Deal cards for FreeCell

From Fōrmulæ wiki
Jump to: navigation, search

This page is the answer to the task Deal cards for FreeCell in the Rosetta Code.

Description (from Rosetta Code)

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. (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. Newer versions from Microsoft have 1 million deals, numbered from 1 to 1000000; some implementations allow numbers outside that range.

The algorithm uses this linear congruential generator from Microsoft C:

The algorithm follows:

  1. Seed the RNG with the number of the deal.
  2. 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.
  3. Until the array is empty:
    • Choose a random card at indexnext random number (mod array length).
    • Swap this random card with the last card of the array.
    • Remove this random card from the array. (Array length goes down by 1.)
    • Deal this random card.
  4. 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.
Order to deal cards Game #1 Game #617
 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
JD 2D 9H JC 5D 7H 7C 5H
KD KC 9S 5S AD QC KH 3H
2S KS 9D QD JS AS AH 3C
4C 5C TS QH 4H AC 4D 7S
3S TD 4S TH 8H 2C JH 7D
6D 8S 8D QS 6C 3D 8C TC
6S 9C 2H 6H
7D AD 5C 3S 5S 8C 2D AH
TD 7S QD AC 6D 8H AS KH
TH QC 3H 9D 6S 8D 3D TC
KD 5H 9S 3C 8S 7H 4D JS
4C QS 9C 9H 7C 6H 2C 2S
4S TS 2H 5D JC 6C JH QH
JD KS KC 4H

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

Write a program to take a deal number and deal cards in the same order as this algorithm. The program may display the cards with ASCII, with Unicode, by drawing graphics, or any other way.

Program

The same program when the flowchart package visualization is selected. Click/tap to enlarge

DealCardsFreeCellCode.png

Explanation

There is no need to remove from a deal to be added to another one, it can be performed on a single array. It is and iteration from 52 to 1 indicating the end of the first array, and therefore the start of a second one after each swap. The only inconvenience is that second array contains the information in reversed order, but when it is shown it is also read in reversed order.

The number 127,185 is the decimal number of the 🃑 Unicode character.

In the Unicode playing cards characters, there is the Knight, between the Jack and Queen suits, which is not used, so it is skipped in the order.

Case 1. Deal #1

In order to show the result in bigger characters, we use the SetFont expression. The Null expressions are the font name, the indicator of italic and bold attributes, which are not being changed, only the font size is indicated.

DealCardsFreeCellOutput1.png

Case 2. Deal #617

DealCardsFreeCellOutput2.png