Generate All Subsets Powerset in DSA Go - 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

How many subsets does a set with n elements have?

A set with n elements has 2^n subsets in its powerset.

intermediate

What is the main idea behind generating all subsets using backtracking?

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

beginner

In Go, which data structure is commonly used to store subsets during powerset generation?

Slices are commonly used in Go to store subsets because they are dynamic and easy to append elements to.

beginner

Why is the empty subset always included in the powerset?

The empty subset represents the choice of selecting no elements, which is a valid subset by definition.

How many subsets will the powerset of a set with 3 elements contain?

A 8

B 6

C 9

D 3

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

Which approach is commonly used to generate all subsets of a set?

A Sorting

B Backtracking

C Binary Search

D Hashing

Backtracking explores all combinations by including or excluding each element.

In Go, which keyword is used to add an element to a slice?

A add

B push

C append

D insert

The append function is used to add elements to slices in Go.

What does the empty subset represent in a powerset?

A Subset with all elements

B Subset with one element

C Subset with half elements

D Subset with no elements

The empty subset contains no elements and is always part of the powerset.

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

A {2, 3}

B {}

C {1}

D {1, 2}

{2, 3} contains an element (3) not in the original set, so it is not a subset.

Explain how to generate all subsets (powerset) of a set using backtracking.

Think about making a choice for each element step-by-step.

Describe the output of generating the powerset of the set {a, b}.

List all combinations of elements.

Practice

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

easy

A. The set of elements repeated twice

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

C. The set itself without any subsets

D. Only the subsets with exactly two elements

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 incorrect concepts.

3. Final Answer:

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

4. Quick Check:

   powerset = all subsets [OK]

Hint: Powerset means every subset possible [OK]

Common Mistakes:

• Thinking powerset excludes empty set
• Confusing powerset with subsets of fixed size
• Assuming powerset duplicates elements

2. Which of the following Go code snippets correctly initializes an empty slice of slices of integers to store subsets?

easy

A. var subsets [][]int = []int{}

B. var subsets []int = []int{}

C. var subsets []int = [][]int{}

D. var subsets [][]int = [][]int{}

Solution

1. Step 1: Identify the type for storing subsets

   Subsets are slices of integers, so a slice of slices of int is needed: [][]int.

2. Step 2: Check initialization syntax

   var subsets [][]int = [][]int{} correctly initializes an empty slice of slices of int. Other options mismatch types.

3. Final Answer:

   var subsets [][]int = [][]int{} -> Option D

4. Quick Check:

   Correct slice of slices initialization [OK]

Hint: Use [][]int for slice of int slices [OK]

Common Mistakes:

• Using []int instead of [][]int for subsets
• Mixing types in initialization
• Incorrect empty slice syntax

3. What is the output of the following Go code that generates all subsets of []int{1, 2}?

func subsets(nums []int) [][]int {
    res := [][]int{{}}
    for _, num := range nums {
        newSubsets := [][]int{}
        for _, subset := range res {
            newSubset := append([]int{}, subset...)
            newSubset = append(newSubset, num)
            newSubsets = append(newSubsets, newSubset)
        }
        res = append(res, newSubsets...)
    }
    return res
}

func main() {
    result := subsets([]int{1, 2})
    fmt.Println(result)
}

medium

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

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

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

D. [[], [2], [1]]

Solution

1. Step 1: Trace initial state and first iteration

   Start with res = [[]]. For num=1, add subsets [1], so res = [[], [1]].

2. Step 2: Trace second iteration

   For num=2, add subsets [2] and [1,2], so res = [[], [1], [2], [1, 2]].

3. Final Answer:

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

4. Quick Check:

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

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

Common Mistakes:

• Missing empty subset in result
• Not appending new subsets correctly
• Confusing order of subsets

4. The following Go code attempts to generate all subsets of []int{1, 2}. What is the bug?

func subsets(nums []int) [][]int {
    res := [][]int{{}}
    for _, num := range nums {
        for i := range res {
            res[i] = append(res[i], num)
            res = append(res, [][]int{res[i]})
        }
    }
    return res
}

medium

A. Appending to res[i] modifies original subsets causing duplicates

B. res is not initialized properly

C. Loop variable num is not used

D. Function returns nil instead of subsets

Solution

1. Step 1: Understand slice append behavior in loop

   Appending to res[i] modifies the original slice in res because slices share underlying arrays.

2. Step 2: Identify consequence of modifying original subsets

   This causes all subsets to be changed and duplicates appear, breaking correct subset generation.

3. Final Answer:

   Appending to res[i] modifies original subsets causing duplicates -> Option A

4. Quick Check:

   Modify copy, not original slice [OK]

Hint: Copy slice before append to avoid modifying original [OK]

Common Mistakes:

• Appending directly to loop variable slice
• Not creating new slice copy
• Ignoring slice reference behavior

5. Given a set []int{1, 2, 2} with duplicate elements, which approach correctly generates all unique subsets (powerset without duplicates)?

hard

A. Sort input, then use backtracking skipping duplicates when choosing elements

B. Use a map to store subsets as keys without sorting input

C. Generate all subsets and then remove duplicates by comparing slices

D. Ignore duplicates and generate subsets normally

Solution

1. Step 1: Understand duplicate handling in subsets

   Duplicates cause repeated subsets if not handled carefully.

2. Step 2: Use sorting and skip duplicates during backtracking

   Sorting input helps detect duplicates. Skipping duplicates when choosing elements avoids repeated subsets efficiently.

3. Final Answer:

   Sort input, then use backtracking skipping duplicates when choosing elements -> Option A

4. Quick Check:

   Sort + skip duplicates = unique subsets [OK]

Hint: Sort input and skip duplicates during recursion [OK]

Common Mistakes:

• Not sorting input before backtracking
• Removing duplicates after generation (inefficient)
• Ignoring duplicates causing repeated subsets