Solution: Subsets
Explore how to generate all subsets of a given integer array by applying the subsets pattern. Learn to use binary representation and bitwise operations to efficiently create every possible subset, including the empty set, while avoiding duplicates. Understand the exponential time complexity and how to implement this pattern step-by-step in Python.
Statement
Given an array of integers, nums, find all possible subsets of nums, including the empty set.
Note: The solution set must not contain duplicate subsets. You can return the solution in any order.
Constraints:
-
nums.length -
nums[i] - All the numbers of
numsare unique.
Pattern: Subsets
Problems such as this one, where we need to find all possible subsets of a given set, can be efficiently solved using the subsets pattern. This pattern involves generating all possible subsets of a given set by using binary representations of indices to represent which elements should be included in each subset. This approach allows us to solve a wide range of problems that involve generating all possible subsets of a set.
Solution
Generating all possible subsets of a given set inherently involves exploring different combinations of elements, which aligns well with the subset technique. First, the total number of potential subsets is calculated using: