How to Generate All Possible Combinations from N Arrays with M Elements Each in JavaScript?

Generating Combinations from N Arrays with M Elements in JavaScript [Duplicate]

Introduction
Combining elements from multiple arrays can yield numerous combinations, which are often essential in statistical analysis or combinatorial problems. This article presents a comprehensive solution in JavaScript to generate all possible combinations from N arrays, each containing M elements.

Recursive Approach
The provided solution employs a recursive helper function to construct combinations incrementally. The function iterates through each array, including its elements in the resulting combination. If the current array is the last one, the completed combination is added to the result array. Otherwise, the function recurses with the updated combination and proceeds to the next array.

Implementation

function cartesian(...args) {
    var r = [], max = args.length - 1;
    function helper(arr, i) {
        for (var j = 0, l = args[i].length; j < l; j++) {
            var a = arr.slice(0); // clone arr
            a.push(args[i][j]);
            if (i == max)
                r.push(a);
            else
                helper(a, i + 1);
        }
    }
    helper([], 0);
    return r;
}

Usage
To generate combinations from a list of arrays, we pass the arrays as arguments to the cartesian function.

cartesian([0, 1], [0, 1, 2, 3], [0, 1, 2]);

The result will be an array containing all possible combinations:

[
  [0, 0, 0],
  [0, 0, 1],
  [0, 0, 2],
  [0, 1, 0],
  [0, 1, 1],
  [0, 1, 2],
  [0, 2, 0],
  [0, 2, 1],
  [0, 2, 2],
  // ...
]

Note
If we prefer to pass an array of arrays instead of individual arguments, we can modify the function signature to function cartesian(args).

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