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All Subsets of a Set (Power Set)

Certification: Advanced Level Accuracy: 100% Submissions: 3 Points: 15

Write a Python function that generates all possible subsets (power set) of a given set represented as a list of distinct integers. The solution should not contain duplicate subsets.

Example 1
    
  
  • Input: [1, 2, 3]
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  • Output: [[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]
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  • Explanation:
    
      
      
    • Step 1: Start with an empty subset.
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    • Step 2: For each element in the input set, create new subsets by including and excluding it.
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    • Step 3: For element 1, create [] and [1].
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    • Step 4: For element 2, create [] and [1] (excluding 2), and [2] and [1, 2] (including 2).
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    • Step 5: For element 3, similarly create all combinations with and without 3.
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    • Step 6: Return all 2^3 = 8 possible subsets.
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Example 2
    
  
  • Input: [0]
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  • Output: [[], [0]]
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  • Explanation:
    
      
      
    • Step 1: Start with an empty subset [].
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    • Step 2: Create a new subset by including the element 0: [0].
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    • Step 3: Return both subsets: [] (empty set) and [0] (the set itself).
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Constraints
    
  
  • 0 ≤ len(nums) ≤ 10
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  • -10 ≤ nums[i] ≤ 10
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  • All the numbers of nums are unique
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  • Time Complexity: O(2^n), where n is the length of the input list
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  • Space Complexity: O(2^n)
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Hint
Solution

Solution Hints

    
  
  • Use a recursive approach to generate all subsets
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  • For each element, consider two cases: include it or exclude it
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  • Alternatively, use bit manipulation to generate all subsets
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  • A set with n elements has 2^n subsets
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  • You can also use an iterative approach with binary representation
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Steps to solve by this approach:

 Step 1: Find the total number of possible subsets using the formula 2^n for n elements.

 Step 2: Generate numbers from 0 to 2^n-1, where each number represents a unique subset.

 Step 3: For each number, use its binary representation to determine whether to include elements.

 Step 4: If the jth bit of binary representation of i is set, include the jth element in the subset.

 Step 5: Collect all generated subsets into the power set.

Submitted Code :