Set Game

An algorithm to find valid sets in the Game Set. This isn't a complete game, just the logic & algorithm to check if a valid set exists so that a hint can be provided.

Java Version

The more robust version is in SetGame.java

Card Objects

• The Card class defines a data structure to hold 4 pieces of information about a card: number, shape, shading & color
• All are represented as integers for ease of calculation
• Displaying a card color would just be defining some draw() method that showed a different color based on the integer value

N Choose 3 Algorithm

While computationally intractable, finding all possible subsets of size 3 can be done iteratively without too much trouble

• printCombinations() extracts the same logic from findSets() to find all subsets of size 3 using 3 nested loops
• The trick to to have the inner loop start it's index at 1 greater than the parent loop's current index
• This pattern could be continued to find combinations for specific values of k
• Doesn't work for arbitrary k because that would likely involve a recursive implementation

Checking For Valid Sets

• Cards have 4 attributes and each attribute must either be the same for all 3 cards, or all different
• Since number, shape, shading & color are all integers, checking valid sets is done by examining each attribute and passing the 3 values to areAllEqual(int num1, int num2, int num3) and areAllDifferent(int num1, int num2, int num3)

Python Version

The 1st attempt where I came up with the n choose 3 implementation