How to Efficiently Calculate the Cartesian Product of Multiple Arrays in JavaScript?

Implementing the Cartesian Product of Multiple Arrays in JavaScript

The Cartesian product of multiple arrays comprises every possible combination of elements from the input arrays. This operation is essential for generating all possible combinations or permutations from a set of data.

The 1-Line Answer (ES2020)

const cartesian = (...a) => a.reduce((a, b) => a.flatMap(d => b.map(e => [d, e].flat())));

Explanation

The Cartesian product is computed in the following manner:

1. Reduce: Use this method to iterate over each array and combine them.
2. flatMap: Flatten the reduced array by combining all possible combinations of elements from two input arrays.
3. flat: Simplify the nested array by removing empty arrays or elements.

Example

To apply the Cartesian product on arrays with values, consider the following example:

const output = cartesian([1, 2], [10, 20], [100, 200, 300]);

The expected output is:

[
  [1, 10, 100],
  [1, 10, 200],
  [1, 10, 300],
  [1, 20, 100],
  [1, 20, 200],
  [1, 20, 300],
  [2, 10, 100],
  [2, 10, 200],
  [2, 10, 300],
  [2, 20, 100],
  [2, 20, 200],
  [2, 20, 300],
]

This demonstrates the calculation of all possible combinations of elements from the given arrays, resulting in a complete Cartesian product.

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