# 78. Subsets

Updated: 2023-03-05

LeetCode problem

In this solution, we start with an empty list in the results array.

For each element in the nums array, we append that element to all of the subsets in the results array to create new subsets, and then add these new subsets to the results array.

By doing this for all elements in nums, we generate all possible subsets.

class Solution:
def subsets(self, nums: List[int]) -> List[List[int]]:
res = [[]]
for i in nums:
for j in range(len(res)):
cur = []
cur.append(i)
cur.extend(res[j])
res.append(cur)
return res


Approach 2:

class Solution:
def subsets(self, nums: List[int]) -> List[List[int]]:
res = []

def dfs(start: int, path: List[int]) -> None:
res.append(path)

for i in range(start, len(nums)):
dfs(i + 1, path + [nums[i]])

dfs(0, [])
return res


This is a recursive solution that uses a depth-first search (DFS) approach to generate all possible subsets of the input list nums. The function takes two parameters start and path, where

• start represents the starting index of the current subset
• path represents the current subset being constructed.

The base case of the recursion is when start is greater than or equal to the length of nums, at which point the current path is added to the final result res.

For each recursive call, the function iterates through the remaining elements of nums starting at index start, and appends each element to the path list. Then, the function recursively calls itself with the next index i+1 as the new starting point for the next subset, and the updated path list.

As the recursion returns, each subset is added to the res list, and the path list is updated by removing the last element that was added in the previous recursive call.

Finally, the function is initialized with an empty path list and a starting index start of 0, and the final res list is returned after all subsets have been generated.

LeetCode Editorial:

• Approach 2: Backtracking

• Approach 3: Lexicographic (Binary Sorted) Subsets