how to get all proper subsets of a set in typescript

To get all proper subsets of a set in TypeScript, we can use a recursive approach. A proper subset is defined as a subset that does not contain all the elements of the original set. Here's the TypeScript code to achieve this:

function getProperSubsets(set: Set<any>): Set<Set<any>> {
  const subsets: Set<Set<any>> = new Set();

  function recurse(subset: Set<any>, remaining: Set<any>) {

    for (let item of remaining) {
      const newSubset = new Set(subset);

      const newRemaining = new Set(remaining);

      recurse(newSubset, newRemaining);

  recurse(new Set(), set);

  subsets.delete(set); // remove the full set

  return subsets;
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The getProperSubsets function takes a Set as its argument and returns a Set of Sets representing all proper subsets of the input set. It initializes an empty Set called subsets to hold the result.

The recurse function is a helper function that takes in two arguments: subset and remaining. subset is a Set representing the current subset being generated, and remaining is a Set representing the elements still available to add to the subset.

The recurse function first adds the current subset to subsets. Then, for each element in remaining, it creates a new subset that includes that element, and a new remaining set that excludes that element, and recursively calls the recurse function with these new sets.

Finally, the getProperSubsets function returns the subsets set with the full set removed.

Here's an example usage of the getProperSubsets function:

const mySet = new Set([1, 2, 3]);
const properSubsets = getProperSubsets(mySet);
console.log(properSubsets); // Set { Set { 1 }, Set { 2 }, Set { 3 }, Set { 1, 2 }, Set { 1, 3 }, Set { 2, 3 } }
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