# Cartesian product of two sets in JavaScript

JavascriptWeb DevelopmentFront End TechnologyObject Oriented Programming

## Cartesian Product

Inset theory a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.

We are required to write a JavaScript function that takes in two arrays let us call them arr1 and arr2, they both represent two distinct sets.

The function should construct a 2-D array that contains the cartesian product of those two sets and finally return that array.

## Example

Following is the code −

const arr1 = [1, 2, 3, 4];
const arr2 = [5, 6, 7, 8];
const cartesianProduct = (arr1 = [], arr2 = []) => {
if (!arr1 || !arr2 || !arr1.length || !arr2.length) {
return null;
};
const res = [];
for (let i = 0; i < arr1.length; i += 1) {
for (let j = 0; j < arr2.length; j += 1) {
res.push([arr1[i], arr2[j]]);
};
};
return res;
};
console.log(cartesianProduct(arr1, arr2));

## Output

Following is the output on console −

[
[ 1, 5 ], [ 1, 6 ],
[ 1, 7 ], [ 1, 8 ],
[ 2, 5 ], [ 2, 6 ],
[ 2, 7 ], [ 2, 8 ],
[ 3, 5 ], [ 3, 6 ],
[ 3, 7 ], [ 3, 8 ],
[ 4, 5 ], [ 4, 6 ],
[ 4, 7 ], [ 4, 8 ]
]