Round-robin tournament schedule

From Rosetta Code
Round-robin tournament schedule 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.

A round-robin tournament is also known as an all-play-all-tournament; each participant plays every other participant once.

For N participants the number of rounds is N-1 if N is an even number. When there are an odd number of participants then each round one contestor has no opponent (AKA as a "bye"). The number of rounds is N in that case.

Task

Write a program that prints out a tournament schedule for 12 participants (represented by numbers 1 to 12).

See also


AWK[edit]

# syntax: GAWK -f ROUND-ROBIN_TOURNAMENT_SCHEDULE.AWK
BEGIN {
    main(1)
    main(2)
    main(5,"The Bizzaros")
    main(12)
    exit(0)
}
function main(n,description,  arr,i,j,leng,tmp) {
    if (n < 2) {
      printf("\n%d is too few participants\n",n)
      return
    }
    printf("\n%d players  %s\n",n,description)
    for (i=1; i<=n; i++) {
      arr[i] = i
    }
    if (n % 2 == 1) {
      arr[++n] = 0 # a "bye"
    }
    leng = length(n-1)
    for (i=1; i<n; i++) {
      printf("\nround %*d:",leng,i)
      for (j=1; j<=n/2; j++) {
        printf("%4s",arr[j]==0?"bye":arr[j])
      }
      printf("\n%*s",leng+7,"")
      for (j=n; j>n/2; j--) {
        printf("%4s",arr[j]==0?"bye":arr[j])
      }
      printf("\n")
      tmp = arr[n]
      for (j=n; j>2; j--) {
        arr[j] = arr[j-1]
      }
      arr[2] = tmp
    }
}
Output:
1 is too few participants

2 players

round 1:   1
           2

5 players  The Bizzaros

round 1:   1   2   3
         bye   5   4

round 2:   1 bye   2
           5   4   3

round 3:   1   5 bye
           4   3   2

round 4:   1   4   5
           3   2 bye

round 5:   1   3   4
           2 bye   5

12 players

round  1:   1   2   3   4   5   6
           12  11  10   9   8   7

round  2:   1  12   2   3   4   5
           11  10   9   8   7   6

round  3:   1  11  12   2   3   4
           10   9   8   7   6   5

round  4:   1  10  11  12   2   3
            9   8   7   6   5   4

round  5:   1   9  10  11  12   2
            8   7   6   5   4   3

round  6:   1   8   9  10  11  12
            7   6   5   4   3   2

round  7:   1   7   8   9  10  11
            6   5   4   3   2  12

round  8:   1   6   7   8   9  10
            5   4   3   2  12  11

round  9:   1   5   6   7   8   9
            4   3   2  12  11  10

round 10:   1   4   5   6   7   8
            3   2  12  11  10   9

round 11:   1   3   4   5   6   7
            2  12  11  10   9   8

Common Lisp[edit]

Draft

Program[edit]

;; 221130  Draft

(defun planning-tournoi (joueurs &aux (stop ()))
  (labels ((tour (sac &optional (lst ()) &aux (duo ()))
             (unless (intersection lst stop :test #'equal)
               (cond (sac
                 (dolist (i sac)
                      (dolist (j (rest (member i sac)))
                        (setf duo (list i j))
                        (tour (set-difference sac duo) (list* duo lst)))))
                  (t (print (reverse lst))
                     (setf stop (nconc stop lst)))))))
          (tour joueurs)))

Execution[edit]

(planning-tournoi '(A B C D E *))
Output:
((A B) (C D) (E *)) 
((A C) (B E) (D *)) 
((A D) (B *) (C E)) 
((A E) (B D) (C *)) 
((A *) (B C) (D E))
(planning-tournoi '(1 2 3 4 5 6 7 8 9 10 11 12))
Output:
((1 2) (3 4) (5 6) (7 8) (9 10) (11 12))
((1 3) (2 4) (5 7) (6 8) (9 11) (10 12))
((1 4) (2 3) (5 8) (6 7) (9 12) (10 11))
((1 5) (2 6) (3 9) (4 10) (7 11) (8 12))
((1 6) (2 5) (3 10) (4 9) (7 12) (8 11))
((1 7) (2 8) (3 11) (4 12) (5 9) (6 10))
((1 8) (2 7) (3 12) (4 11) (5 10) (6 9))
((1 9) (2 10) (3 7) (4 8) (5 11) (6 12))
((1 10) (2 9) (3 8) (4 7) (5 12) (6 11))
((1 11) (2 12) (3 5) (4 6) (7 9) (8 10))
((1 12) (2 11) (3 6) (4 5) (7 10) (8 9))

cyril nocton (cyril.nocton@gmail.com) w/ google translate

FreeBASIC[edit]

function nob( n as uinteger, i as uinteger, bye as boolean ) as string
    'helper function to allow byes to be printed intelligently
    dim as string pad
    if n > 9 then pad = " " else pad = ""
    if n = i and bye then 
        return pad+"B" 
    else 
        if i<10 then return pad + str(i) else return str(i)
    end if
end function

sub roundrob( byval n as uinteger )
    dim as boolean bye = false
    if n mod 2 = 1 then      'if there is an odd number of competitors
        bye = 1              'make note of this fact
        n += 1               'and treat the tournament as having one more competitor
    end if
    dim as uinteger schd(1 to n), r, i, temp1, temp2
    for i = 1 to n
        schd(i) =i           'initial population of the array with numbers 1-n
    next i
    for r = 1 to n-1
        print using "Round ##:   ";r;
        for i = 1 to n/2     'print the pairings according to the scheme
                             '1 2 3 4
                             '5 6 7 8
            print using "(& - &)  ";nob(n,schd(i),bye);nob(n,schd(i+n\2),bye);
        next i
        print
        'now move positions 2-n around clockwise
        temp1 = schd(n/2)    'need to track two temporary variables
        temp2 = schd(n/2+1)
        for i = n/2 to 3 step -1  'top row
            schd(i) = schd(i-1)
        next i
        for i = n/2+1 to n-1      'bottom row
            schd(i) = schd(i+1)
        next i
        schd(n) = temp1           'fill in the ones that "jumped" between rows
        schd(2) = temp2
    next r
end sub

print "Twelve teams"
roundrob(12)
print "Nine teams with byes"
roundrob(9)
Output:

Twelve teams Round 1: ( 1 - 7) ( 2 - 8) ( 3 - 9) ( 4 - 10) ( 5 - 11) ( 6 - 12) Round 2: ( 1 - 8) ( 7 - 9) ( 2 - 10) ( 3 - 11) ( 4 - 12) ( 5 - 6) Round 3: ( 1 - 9) ( 8 - 10) ( 7 - 11) ( 2 - 12) ( 3 - 6) ( 4 - 5) Round 4: ( 1 - 10) ( 9 - 11) ( 8 - 12) ( 7 - 6) ( 2 - 5) ( 3 - 4) Round 5: ( 1 - 11) (10 - 12) ( 9 - 6) ( 8 - 5) ( 7 - 4) ( 2 - 3) Round 6: ( 1 - 12) (11 - 6) (10 - 5) ( 9 - 4) ( 8 - 3) ( 7 - 2) Round 7: ( 1 - 6) (12 - 5) (11 - 4) (10 - 3) ( 9 - 2) ( 8 - 7) Round 8: ( 1 - 5) ( 6 - 4) (12 - 3) (11 - 2) (10 - 7) ( 9 - 8) Round 9: ( 1 - 4) ( 5 - 3) ( 6 - 2) (12 - 7) (11 - 8) (10 - 9) Round 10: ( 1 - 3) ( 4 - 2) ( 5 - 7) ( 6 - 8) (12 - 9) (11 - 10) Round 11: ( 1 - 2) ( 3 - 7) ( 4 - 8) ( 5 - 9) ( 6 - 10) (12 - 11) Nine teams with byes Round 1: ( 1 - 6) ( 2 - 7) ( 3 - 8) ( 4 - 9) ( 5 - B) Round 2: ( 1 - 7) ( 6 - 8) ( 2 - 9) ( 3 - B) ( 4 - 5) Round 3: ( 1 - 8) ( 7 - 9) ( 6 - B) ( 2 - 5) ( 3 - 4) Round 4: ( 1 - 9) ( 8 - B) ( 7 - 5) ( 6 - 4) ( 2 - 3) Round 5: ( 1 - B) ( 9 - 5) ( 8 - 4) ( 7 - 3) ( 6 - 2) Round 6: ( 1 - 5) ( B - 4) ( 9 - 3) ( 8 - 2) ( 7 - 6) Round 7: ( 1 - 4) ( 5 - 3) ( B - 2) ( 9 - 6) ( 8 - 7) Round 8: ( 1 - 3) ( 4 - 2) ( 5 - 6) ( B - 7) ( 9 - 8) Round 9: ( 1 - 2) ( 3 - 6) ( 4 - 7) ( 5 - 8) ( B - 9)

Go[edit]

Translation of: Wren
package main

import "fmt"

func rotate(lst []int) {
    len := len(lst)
    last := lst[len-1]
    for i := len - 1; i >= 1; i-- {
        lst[i] = lst[i-1]
    }
    lst[0] = last
}

func roundRobin(n int) {
    lst := make([]int, n-1)
    for i := 0; i < len(lst); i++ {
        lst[i] = i + 2
    }
    if n%2 == 1 {
        lst = append(lst, 0) // 0 denotes a bye
        n++
    }
    for r := 1; r < n; r++ {
        fmt.Printf("Round %2d", r)
        lst2 := append([]int{1}, lst...)
        for i := 0; i < n/2; i++ {
            fmt.Printf(" (%2d vs %-2d)", lst2[i], lst2[n-1-i])
        }
        fmt.Println()
        rotate(lst)
    }
}

func main() {
    fmt.Println("Round robin for 12 players:\n")
    roundRobin(12)
    fmt.Println("\n\nRound robin for 5 players (0 denotes a bye) :\n")
    roundRobin(5)
}
Output:
Same as Wren example.

J[edit]

Implementation (using the wikipedia circle method):

circ=: {{
  if. 1=2|y do.
    assert. 1<y
    <:(#~ [: */"1 *)"2 circ y+1
  else.
    ids=. i.y
    (-:y) ({.,.|.@}.)"_1] 0,.(}:ids)|."0 1}.ids
  end.
}}

Task example:

   rplc&'j:'"1":j./"1>:circ 12
1:12  2:11 3:10  4:9  5:8   6:7
 1:2  3:12 4:11 5:10  6:9   7:8
 1:3   4:2 5:12 6:11 7:10   8:9
 1:4   5:3  6:2 7:12 8:11  9:10
 1:5   6:4  7:3  8:2 9:12 10:11
 1:6   7:5  8:4  9:3 10:2 11:12
 1:7   8:6  9:5 10:4 11:3  12:2
 1:8   9:7 10:6 11:5 12:4   2:3
 1:9  10:8 11:7 12:6  2:5   3:4
1:10  11:9 12:8  2:7  3:6   4:5
1:11 12:10  2:9  3:8  4:7   5:6

(Here, circ uses index values which start at zero, so we need to add 1 to every index. Then we form the id pairs as complex numbers and replace the 'j' used to separate real from imaginary in their character representation with ':' for a hopefully compact and easy-to-read display.)

((Note that we could have instead centered each id pair on the ':' with only slightly more work. But it's not clear that that results in a more pleasing display.)):

   ,/"2(' ',_2&{.@[,':',2&{.@])&":/"1>:circ 12
  1:12  2:11  3:10  4:9   5:8   6:7 
  1:2   3:12  4:11  5:10  6:9   7:8 
  1:3   4:2   5:12  6:11  7:10  8:9 
  1:4   5:3   6:2   7:12  8:11  9:10
  1:5   6:4   7:3   8:2   9:12 10:11
  1:6   7:5   8:4   9:3  10:2  11:12
  1:7   8:6   9:5  10:4  11:3  12:2 
  1:8   9:7  10:6  11:5  12:4   2:3 
  1:9  10:8  11:7  12:6   2:5   3:4 
  1:10 11:9  12:8   2:7   3:6   4:5 
  1:11 12:10  2:9   3:8   4:7   5:6

Julia[edit]

""" https://rosettacode.org/mw/index.php?title=Round-robin_tournament_schedule """

function schurig(N, verbose = true)
    """ Taken from https://en.wikipedia.org/wiki/Round-robin_tournament
        #Original_construction_of_pairing_tables_by_Richard_Schurig_(1886) """
    nrows = isodd(N) ? N : N - 1
    ncols = (N + 1) ÷ 2
    players = mod1.(reshape(collect(1:nrows*ncols), ncols, nrows)', nrows)
    opponents = zero(players)
    table = [(0, 0) for _ in 1:nrows, _ in 1:ncols]
    for i in 1:nrows
        oldrow = i == nrows ? 1 : i + 1
        verbose && print("\n", rpad("Round $i:", 10))
        for j in 1:ncols
            oldcol = ncols - j + 1
            opponents[i, j] = players[oldrow, oldcol]
            j == 1 && (opponents[i, j] = iseven(N) ? N : 0)
            table[i, j] = (sort([players[i, j], opponents[i, j]])...,)
            if verbose
                s1, s2 = string.(table[i, j])
                print(rpad("($(s1 == "0" ? "Bye" : s1) - $s2)", 10))
            end
        end
    end
    return table
end

print("Schurig table for round robin with 12 players:")
schurig(12)
print("\n\nSchurig table for round robin with 7 players:")
schurig(7)
Output:
Schurig table for round robin with 12 players:
Round 1:  (1 - 12)  (2 - 11)  (3 - 10)  (4 - 9)   (5 - 8)   (6 - 7)   
Round 2:  (7 - 12)  (6 - 8)   (5 - 9)   (4 - 10)  (3 - 11)  (1 - 2)
Round 3:  (2 - 12)  (1 - 3)   (4 - 11)  (5 - 10)  (6 - 9)   (7 - 8)
Round 4:  (8 - 12)  (7 - 9)   (6 - 10)  (5 - 11)  (1 - 4)   (2 - 3)
Round 5:  (3 - 12)  (2 - 4)   (1 - 5)   (6 - 11)  (7 - 10)  (8 - 9)
Round 6:  (9 - 12)  (8 - 10)  (7 - 11)  (1 - 6)   (2 - 5)   (3 - 4)
Round 7:  (4 - 12)  (3 - 5)   (2 - 6)   (1 - 7)   (8 - 11)  (9 - 10)
Round 8:  (10 - 12) (9 - 11)  (1 - 8)   (2 - 7)   (3 - 6)   (4 - 5)
Round 9:  (5 - 12)  (4 - 6)   (3 - 7)   (2 - 8)   (1 - 9)   (10 - 11)
Round 10: (11 - 12) (1 - 10)  (2 - 9)   (3 - 8)   (4 - 7)   (5 - 6)
Round 11: (6 - 12)  (5 - 7)   (4 - 8)   (3 - 9)   (2 - 10)  (1 - 11)

Schurig table for round robin with 7 players:
Round 1:  (Bye - 1) (2 - 7)   (3 - 6)   (4 - 5)
Round 2:  (Bye - 5) (4 - 6)   (3 - 7)   (1 - 2)
Round 3:  (Bye - 2) (1 - 3)   (4 - 7)   (5 - 6)
Round 4:  (Bye - 6) (5 - 7)   (1 - 4)   (2 - 3)
Round 5:  (Bye - 3) (2 - 4)   (1 - 5)   (6 - 7)
Round 6:  (Bye - 7) (1 - 6)   (2 - 5)   (3 - 4)
Round 7:  (Bye - 4) (3 - 5)   (2 - 6)   (1 - 7)

Perl[edit]

Even[edit]

#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Round-robin_tournament_schedule
use warnings;

my $n = 12;
my @teams = 1 .. $n;
for (1 .. $n-1) 
  {
  @teams[0,$n-1,1..$n-2] = @teams;
  printf 'Round %2d:' . '%4d vs %2d'x($n/2) . "\n", $_, @teams[ map { $_, $n-1-$_} 0..($n/2)-1 ];
  }
Output:
Round  1:   1 vs 2    3 vs 12   4 vs 11   5 vs 10   6 vs 9    7 vs 8 
Round  2:   1 vs 3    4 vs 2    5 vs 12   6 vs 11   7 vs 10   8 vs 9 
Round  3:   1 vs 4    5 vs 3    6 vs 2    7 vs 12   8 vs 11   9 vs 10
Round  4:   1 vs 5    6 vs 4    7 vs 3    8 vs 2    9 vs 12  10 vs 11
Round  5:   1 vs 6    7 vs 5    8 vs 4    9 vs 3   10 vs 2   11 vs 12
Round  6:   1 vs 7    8 vs 6    9 vs 5   10 vs 4   11 vs 3   12 vs 2 
Round  7:   1 vs 8    9 vs 7   10 vs 6   11 vs 5   12 vs 4    2 vs 3 
Round  8:   1 vs 9   10 vs 8   11 vs 7   12 vs 6    2 vs 5    3 vs 4 
Round  9:   1 vs 10  11 vs 9   12 vs 8    2 vs 7    3 vs 6    4 vs 5 
Round 10:   1 vs 11  12 vs 10   2 vs 9    3 vs 8    4 vs 7    5 vs 6 
Round 11:   1 vs 12   2 vs 11   3 vs 10   4 vs 9    5 vs 8    6 vs 7 

Even and Odd[edit]

use strict;
use warnings;
use feature 'say';
use List::AllUtils <pairwise all>;

sub round_robin {
    my($n) = @_;
    my($round,@pairings);
    my @players = (1,0)[$n%2] .. $n;
    my $half    = +@players / 2;

    while () {
        my @a =         @players[    0 ..   $half-1];
        my @b = reverse @players[$half .. $#players];
        push @pairings, sprintf "Round %2d: %s\n", ++$round, join ' ', pairwise { sprintf "%3d vs %2d", $a, $b } @a, @b;
        push @players, splice @players, 1, @players-2;
        last if all { $players[$_-1] < $players[$_] } 1..$#players;
    }
    @pairings
}

say join '', round_robin 12;
say '';
say join '', map { s/0 vs /Bye: /r } round_robin 7;
Output:
Round  1:   1 vs 12   2 vs 11   3 vs 10   4 vs  9   5 vs  8   6 vs  7
Round  2:   1 vs 11  12 vs 10   2 vs  9   3 vs  8   4 vs  7   5 vs  6
Round  3:   1 vs 10  11 vs  9  12 vs  8   2 vs  7   3 vs  6   4 vs  5
Round  4:   1 vs  9  10 vs  8  11 vs  7  12 vs  6   2 vs  5   3 vs  4
Round  5:   1 vs  8   9 vs  7  10 vs  6  11 vs  5  12 vs  4   2 vs  3
Round  6:   1 vs  7   8 vs  6   9 vs  5  10 vs  4  11 vs  3  12 vs  2
Round  7:   1 vs  6   7 vs  5   8 vs  4   9 vs  3  10 vs  2  11 vs 12
Round  8:   1 vs  5   6 vs  4   7 vs  3   8 vs  2   9 vs 12  10 vs 11
Round  9:   1 vs  4   5 vs  3   6 vs  2   7 vs 12   8 vs 11   9 vs 10
Round 10:   1 vs  3   4 vs  2   5 vs 12   6 vs 11   7 vs 10   8 vs  9
Round 11:   1 vs  2   3 vs 12   4 vs 11   5 vs 10   6 vs  9   7 vs  8

Round  1:   Bye:  7   1 vs  6   2 vs  5   3 vs  4
Round  2:   Bye:  6   7 vs  5   1 vs  4   2 vs  3
Round  3:   Bye:  5   6 vs  4   7 vs  3   1 vs  2
Round  4:   Bye:  4   5 vs  3   6 vs  2   7 vs  1
Round  5:   Bye:  3   4 vs  2   5 vs  1   6 vs  7
Round  6:   Bye:  2   3 vs  1   4 vs  7   5 vs  6
Round  7:   Bye:  1   2 vs  7   3 vs  6   4 vs  5

Phix[edit]

Based on the circle with rotor diagrams on the wikipedia page, and implements home/away.

with javascript_semantics

function round_robin(integer n)
    --
    -- As per the wikipedia page, we do something like this:
    --
    -- even(n), say 6:  in round 1 we have 6 & 1,2,3,4,5 -> {{6,1},{2,5},{3,4}},
    --                           2             2,3,4,5,1 -> {{6,2},{3,1},{4,5}},
    --                           3             3,4,5,1,2 -> {{6,3},{4,2},{5,1}},
    --                           4             4,5,1,2,3 -> {{6,4},{5,3},{1,2}},
    --                           5             5,1,2,3,4 -> {{6,5},{1,4},{2,3}}
    --
    -- for an odd(n), say 5, simply replace all the 6 above with 0 (a bye).
    --
    -- As per the wikipedia diagram, we pick a rotor (6/0) and arrange the rest
    -- in a circle, and as it rotates around the circle we play it against that
    -- one then pick off second/last, third/last-but-one, and so forth from the
    -- perspective of the rotor. There must obviously be an odd number of teams
    -- in the circle itself, otherwise pairing-offs won't meet in the middle.
    --
    -- However, rather than physically rotate the {1,2,3,4,5}, we'll just say
    -- that anything past 5 starts from 1 again (the -= n below), and use the
    -- shorthand of l [===length(result)] as our starting position/offset.
    --
    -- Not shown above, but we'll also use even/odd rules for home/away matches.
    --
    integer rotor  = iff(even(n)?n:0),
            l = 0 -- length(result), shorthand
    n -= even(n) -- (circle must be odd)
    sequence result = {}
    for rownd=1 to n do -- (since "round" is a builtin)
        sequence games = {iff(even(rownd) or rotor=0?{rownd,rotor}:{rotor,rownd})}
        integer opponent = n -- pair rest off from last inwards,
        for m=2 to (n+1)/2 do -- such that m plays current opponent
            integer rom = m+l,          -- all shifted by
                    rop = opponent+l    -- l as an offset
            if rom>n then rom -= n end if 
            if rop>n then rop -= n end if 
            games &= iff(odd(m)?{{rom,rop}}:{{rop,rom}})
            opponent -= 1
        end for
        result = append(result,games)
        l += 1 -- (obviously "l = length(result)" works fine here too)
    end for
    return result
end function

function vs(sequence pair)  -- (display helper)
    return sprintf(iff(pair[2]=0?"%2d bye  ":"%2d vs %-2d"),pair)
end function

for test=12 to 3 by -9 do
    sequence res = round_robin(test)
    printf(1,"\nFor %d teams:\n",test)
    for r=1 to length(res) do
        printf(1,"Round %2d: %s\n",{r,join(apply(res[r],vs))})
    end for
end for
Output:
For 12 teams:
Round  1: 12 vs 1  11 vs 2   3 vs 10  9 vs 4   5 vs 8   7 vs 6
Round  2:  2 vs 12  1 vs 3   4 vs 11 10 vs 5   6 vs 9   8 vs 7
Round  3: 12 vs 3   2 vs 4   5 vs 1  11 vs 6   7 vs 10  9 vs 8
Round  4:  4 vs 12  3 vs 5   6 vs 2   1 vs 7   8 vs 11 10 vs 9
Round  5: 12 vs 5   4 vs 6   7 vs 3   2 vs 8   9 vs 1  11 vs 10
Round  6:  6 vs 12  5 vs 7   8 vs 4   3 vs 9  10 vs 2   1 vs 11
Round  7: 12 vs 7   6 vs 8   9 vs 5   4 vs 10 11 vs 3   2 vs 1
Round  8:  8 vs 12  7 vs 9  10 vs 6   5 vs 11  1 vs 4   3 vs 2
Round  9: 12 vs 9   8 vs 10 11 vs 7   6 vs 1   2 vs 5   4 vs 3
Round 10: 10 vs 12  9 vs 11  1 vs 8   7 vs 2   3 vs 6   5 vs 4
Round 11: 12 vs 11 10 vs 1   2 vs 9   8 vs 3   4 vs 7   6 vs 5

For 3 teams:
Round  1:  1 bye    3 vs 2
Round  2:  2 bye    1 vs 3
Round  3:  3 bye    2 vs 1

While I "optimised away" the need for a physical rotate, obviously not because I was concerned with performance but more in the hope of creating shorter and more elegant code, in the end it made little difference. Should it be more to your taste, you can remove "l" and replace the inner loop above with:

    sequence circle = tagset(n)
    for rownd=1 to n do -- (since "round" is a bultin)
        integer r = circle[1]
        sequence games = {iff(even(rownd) or rotor=0?{r,rotor}:{rotor,r})}
        integer ldx = 2, rdx = n
        while ldx<rdx do
            integer teama = circle[ldx],
                    teamb = circle[rdx]
            games &= {iff(odd(ldx)?{teama,teamb},{teamb,teama})}
            ldx += 1
            rdx -= 1
        end while
        result = append(result,games)
        circle = circle[2..$]&circle[1] -- (physically rotate it)
    end for

Picat[edit]

Constraint modelling[edit]

import sat.

main =>
  nolog,
  N = 12,
  tournament_cp(N, NumRounds,NumPairs,_,X,Bye),
  print_tournament(X,NumRounds,NumPairs,Bye),
  nl.

tournament_cp(N, NumRounds,NumPairs,Extras, X,Bye) =>
  % Adjust for odd number of players.
  % The bye (Dummy) player is N+1.
  if N mod 2 == 1 then
    N := N + 1,
    Bye = N
  end,

  NumRounds = N-1,
  NumPairs = N div 2,

  X = new_array(NumRounds,NumPairs,2),
  X :: 1..N,

  % ensure that all players play each other
  foreach(P1 in 1..N, P2 in P1+1..N)
    sum([X[Round,P,1] #= P1 #/\ X[Round,P,2] #= P2 : Round in 1..NumRounds, P in 1..NumPairs]) #= 1
  end,
  
  foreach(Round in 1..NumRounds)
    all_different([X[Round,I,J] : I in 1..NumPairs, J in 1..2]),
    
    % symmetry breaking
    % - all first players in increasing order
    increasing_strict([X[Round,I,1] : I in 1..NumPairs]),
    % - player 1 < player 2
    foreach(P in 1..NumPairs)
       X[Round,P,1] #< X[Round,P,2]
    end
  end,

  if Extras != [] then
    foreach([P1,P2,Round] in Extras)
      sum([X[Round,P,1] #= P1 #/\ X[Round,P,2] #= P2 : P in 1..NumPairs]) #= 1
    end
  end,
  solve($[ff,split],X).

print_tournament(X,NumRounds,NumPairs,Bye) =>
  N = X[1].len,
  foreach(Round in 1..NumRounds)
    printf("Round %2d: ", Round),
    if N > 10 then nl end,
    foreach(P in 1..NumPairs)
      P2Val = X[Round,P,2],
      if var(Bye) ; P2Val != Bye then
        printf("(%2w vs %2w) ",X[Round,P,1],P2Val),
        if N > 10 then nl end
      end
    end,
    nl
  end,
  nl.
Output:
Round  1: ( 1 vs 11) ( 2 vs  5) ( 3 vs  6) ( 4 vs 12) ( 7 vs  9) ( 8 vs 10) 
Round  2: ( 1 vs  5) ( 2 vs  4) ( 3 vs 10) ( 6 vs  7) ( 8 vs  9) (11 vs 12) 
Round  3: ( 1 vs  6) ( 2 vs  8) ( 3 vs  5) ( 4 vs 11) ( 7 vs 10) ( 9 vs 12) 
Round  4: ( 1 vs 12) ( 2 vs 11) ( 3 vs  7) ( 4 vs  6) ( 5 vs  8) ( 9 vs 10) 
Round  5: ( 1 vs  9) ( 2 vs  6) ( 3 vs 12) ( 4 vs  5) ( 7 vs  8) (10 vs 11) 
Round  6: ( 1 vs  4) ( 2 vs  3) ( 5 vs  7) ( 6 vs 10) ( 8 vs 12) ( 9 vs 11) 
Round  7: ( 1 vs  2) ( 3 vs  4) ( 5 vs 10) ( 6 vs  9) ( 7 vs 12) ( 8 vs 11) 
Round  8: ( 1 vs  3) ( 2 vs 12) ( 4 vs 10) ( 5 vs  9) ( 6 vs  8) ( 7 vs 11) 
Round  9: ( 1 vs 10) ( 2 vs  7) ( 3 vs  8) ( 4 vs  9) ( 5 vs 11) ( 6 vs 12) 
Round 10: ( 1 vs  8) ( 2 vs 10) ( 3 vs  9) ( 4 vs  7) ( 5 vs 12) ( 6 vs 11) 
Round 11: ( 1 vs  7) ( 2 vs  9) ( 3 vs 11) ( 4 vs  8) ( 5 vs  6) (10 vs 12) 

Constraint model with extra constraints[edit]

The constraint model is slower than the algorithmic approach for larger number of players. The advantage of a constraint model is that it is quite easy to add extra constraint, such that some players must play in a certain round (e.g. for availability reasons etc).

Here are some extra constraints:

  • 1 vs 2 must be played the third round
  • 5 vs 9 must be played in the 7th round
  • 2 vs 3 must be played in the last round
  • 7 vs 12 must be played in the last round
main =>
  nolog,
  N = 12,  
  Extras = [[1,2,3],
            [5,9,7],
            [2,3,N-1],
            [7,12,N-1]],
  tournament_cp(N, NumRounds,NumPairs,Extras,X,Bye),
  print_tournament(X,NumRounds,NumPairs,Bye).
Output:
Round  1: ( 1 vs 11) ( 2 vs  4) ( 3 vs 12) ( 5 vs  8) ( 6 vs  9) ( 7 vs 10) 
Round  2: ( 1 vs 12) ( 2 vs 11) ( 3 vs  9) ( 4 vs  7) ( 5 vs 10) ( 6 vs  8) 
Round  3: ( 1 vs  2) ( 3 vs 10) ( 4 vs 12) ( 5 vs 11) ( 6 vs  7) ( 8 vs  9) 
Round  4: ( 1 vs  4) ( 2 vs  6) ( 3 vs 11) ( 5 vs 12) ( 7 vs  8) ( 9 vs 10) 
Round  5: ( 1 vs 10) ( 2 vs  7) ( 3 vs  5) ( 4 vs  6) ( 8 vs 12) ( 9 vs 11) 
Round  6: ( 1 vs  6) ( 2 vs  5) ( 3 vs  4) ( 7 vs  9) ( 8 vs 11) (10 vs 12) 
Round  7: ( 1 vs  3) ( 2 vs 12) ( 4 vs  8) ( 5 vs  9) ( 6 vs 10) ( 7 vs 11) 
Round  8: ( 1 vs  7) ( 2 vs  8) ( 3 vs  6) ( 4 vs  5) ( 9 vs 12) (10 vs 11) 
Round  9: ( 1 vs  8) ( 2 vs  9) ( 3 vs  7) ( 4 vs 10) ( 5 vs  6) (11 vs 12) 
Round 10: ( 1 vs  9) ( 2 vs 10) ( 3 vs  8) ( 4 vs 11) ( 5 vs  7) ( 6 vs 12) 
Round 11: ( 1 vs  5) ( 2 vs  3) ( 4 vs  9) ( 6 vs 11) ( 7 vs 12) ( 8 vs 10) 

For this small tournament it took about the same time with and without these extra constraints (0.08s).

Number of solutions[edit]

Here are the number of different solutions for N = [2,4,6,8] with the symmetry constraints (but without the extra round constraints). The number of odd N players is the same as the number of N-1 players.

Here the cp solver is used since it's faster than the sat solver for generating all solutions.

import cp. 

main =>
  foreach(N in 2..2..8)
    Count = count_all(tournament_cp(N, _NumRounds,_NumPairs,_Extras,_X,_Bye)),
    println(N=Count)
  end.
Output:
2 = 1
4 = 6
6 = 720
8 = 31449600

This seems to be related to the OEIS sequence "A036981: (2n+1) X (2n+1) symmetric matrices each of whose rows is a permutation of 1..(2n+1)". The next term (for N=10) would be 444733651353600 which takes too long to check.


Raku[edit]

my @players = (1,0)[$_%2] .. $_ given 12;
my $half = +@players div 2;
my $round = 0;

loop {
    printf "Round %2d: %s\n", ++$round, "{ zip( @players[^$half], @players[$half..*].reverse ).map: { sprintf "(%2d vs %-2d)", |$_ } }";
    @players[1..*].=rotate(-1);
    last if [<] @players;
}
Output:
Round  1: ( 1 vs 12) ( 2 vs 11) ( 3 vs 10) ( 4 vs 9 ) ( 5 vs 8 ) ( 6 vs 7 )
Round  2: ( 1 vs 11) (12 vs 10) ( 2 vs 9 ) ( 3 vs 8 ) ( 4 vs 7 ) ( 5 vs 6 )
Round  3: ( 1 vs 10) (11 vs 9 ) (12 vs 8 ) ( 2 vs 7 ) ( 3 vs 6 ) ( 4 vs 5 )
Round  4: ( 1 vs 9 ) (10 vs 8 ) (11 vs 7 ) (12 vs 6 ) ( 2 vs 5 ) ( 3 vs 4 )
Round  5: ( 1 vs 8 ) ( 9 vs 7 ) (10 vs 6 ) (11 vs 5 ) (12 vs 4 ) ( 2 vs 3 )
Round  6: ( 1 vs 7 ) ( 8 vs 6 ) ( 9 vs 5 ) (10 vs 4 ) (11 vs 3 ) (12 vs 2 )
Round  7: ( 1 vs 6 ) ( 7 vs 5 ) ( 8 vs 4 ) ( 9 vs 3 ) (10 vs 2 ) (11 vs 12)
Round  8: ( 1 vs 5 ) ( 6 vs 4 ) ( 7 vs 3 ) ( 8 vs 2 ) ( 9 vs 12) (10 vs 11)
Round  9: ( 1 vs 4 ) ( 5 vs 3 ) ( 6 vs 2 ) ( 7 vs 12) ( 8 vs 11) ( 9 vs 10)
Round 10: ( 1 vs 3 ) ( 4 vs 2 ) ( 5 vs 12) ( 6 vs 11) ( 7 vs 10) ( 8 vs 9 )
Round 11: ( 1 vs 2 ) ( 3 vs 12) ( 4 vs 11) ( 5 vs 10) ( 6 vs 9 ) ( 7 vs 8 )

Ruby[edit]

def round_robin( n )
  rotating_players = (2..n).map(&:to_s) #player 1 to be added later
  rotating_players << "bye" if n.odd? 
  Array.new(rotating_players.size) do |r|
    all = ["1"] + rotating_players.rotate(-r)
    [all[0, all.size/2], all[all.size/2..].reverse]
  end
end

round_robin(12).each.with_index(1) do |round, i|
  puts "Round #{i}"
  round.each do |players|
    puts players.map{|player| player.ljust(4)}.join
  end
  puts
end
Output:
Round 1
1   2   3   4   5   6   
12  11  10  9   8   7   

Round 2
1   12  2   3   4   5   
11  10  9   8   7   6   

Round 3
1   11  12  2   3   4   
10  9   8   7   6   5   

Round 4
1   10  11  12  2   3   
9   8   7   6   5   4   

Round 5
1   9   10  11  12  2   
8   7   6   5   4   3   

Round 6
1   8   9   10  11  12  
7   6   5   4   3   2   

Round 7
1   7   8   9   10  11  
6   5   4   3   2   12  

Round 8
1   6   7   8   9   10  
5   4   3   2   12  11  

Round 9
1   5   6   7   8   9   
4   3   2   12  11  10  

Round 10
1   4   5   6   7   8   
3   2   12  11  10  9   

Round 11
1   3   4   5   6   7   
2   12  11  10  9   8   

Wren[edit]

Library: Wren-fmt
import "./fmt" for Fmt

var rotate = Fn.new { |lst|
    var last = lst[-1]
    for (i in lst.count-1..1) lst[i] = lst[i-1]
    lst[0] = last
}

var roundRobin = Fn.new { |n|
    var lst = (2..n).toList
    if (n % 2 == 1) {
        lst.add(0) // 0 denotes a bye
        n = n + 1
    }
    for (r in 1...n) {
        Fmt.write("Round $2d", r)
        var lst2 = [1] + lst
        for (i in 0...n/2) Fmt.write(" ($2d vs $-2d)", lst2[i], lst2[n - 1 - i])
        System.print()
        rotate.call(lst)
    }
}

System.print("Round robin for 12 players:\n")
roundRobin.call(12)
System.print("\n\nRound robin for 5 players (0 denotes a bye) :\n")
roundRobin.call(5)
Output:
Round robin for 12 players:

Round  1 ( 1 vs 12) ( 2 vs 11) ( 3 vs 10) ( 4 vs 9 ) ( 5 vs 8 ) ( 6 vs 7 )
Round  2 ( 1 vs 11) (12 vs 10) ( 2 vs 9 ) ( 3 vs 8 ) ( 4 vs 7 ) ( 5 vs 6 )
Round  3 ( 1 vs 10) (11 vs 9 ) (12 vs 8 ) ( 2 vs 7 ) ( 3 vs 6 ) ( 4 vs 5 )
Round  4 ( 1 vs 9 ) (10 vs 8 ) (11 vs 7 ) (12 vs 6 ) ( 2 vs 5 ) ( 3 vs 4 )
Round  5 ( 1 vs 8 ) ( 9 vs 7 ) (10 vs 6 ) (11 vs 5 ) (12 vs 4 ) ( 2 vs 3 )
Round  6 ( 1 vs 7 ) ( 8 vs 6 ) ( 9 vs 5 ) (10 vs 4 ) (11 vs 3 ) (12 vs 2 )
Round  7 ( 1 vs 6 ) ( 7 vs 5 ) ( 8 vs 4 ) ( 9 vs 3 ) (10 vs 2 ) (11 vs 12)
Round  8 ( 1 vs 5 ) ( 6 vs 4 ) ( 7 vs 3 ) ( 8 vs 2 ) ( 9 vs 12) (10 vs 11)
Round  9 ( 1 vs 4 ) ( 5 vs 3 ) ( 6 vs 2 ) ( 7 vs 12) ( 8 vs 11) ( 9 vs 10)
Round 10 ( 1 vs 3 ) ( 4 vs 2 ) ( 5 vs 12) ( 6 vs 11) ( 7 vs 10) ( 8 vs 9 )
Round 11 ( 1 vs 2 ) ( 3 vs 12) ( 4 vs 11) ( 5 vs 10) ( 6 vs 9 ) ( 7 vs 8 )


Round robin for 5 players (0 denotes a bye) :

Round  1 ( 1 vs 0 ) ( 2 vs 5 ) ( 3 vs 4 )
Round  2 ( 1 vs 5 ) ( 0 vs 4 ) ( 2 vs 3 )
Round  3 ( 1 vs 4 ) ( 5 vs 3 ) ( 0 vs 2 )
Round  4 ( 1 vs 3 ) ( 4 vs 2 ) ( 5 vs 0 )
Round  5 ( 1 vs 2 ) ( 3 vs 0 ) ( 4 vs 5 )

XPL0[edit]

def N = 12;     \number of players (must be even)
int I, Player(N+1), Round, Temp;
[for I:= 1 to N do Player(I):= I;
for Round:= 1 to N-1 do
    [IntOut(0, Round);  ChOut(0, ^:);
    for I:= 1 to N/2 do
        [ChOut(0, 9\tab\);  IntOut(0, Player(I))];
    CrLf(0);
    for I:= N downto N/2+1 do
        [ChOut(0, 9\tab\);  IntOut(0, Player(I))];
    CrLf(0);  CrLf(0);
    Temp:= Player(N);   \rotate
    for I:= N-1 downto 2 do
        Player(I+1):= Player(I);
    Player(2):= Temp;
    ];
]
Output:
1:      1       2       3       4       5       6
        12      11      10      9       8       7

2:      1       12      2       3       4       5
        11      10      9       8       7       6

3:      1       11      12      2       3       4
        10      9       8       7       6       5

4:      1       10      11      12      2       3
        9       8       7       6       5       4

5:      1       9       10      11      12      2
        8       7       6       5       4       3

6:      1       8       9       10      11      12
        7       6       5       4       3       2

7:      1       7       8       9       10      11
        6       5       4       3       2       12

8:      1       6       7       8       9       10
        5       4       3       2       12      11

9:      1       5       6       7       8       9
        4       3       2       12      11      10

10:     1       4       5       6       7       8
        3       2       12      11      10      9

11:     1       3       4       5       6       7
        2       12      11      10      9       8