018-cartesian-product.js

// A Cartesian product is a mathematical operation that returns the set of all possible ordered pairs (a, b) where a belongs to set A and b belongs to set B. It can also be extended to more than two sets, resulting in the set of all possible ordered tuples (a, b, c, ...) where a belongs to set A, b belongs to set B, c belongs to set C, and so on.

function cartesianProduct(setA, setB) {
  var product = [];
  for (var i = 0; i < setA.length; i++) {
    for (var j = 0; j < setB.length; j++) {
      product.push([setA[i], setB[j]]);
    }
  }
  return product;
}
console.log(cartesianProduct([1, 2], ["a", "b"]));
// Output: [[1, 'a'], [1, 'b'], [2, 'a'], [2, 'b']]

// In terms of time complexity, the function I provided earlier has a time complexity of O(mn), where m and n are the sizes of the sets. This is because for each element in set A, it iterates through all elements in set B, resulting in a total of m*n iterations.

// In terms of space complexity, it has a space complexity of O(mn) as well, because it stores the Cartesian product of the two sets in a new array which is of size m*n.