Power Set Generation (Medium) — Practice with Code Visualizer

You are given an integer array elements containing distinct values. Your task is to compute and return the complete power set of this array — that is, every possible collection of items that can be formed by selecting zero or more elements from the original array.

The power set is a fundamental concept in combinatorics and set theory, representing all possible combinations of elements. For an array of n distinct elements, the power set contains exactly 2ⁿ subsets, ranging from the empty set (selecting nothing) to the full set (selecting everything).

Key Requirements:

The result must include the empty collection (representing the case where no elements are selected).
The result must include the complete original array (representing the case where all elements are selected).
Each element from the input may appear at most once in any given subset.
The subsets in the output may be returned in any order.
The elements within each subset may also appear in any order.

This problem tests your understanding of recursive enumeration, bit manipulation techniques, and the mathematical properties of combinatorial structures.

For an array with 3 elements, we generate 2³ = 8 subsets. These include: the empty set [], three single-element subsets [1], [2], [3], three two-element subsets [1,2], [1,3], [2,3], and the complete set [1,2,3]. Every possible combination of inclusion/exclusion for each element is represented.

For a single-element array, the power set contains exactly 2¹ = 2 subsets: the empty set [] (excluding the element) and the set [0] (including the element).

For two elements, we have 2² = 4 possible subsets: exclude both [], include only first [1], include only second [2], or include both [1,2].

Key Requirements:

The result must include the empty collection (representing the case where no elements are selected).
The result must include the complete original array (representing the case where all elements are selected).
Each element from the input may appear at most once in any given subset.
The subsets in the output may be returned in any order.
The elements within each subset may also appear in any order.

This problem tests your understanding of recursive enumeration, bit manipulation techniques, and the mathematical properties of combinatorial structures.

For a single-element array, the power set contains exactly 2¹ = 2 subsets: the empty set [] (excluding the element) and the set [0] (including the element).

For two elements, we have 2² = 4 possible subsets: exclude both [], include only first [1], include only second [2], or include both [1,2].

Power Set Generation

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Power Set Generation

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