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Subsets LC #78 Medium Backtracking · Power Set
Problem

Given an integer array nums of unique elements, return all possible subsets (the power set). The solution set must not contain duplicate subsets. Return the solution in any order.

Example 1
Input: nums = [1,2,3]
Output: [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]
Explanation: 2³ = 8 subsets for 3 elements.
Example 2
Input: nums = [0]
Output: [[],[0]]
Constraints: 1 ≤ nums.length ≤ 10  |  −10 ≤ nums[i] ≤ 10  |  All numbers are unique.
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Approach
Backtracking — Add at Every Node
Add curr to results at every recursive call (not just leaves). For each element from start: include → recurse with i+1 → backtrack (remove). Generates all 2^n subsets.
Input Array
Current Subset
curr = [ ] (empty)
Results 0 collected
Variables
curr
[ ]
start
0
total found
0
Step Logic
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Algorithm
1
Add current subset at EVERY call (including empty set)
2
For each i from start: include nums[i], recurse with i+1, then backtrack (remove)
3
Base case: loop exhausted → implicit return (curr was already added)
4
2^n subsets total for n elements
Time
O(n·2^n)
Space
O(n)
Why Backtracking Works

Unlike combinations, we add curr to results at every recursive call — this captures all subsets including the empty set. The for loop starting at start prevents duplicates by only going forward. Each element is either included or excluded, giving 2^n total paths.