What is the time and space complexity of Subsets?

Time complexity: O(n * 2^n). Space complexity: O(n * 2^n).

Subsets

Med

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Solution Guide: Subsets

Approach

Enumerate all 2^n bitmasks from 0 to 2^n - 1. For each mask, include element i in the subset whenever bit i is set (mask & (1 << i)). Each mask uniquely represents one subset of the input array.

Complexity Analysis

Time: O(n * 2^n)
Space: O(n * 2^n)

Pattern

Bitmask Enumeration

Why It Works

There is a one-to-one correspondence between n-bit binary numbers and subsets of an n-element set, so iterating all masks generates every possible subset exactly once.

Updated Feb 2026