Deal cards for FreeCell

Free Cell is the solitaire card game that Paul Alfille introduced to the PLATO system in 1978. Jim Horne, at Microsoft, changed the name to FreeCell and reimplemented the game for DOS, then Windows. This version introduced 32000 numbered deals. Later versions have 1 million deals, numbered 1 to 1000000. (The Freecell FAQ tells this history.)

As the game became popular, Jim Horne disclosed the algorithm, and other implementations of FreeCell began to reproduce the Microsoft deals. These deals are numbered from 1 to 32000.

The algorithm uses this linear congruential generator from Microsoft C:

$state_{n+1}\equiv 214013\times state_{n}+2531011{\pmod {2^{31}}}$
$rand_{n}=state_{n}\div 2^{16}$
$rand_{n}$ is in range 0 to 32767.
Rosetta Code has another task, linear congruential generator, with code for this RNG in several languages.

The algorithm follows:

Seed the RNG with the number of the deal.
Create an array of 52 cards: Ace of Clubs, Ace of Diamonds, Ace of Hearts, Ace of Spades, 2 of Clubs, 2 of Diamonds, and so on through the ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. The array indexes are 0 to 51, with Ace of Clubs at 0, and King of Spades at 51.
Perform a shuffle (MISSING instructions)
Deal all 52 cards, face up, across 8 columns. The first 8 cards go in 8 columns, the next 8 cards go on the first 8 cards, and so on.

 1  2  3  4  5  6  7  8
 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52

Deals can be checked against FreeCell solutions to 1000000 games. (Summon a video solution, and it displays the initial deal.)

C

<lang c>#include <stdio.h>

include <stdlib.h>
include <locale.h>

wchar_t s_suits[] = L"♣♦♥♠", s_nums[] = L"A23456789TJQK";

define RMAX32 ((1U << 31) - 1)
define RMAX ((1U << 15) - 1)

static int seed = 1; int rnd(void) { return (seed = (seed * 214013 + 2531011) & RMAX32) >> 16; } void srnd(int x) { seed = x; }

void show(int *c) { int i; for (i = 0; i < 52; c++) { printf(" \033[%dm%lc\033[m%lc", 32 - (1 + *c) % 4 / 2, s_suits[*c % 4], s_nums[*c / 4]); if (!(++i % 8) || i == 52) putchar('\n'); } }

void deal(int s, int *t) { int i, j; srnd(s);

for (i = 0; i < 52; i++) t[i] = 51 - i; for (i = 0; i < 51; i++) { j = 51 - rnd() % (52 - i); s = t[i], t[i] = t[j], t[j] = s; } }

int main(int c, char **v) { int s, card[52]; if (c < 2 || (s = atoi(v[1])) <= 0) s = 11982;

setlocale(LC_ALL, "");

deal(s, card); printf("Hand %d\n", s); show(card);

return 0; }</lang>

J

Paraphrase of C:

<lang j>deck=: ,/ 'KQJT98765432A' ,"0/ 7 u: '♠♥♦♣'

srnd=: 3 :'SEED=:{.y,11982' srnd seed=: do bind 'SEED' rnd=: (2^16) <.@%~ (2^31) srnd@| 2531011 + 214013 * seed

pairs=: i. <@<@~."1@,. <: - ] (| rnd)@- i. NB. indices to swap, for shuffle swaps=: [: > C.&.>/@|.@; NB. implement the specified shuffle deal=: (swaps pairs@#) bind deck

show=: (,"2)@:(_8 ]\ ' '&,.)</lang>

Example use:

<lang j> show deal srnd 1

J♦ 2♦ 9♥ J♣ 5♦ 7♥ 7♣ 5♥
K♦ K♣ 9♠ 5♠ A♦ Q♣ K♥ 3♥
2♠ K♠ 9♦ Q♦ J♠ A♠ A♥ 3♣
4♣ 5♣ T♠ Q♥ 4♥ A♣ 4♦ 7♠
3♠ T♦ 4♠ T♥ 8♥ 2♣ J♥ 7♦
6♦ 8♠ 8♦ Q♠ 6♣ 3♦ 8♣ T♣
6♠ 9♣ 2♥ 6♥</lang>

Tcl

Translation of: C

<lang tcl>proc rnd Template:*r seed {

   upvar 1 ${*r} r
   expr {[set r [expr {($r * 214013 + 2531011) & 0x7fffffff}]] >> 16}

} proc show cards {

   set suits {\u2663 \u2666 \u2665 \u2660}
   set values {A 2 3 4 5 6 7 8 9 T J Q K}
   for {set i 0} {$i < 52} {incr i} {

set c [lindex $cards $i] puts -nonewline [format " \033\[%dm%s\033\[m%s" [expr {32-(1+$c)%4/2}] \ [lindex $suits [expr {$c % 4}]] [lindex $values [expr {$c / 4}]]] if {($i&7)==7 || $i==51} {puts ""}

} proc deal {seed} {

   for {set i 0} {$i < 52} {incr i} {lappend cards [expr {51 - $i}]}
   for {set i 0} {$i < 51} {incr i} {

set j [expr {51 - [rnd]%(52-$i)}] set tmp [lindex $cards $i] lset cards $i [lindex $cards $j] lset cards $j $tmp

   }
   return $cards

}

if {![scan =[lindex $argv 0]= =%d= s] || $s <= 0} {

   set s 11982

} set cards [deal $s] puts "Hand $s" show $cards</lang>