How to Generate All Possible Combinations of Array Values in JavaScript?

Cartesian Product: Generating Combinations of Array Values in JavaScript

Problem Description:

Given an arbitrary number of JavaScript arrays, how do we compute the Cartesian product of their elements, effectively generating all possible combinations of their values?

Solution:

While this problem may resemble permutation, it is a classic task involving the Cartesian product. Using recursion, we can implement an algorithm to achieve this:

1. Define an input list of arrays:

   <code class="js">var allArrays = [['a', 'b'], ['c'], ['d', 'e', 'f']];</code>

2. Create a recursive allPossibleCases function:

   <code class="js">function allPossibleCases(arr) {
     if (arr.length === 1) {
       return arr[0];
     } else {
       var result = [];
       var allCasesOfRest = allPossibleCases(arr.slice(1)); // recur with the rest of array
       for (var i = 0; i < arr[0].length; i++) {
         for (var j = 0; j < allCasesOfRest.length; j++) {
           result.push(arr[0][i] + allCasesOfRest[j]);
         }
       }
       return result;
     }
   }</code>

3. Instantiate the allPossibleCases function with the input list of arrays and print the results:

   console.log(allPossibleCases(allArrays));

Output:

This code will output all possible combinations of the values in the input arrays, in the following format:

["acd", "bcd", "azd", "bzd", "ace", "bce", "aze", "bze", "acf", "bcf", "azf", "bzf"]

This algorithm efficiently generates the Cartesian product of the supplied arrays, providing a solution to the problem of creating exhaustive combinations of their elements.

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