How to resolve the algorithm Set, the card game step by step in the J programming language

Published on 12 May 2024 09:40 PM
#J

How to resolve the algorithm Set, the card game step by step in the J programming language

Table of Contents

Problem Statement

The card game, Set, is played with a pack of 81 cards, each of which depicts either one, two, or three diamonds, ovals, or squiggles. The symbols are coloured red, green, or purple, and the shading is either solid, striped, or open. No two cards are identical. In the game a number of cards are layed out face up and the players try to identify "sets" within the cards. A set is three cards where either the symbols on the cards are all the same or they are all different, the number of symbols on the cards are all the same or all different, the colours are all the same or all different, and the shadings are all the same or all different. For example, this is a set: because each card depicts a different symbol, the number of symbols on each card is different, the colours are all the same, and the shadings are all different. This is not a set: because two of the cards are green and one is purple, so the colours are neither all the same nor all different.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Set, the card game step by step in the J programming language

Source code in the j programming language

deck=: >,{;:each'one two three';'red green purple';'solid striped open';'diamond oval squiggle'
deal=: (?#) { ]

sets=:  {{ >;sets0\y }}
sets0=: {{ <;({:y) sets1\}:y }}
sets1=: {{ <~.;({:y) sets2 m\}:y }}
sets2=: {{ <(m,:n)<@,"2 1 y#~m isset n"1 y }}
isset=: {{ 1=#~.(m=n),(m=y),:n=y }}

disp=: <@(;:inv)"1


   four=: 4 deal deck
   eight=: 8 deal deck
   twelve=: 12 deal deck
   >disp four
one purple striped oval   
one purple striped diamond
three green solid oval    
two red solid oval        
   >disp eight
three green striped diamond  
two green open squiggle      
three purple striped squiggle
one purple solid squiggle    
two green solid oval         
three purple solid squiggle  
two red solid oval           
three purple solid diamond   
   >disp twelve
two red solid squiggle     
three purple open squiggle 
two purple open oval       
one purple open oval       
one green solid oval       
three green striped oval   
one green open oval        
three green open squiggle  
one red open squiggle      
one purple striped squiggle
two purple striped diamond 
two red open diamond       
   disp sets four
┌┐
││
└┘
   disp sets eight
┌┐
││
└┘
   disp sets twelve
┌─────────────────────────┬───────────────────────────┬──────────────────────────┐
│three green open squiggle│one purple striped squiggle│two red solid squiggle    │
├─────────────────────────┼───────────────────────────┼──────────────────────────┤
│one green open oval      │two red open diamond       │three purple open squiggle│
├─────────────────────────┼───────────────────────────┼──────────────────────────┤
│three green open squiggle│two red open diamond       │one purple open oval      │
└─────────────────────────┴───────────────────────────┴──────────────────────────┘

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