Tool to generate Cartesian products of lists/sets by combining the elements to generate the complete list of possible choices.
Cartesian Product - dCode
Tag(s) : Combinatorics
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Cartesian Product
Cartesian Product Generator
Answers to Questions (FAQ)
What is a cartesian product? (Definition)
A Cartesian product is a combination of elements from several sets. The product is written with the symbol ×. It is the totality of the possible combinations among the sets of elements.
How to generate the list of combinations of a cartesian product?
Enter the sets (1 per line) in the generator table and click on generate.
Example: Generation of all playing card figures (jack, queen, king) of each color (spade, heart, diamond, club)
The first set consists of the 3 figures {J,Q,K}, the second set of the 4 colors {♠,♥,♦,♣}.
The Cartesian product is:
| J | ♠ |
| J | ♥ |
| J | ♦ |
| J | ♣ |
| Q | ♠ |
| Q | ♥ |
| Q | ♦ |
| Q | ♣ |
| K | ♠ |
| K | ♥ |
| K | ♦ |
| K | ♣ |
How to calculate the cardinality of the cartesian product?
The cardinality (total number of combinations) is equal to the multiplication of the cardinality of each set.
Example: A garment with 3 color choices and 5 sizes will have $ 3 \times 5 = 15 $ different possibilities
Example: A padlock with 4 wheels that can define a 4-letter code (26 possible letters for each wheel) will have a cardinality of $ 26 \times 26 \times 26 \times 26 = 456976 $ possible words.
Source code
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