Step by Step solution about How to resolve the algorithm Power set step by step in the Kotlin programming language

The provided Kotlin code defines a function named subsets for a set of elements of type T. This function computes all the possible subsets (including the empty set) of the given set using recursion and Kotlin's Sequences (a.k.a. streams).

Here's how this code works:

1. The subsets function is a generic function that operates on a set of elements of type T.

2. It returns a Sequence of sets of type T. A sequence is a lazily evaluated collection that can be iterated multiple times without holding the entire collection in memory.

3. Inside the function, there's a when expression that checks the size of the set (i.e., the number of elements in the set).

4. If the size is 0, it means the set is empty. In this case, the function returns a sequence containing a single element: an empty set.

5. If the size of the set is not 0, it indicates that the set contains at least one element. In this case, the code uses recursion to compute the subsets of the set.

6. It retrieves the first element of the set (head) and creates a new set (tail) with all elements except the head element.

7. The tail set is recursively passed to the subsets function to compute its subsets (tail.subsets()).

8. The subsets of the tail set are then combined with the head element to form additional subsets. This is achieved by mapping each subset of the tail set to a new set containing both the head element and the original subset (e.g., setOf(head) + it).

9. The resulting sequence contains all the subsets of the tail set, as well as additional subsets that include the head element.

10. The + operator used in setOf(head) + it is Kotlin's set union operator. It creates a new set that contains all elements from both the head set (containing only the head element) and the it set (which is each subset of the tail set).

11. Finally, the function returns the sequence containing all the subsets of the original set, including the empty set.

In summary, this code generates all the possible subsets of a given set using a recursive approach and Kotlin's Sequences. It efficiently computes subsets without the need to explicitly create a complete list in memory, making it suitable for large sets.

// purely functional & lazy version, leveraging recursion and Sequences (a.k.a. streams)
fun <T> Set<T>.subsets(): Sequence<Set<T>> =
    when (size) {
        0 -> sequenceOf(emptySet())
        else -> {
            val head = first()
            val tail = this - head
            tail.subsets() + tail.subsets().map { setOf(head) + it }
        }
    }

// if recursion is an issue, you may change it this way:

fun <T> Set<T>.subsets(): Sequence<Set<T>> = sequence {
    when (size) {
        0 -> yield(emptySet<T>())
        else -> {
            val head = first()
            val tail = this@subsets - head
            yieldAll(tail.subsets())
            for (subset in tail.subsets()) {
                yield(setOf(head) + subset)
            }
        }
    }
}