# Finding power set for a set in JavaScript Power Set

The power set of a set S is the set of all of the subsets of S, including the empty set and S itself. The power set of set S is denoted as P(S).

For example

If S = {x, y, z}, the subsets are −

{
{},
{x},
{y},
{z},
{x, y},
{x, z},
{y, z},
{x, y, z}
}

We are required to write a JavaScript function that takes in an array as the only argument. The function should find and return the power set for the input array.

## Example

Following is the code −

const set = ['x', 'y', 'z'];
const powerSet = (arr = []) => {
const res = [];
const { length } = arr;
const numberOfCombinations = 2 ** length;
for (let combinationIndex = 0; combinationIndex < numberOfCombinations; combinationIndex += 1) {
const subSet = [];
for (let setElementIndex = 0; setElementIndex < arr.length;
setElementIndex += 1) {
if (combinationIndex & (1 << setElementIndex)) {
subSet.push(arr[setElementIndex]);
};
};
res.push(subSet);
};
return res;
};
console.log(powerSet(set));

## Output

Following is the output on console −

[
[],
[ 'x' ],
[ 'y' ],
[ 'x', 'y' ],
[ 'z' ],
[ 'x', 'z' ],
[ 'y', 'z' ],
[ 'x', 'y', 'z' ]
]