What is the brute force approach and complexity for Subsets II?

Try every yes/no pattern, sort each subset, and let a set drop the repeats with time complexity O(N² · 2^N) and space complexity O(N · 2^N).

What is the optimal approach and complexity for Subsets II?

Sort, then in each loop skip nums[i] when it equals nums[i − 1] and i > start with optimal time complexity O(N · 2^N) and space complexity O(N).

How do you identify the pattern for Subsets II?

Look for key signals in the prompt: "may contain duplicates" indicates Equal values make the same subset from different positions. The search must build each distinct subset once, not once per position.; "return all possible subsets" indicates The same template as Subsets: each call records its path, and each pick comes from a later index.; "distinct subsets" indicates Two subsets are the same when their values match, so the test compares values, not positions..

Subsets II

Medium·LeetCode #90 Pro OnlySlight Variation

LeetCode

Problem Statement

You are given an array nums that can hold the same value more than once. Return every distinct subset of nums, including the empty subset.

Two subsets count as the same when they hold the same values. So [2] must appear only once in your answer, even when nums has two 2s. The order of the subsets in your answer does not matter.

Input

nums, an array of integers. Values can repeat. It has between 1 and 10 numbers.

Output

A list of all distinct subsets. Each subset is a list of numbers, and no subset appears twice.

Example 1

Input: nums = [1, 2, 2]

Output: [[], [1], [1, 2], [1, 2, 2], [2], [2, 2]]

Picking by position gives 2³ = 8 subsets, but the two 2s make some of them look the same. For example, [2] can be made from either 2. That leaves 6 distinct subsets.

Example 2

Input: nums = [0]

Output: [[], [0]]

Two subsets: the empty one, and the one that holds 0.

Constraints

• 1 ≤ nums.length ≤ 10
• −10 ≤ nums[i] ≤ 10

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“may contain duplicates”

→ Equal values make the same subset from different positions. The search must build each distinct subset once, not once per position.

“return all possible subsets”

→ The same template as Subsets: each call records its path, and each pick comes from a later index.

“distinct subsets”

→ Two subsets are the same when their values match, so the test compares values, not positions.

Approach Complexity Ladder

Brute Force — every subset, sorted, kept in a setO(N² · 2^N)O(N · 2^N)

Try every yes/no pattern, sort each subset, and let a set drop the repeats

Optimal — sort, then skip repeats inside each loopO(N · 2^N)O(N)

Sort, then in each loop skip nums[i] when it equals nums[i − 1] and i > start

Brute Force Intuition

Use the same yes/no loop as in Subsets. Sort each subset, so that [2, 1] and [1, 2] look the same, and insert it into a set. A set keeps one copy of each distinct value, so its contents are the answer.

Recognition rule for this sub-pattern:

Every call is a subset; add only elements to the right of the last one (a start index). Sort first and skip equal neighbours at the same depth to avoid duplicate subsets.

Remember this · Backtracking

Trigger

"All subsets / permutations / combinations", place items under rules (N-Queens, Sudoku), find a path in a grid.

Think

At each step, what are my choices, and how do I undo a choice?

Key question

What is my state, when is it complete, and when do I prune?

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