78. Subsets

Medium LeetCode

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: All possible subsets of [1,2,3] are returned. The empty set [] is also included.

Example 2

Input: nums = [0]

Output: [[],[0]]

Explanation: The only possible subsets are the empty set [] and the set containing the single element [0].

Constraints

• 1 <= nums.length <= 10
• -10 <= nums[i] <= 10
• All the numbers of nums are unique

How to solve the problem

• Backtracking (DFS)

class Solution:
    def subsets(self, nums: List[int]) -> List[List[int]]:
        result = []
        path = []
        def dfs(i):
            if i == len(nums):
                result.append(path.copy())
                return 
            dfs(i+1)
            path.append(nums[i])
            dfs(i+1)
            path.pop()
        dfs(0)
        return result

Complexity

• Time complexity: O(K*C(n, k))
• Space complexity: O(K*C(n, k))