Generate subsets
Detailed guide and Python implementation for the 'Generate subsets' problem.
1. Concept Overview
The 'Generate subsets' problem is a key challenge in the Recursion section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Generate subsets.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Generate subsets carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Write a function generate_subsets(arr) that takes a list of distinct integers and returns all possible subsets (the power set). Return the result as a sorted list of sorted lists. Include the empty subset. Sort each individual subset, then sort the list of subsets by length first, then lexicographically.
- •0 <= len(arr) <= 10
- •All elements in arr are distinct
- •-100 <= arr[i] <= 100
Examples
arr = [1, 2, 3]
[[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]
An array of 3 elements has 2^3 = 8 subsets, including the empty set and the full set.
arr = [1, 2]
[[], [1], [2], [1, 2]]
2^2 = 4 subsets.
arr = [5]
[[], [5]]
2^1 = 2 subsets: the empty set and [5].
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def subsets(s):
res = []
def backtrack(start, path):
res.append("".join(path))
for i in range(start, len(s)):
path.append(s[i]); backtrack(i + 1, path); path.pop()
backtrack(0, [])
return resBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def subsets(s, curr="", idx=0, res=[]):
if idx == len(s): res.append(curr); return
subsets(s, curr + s[idx], idx + 1, res)
subsets(s, curr, idx + 1, res)
return resAlgorithm Pattern Checklist
When dealing with Recursion data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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