Generate All Subsets Powerset in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a powerset in the context of sets?

A powerset is the set of all possible subsets of a given set, including the empty set and the set itself.

beginner

Which data structure is commonly used to store subsets when generating a powerset?

A list of lists (or array of arrays) is commonly used to store all subsets generated in the powerset.

intermediate

What is the time complexity of generating all subsets (powerset) of a set with n elements?

The time complexity is O(2^n) because there are 2^n possible subsets.

beginner

In Java, which method can be used to add a new subset to the list of subsets when generating a powerset?

The add() method of the List interface is used to add a new subset to the list of subsets.

intermediate

Explain the backtracking approach to generate all subsets.

Backtracking builds subsets by choosing to include or exclude each element recursively, exploring all possible combinations step-by-step.

How many subsets does a set with 3 elements have?

A 6

B 9

C 3

D 8

A set with n elements has 2^n subsets. For 3 elements, 2^3 = 8 subsets.

Which of the following is NOT a subset of {1, 2}?

A {} (empty set)

B {2, 3}

C {1}

D {1, 2}

Subset elements must come from the original set. {2, 3} contains 3 which is not in {1, 2}.

What is the base case in recursive generation of subsets?

A When all subsets are printed

B When the subset size equals the input set size

C When the input set is empty

D When the subset contains one element

The base case is when there are no more elements to process, i.e., the input set is empty.

Which Java collection is best to store subsets dynamically?

A ArrayList

B LinkedList

C HashSet

D Array

ArrayList allows dynamic resizing and easy addition of subsets.

What does the powerset of an empty set contain?

A Set with one empty subset

B No subsets

C Empty set only

D Set with one element

The powerset of an empty set contains one subset: the empty set itself.

Describe the step-by-step process to generate all subsets of a set using recursion.

Think about how you build subsets by choosing elements one by one.

Explain why the number of subsets of a set with n elements is 2^n.

Consider binary decisions for each element.

Practice

1. What does the term powerset mean in the context of subsets?

easy

A. All possible subsets of a given set, including empty and full set

B. Only the subsets with exactly two elements

C. The set of elements that are not in the original set

D. The largest subset of a given set

Solution

1. Step 1: Understand the definition of powerset

   The powerset of a set is the collection of all possible subsets, including the empty set and the set itself.

2. Step 2: Compare options with definition

   All possible subsets of a given set, including empty and full set correctly describes the powerset as all subsets. Other options describe partial or unrelated concepts.

3. Final Answer:

   All possible subsets of a given set, including empty and full set -> Option A

4. Quick Check:

   powerset = all subsets [OK]

Hint: Powerset means every subset possible, including empty [OK]

Common Mistakes:

• Thinking powerset excludes empty set
• Confusing powerset with subsets of fixed size
• Assuming powerset means complement sets

2. Which of the following Java method signatures correctly represents a function that returns all subsets of an integer array?

easy

A. public int generateSubsets(int[] nums)

B. public void generateSubsets(int[] nums)

C. public List generateSubsets(int[] nums)

D. public List<Integer> generateSubsets(int nums)

Solution

1. Step 1: Identify return type for all subsets

   All subsets of an integer array require returning a list of lists of integers, so return type should be List.

2. Step 2: Check method parameters and return type

   public List generateSubsets(int[] nums) matches correct return type and parameter. Options A and C have wrong return types, and D has wrong parameter type.

3. Final Answer:

   public List<List<Integer>> generateSubsets(int[] nums) -> Option C

4. Quick Check:

   Return type must hold all subsets = List of List [OK]

Hint: Return type for subsets is List of List of Integers [OK]

Common Mistakes:

• Using int return type instead of list
• Using void return type without output
• Passing single int instead of int array

3. What is the output of the following Java code snippet?

public static List subsets(int[] nums) {
    List result = new ArrayList<>();
    result.add(new ArrayList<>());
    for (int num : nums) {
        int size = result.size();
        for (int i = 0; i < size; i++) {
            List<Integer> subset = new ArrayList<>(result.get(i));
            subset.add(num);
            result.add(subset);
        }
    }
    return result;
}

// Called with nums = {1, 2}

medium

A. [[], [1], [2], [1, 2]]

B. [[1], [2], [1, 2]]

C. [[], [1, 2]]

D. [[1], [2]]

Solution

1. Step 1: Initialize result with empty subset

   Initially, result = [[]].

2. Step 2: Iterate over nums and add new subsets

   For num=1, add [1] to result: result = [[], [1]]. For num=2, add [2] and [1,2]: result = [[], [1], [2], [1, 2]].

3. Final Answer:

   [[], [1], [2], [1, 2]] -> Option A

4. Quick Check:

   All subsets of {1,2} = [[], [1], [2], [1, 2]] [OK]

Hint: Start with empty set, add each number to existing subsets [OK]

Common Mistakes:

• Forgetting to include empty subset
• Adding subsets in wrong order
• Missing combined subsets like [1, 2]

4. Identify the error in the following Java code that attempts to generate all subsets of an integer array:

public static List subsets(int[] nums) {
    List result = new ArrayList<>();
    for (int num : nums) {
        int size = result.size();
        for (int i = 0; i < size; i++) {
            List<Integer> subset = new ArrayList<>(result.get(i));
            subset.add(num);
            result.add(subset);
        }
    }
    result.add(new ArrayList<>());
    return result;
}

medium

A. The input array should be converted to a list first

B. The inner loop should run from size-1 to 0

C. The method should return an int, not a list

D. Empty subset is added at the end, should be added before loop

Solution

1. Step 1: Check when empty subset is added

   Empty subset must be added before starting to build subsets, so that initial subsets exist.

2. Step 2: Analyze code flow

   Here, empty subset is added after loops, so result.size() is zero initially and inner loop never runs, producing empty result except empty subset at end.

3. Final Answer:

   Empty subset is added at the end, should be added before loop -> Option D

4. Quick Check:

   Empty subset must be first for subsets to build [OK]

Hint: Add empty subset before loops to start building subsets [OK]

Common Mistakes:

• Adding empty subset after loops
• Incorrect loop ranges causing no subsets
• Returning wrong data type

5. Given an integer array nums that may contain duplicates, which modification to the standard subsets generation algorithm ensures the powerset contains no duplicate subsets?

hard

A. Only generate subsets of fixed size to avoid duplicates

B. Sort the array first and skip adding subsets that duplicate the last added subset

C. Generate subsets normally without changes; duplicates are automatically handled

D. Use a HashSet to store subsets and convert back to list at the end

Solution

1. Step 1: Understand duplicates in subsets

   Duplicates in input cause duplicate subsets if not handled.

2. Step 2: Use sorting and skip duplicates

   Sorting groups duplicates together. While generating subsets, skip adding subsets that duplicate the last added subset to avoid duplicates.

3. Final Answer:

   Sort the array first and skip adding subsets that duplicate the last added subset -> Option B

4. Quick Check:

   Sort + skip duplicates = unique subsets [OK]

Hint: Sort input and skip duplicates during subset generation [OK]

Common Mistakes:

• Ignoring duplicates causing repeated subsets
• Using HashSet but forgetting order or conversion
• Assuming duplicates don't affect subsets