   count += 1
   print "(#{count}) Is #{item} < #{x}? "
   gets.start_with?('y')
 } || sortedItems.length # if insertion point is at the end, bsearch_index returns nil
 sortedItems.insert(spotToInsert, item)

} p sortedItems</lang>

Output:
Inserting 'violet' into []
Inserting 'red' into ["violet"]
(1) Is red < violet? y
Inserting 'green' into ["red", "violet"]
(2) Is green < violet? y
(3) Is green < red? n
Inserting 'indigo' into ["red", "green", "violet"]
(4) Is indigo < green? n
(5) Is indigo < violet? y
Inserting 'blue' into ["red", "green", "indigo", "violet"]
(6) Is blue < indigo? y
(7) Is blue < green? n
Inserting 'yellow' into ["red", "green", "blue", "indigo", "violet"]
(8) Is yellow < blue? y
(9) Is yellow < green? y
(10) Is yellow < red? n
Inserting 'orange' into ["red", "yellow", "green", "blue", "indigo", "violet"]
(11) Is orange < blue? y
(12) Is orange < yellow? y
(13) Is orange < red? n
["red", "orange", "yellow", "green", "blue", "indigo", "violet"]

Ruby: Standard sort with custom comparator

<lang ruby>items = ["violet", "red", "green", "indigo", "blue", "yellow", "orange"] count = 0 p items.sort {|a, b| 

 count += 1
 print "(#{count}) Is #{a} <, =, or > #{b}. Answer -1, 0, or 1: "
 gets.to_i

}</lang>

Output:
(1) Is violet <, =, or > red. Answer -1, 0, or 1: 1
(2) Is violet <, =, or > green. Answer -1, 0, or 1: 1
(3) Is red <, =, or > green. Answer -1, 0, or 1: -1
(4) Is violet <, =, or > indigo. Answer -1, 0, or 1: 1
(5) Is green <, =, or > indigo. Answer -1, 0, or 1: -1
(6) Is violet <, =, or > blue. Answer -1, 0, or 1: 1
(7) Is indigo <, =, or > blue. Answer -1, 0, or 1: 1
(8) Is green <, =, or > blue. Answer -1, 0, or 1: -1
(9) Is violet <, =, or > yellow. Answer -1, 0, or 1: 1
(10) Is indigo <, =, or > yellow. Answer -1, 0, or 1: 1
(11) Is blue <, =, or > yellow. Answer -1, 0, or 1: 1
(12) Is green <, =, or > yellow. Answer -1, 0, or 1: 1
(13) Is red <, =, or > yellow. Answer -1, 0, or 1: -1
(14) Is violet <, =, or > orange. Answer -1, 0, or 1: 1
(15) Is indigo <, =, or > orange. Answer -1, 0, or 1: 1
(16) Is blue <, =, or > orange. Answer -1, 0, or 1: 1
(17) Is green <, =, or > orange. Answer -1, 0, or 1: 1
(18) Is yellow <, =, or > orange. Answer -1, 0, or 1: 1
(19) Is red <, =, or > orange. Answer -1, 0, or 1: -1
["red", "orange", "yellow", "green", "blue", "indigo", "violet"]

Wren

Translation of: Python
Library: Wren-ioutil
Library: Wren-fmt

<lang ecmascript>import "/ioutil" for Input import "/fmt" for Fmt

// Inserts item x in list a, and keeps it sorted assuming a is already sorted. // If x is already in a, inserts it to the right of the rightmost x. var insortRight = Fn.new{ |a, x, q| 

   var lo = 0
   var hi = a.count
   while (lo < hi) {
       var mid = ((lo + hi)/2).floor
       q = q + 1
       var prompt = Fmt.swrite("$2d: Is $6s less than $6s ? y/n: ", q, x, a[mid])
       var less = Input.option(prompt, "yn") == "y"
       if (less) {
           hi = mid
       } else {
           lo = mid + 1
       }
    }
    a.insert(lo, x)
    return q

}

var order = Fn.new { |items| 

   var ordered = []
   var q = 0
   for (item in items) {
       q = insortRight.call(ordered, item, q)
   }
   return ordered

}

var items = "violet red green indigo blue yellow orange".split(" ") var ordered = order.call(items) System.print("\nThe colors of the rainbow, in sorted order, are:") System.print(ordered)</lang>

Output:
 1: Is    red less than violet ? y/n: y
 2: Is  green less than violet ? y/n: y
 3: Is  green less than    red ? y/n: n
 4: Is indigo less than  green ? y/n: n
 5: Is indigo less than violet ? y/n: y
 6: Is   blue less than indigo ? y/n: y
 7: Is   blue less than  green ? y/n: n
 8: Is yellow less than   blue ? y/n: y
 9: Is yellow less than  green ? y/n: y
10: Is yellow less than    red ? y/n: n
11: Is orange less than   blue ? y/n: y
12: Is orange less than yellow ? y/n: y
13: Is orange less than    red ? y/n: n

The colors of the rainbow, in sorted order, are:
[red, orange, yellow, green, blue, indigo, violet]
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