Generate All Subsets Powerset in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to start generating subsets by adding an empty subset.

DSA Python

def subsets(nums):
    result = [[]]
    for num in nums:
        new_subsets = []
        for curr in result:
            new_subsets.append(curr + [[1]])
        result.extend(new_subsets)
    return result

print(subsets([1, 2]))

Drag options to blanks, or click blank then click option'

Acurr

Bnum

Cnums

Dresult

Attempts:

3 left

💡 Hint

Common Mistakes

Using the whole list instead of the current number

Using the current subset instead of the number

The variable num is the current number to add to existing subsets to form new subsets.

2fill in blank

medium

Complete the code to generate all subsets using recursion.

DSA Python

def subsets_recursive(nums):
    def backtrack(start, path):
        result.append(path[:])
        for i in range(start, len(nums)):
            path.append(nums[i])
            backtrack(i + 1, path)
            path.pop()

    result = []
    backtrack(0, [])
    return [1]

print(subsets_recursive([1, 2]))

Drag options to blanks, or click blank then click option'

Aresult

Bpath

Cnums

Dstart

Attempts:

3 left

💡 Hint

Common Mistakes

Returning the current path instead of all results

Returning the input list

The function returns result, which holds all subsets collected during recursion.

3fill in blank

hard

Fix the error in the iterative subset generation code by filling the blank.

DSA Python

def subsets(nums):
    result = [[]]
    for num in nums:
        new_subsets = []
        for curr in result:
            new_subsets.append(curr + [[1]])
        result.extend(new_subsets)
    return result

print(subsets([1, 2, 3]))

Drag options to blanks, or click blank then click option'

Aresult

Bnums

Ccurr

Dnum

Attempts:

3 left

💡 Hint

Common Mistakes

Adding the whole list instead of the current number

Adding the current subset to itself

The current number num must be added to each existing subset to form new subsets.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each subset to its length.

DSA Python

nums = [1, 2, 3]
subsets = [[]]
for num in nums:
    subsets += [curr + [num] for curr in subsets]
subset_lengths = { [1]: [2] for subset in subsets }
print(subset_lengths)

Drag options to blanks, or click blank then click option'

Asubset

Blen(subset)

Csubset_lengths

Dsubset + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using the dictionary name as key

Using invalid expressions for length

The dictionary maps each subset to its length using len(subset).

5fill in blank

hard

Fill all three blanks to create a list comprehension that filters subsets with length greater than 1.

DSA Python

nums = [1, 2, 3]
subsets = [[]]
for num in nums:
    subsets += [curr + [num] for curr in subsets]
filtered = [[1] for [2] in subsets if len([3]) > 1]
print(filtered)

Drag options to blanks, or click blank then click option'

Asubset

Dnum

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names in parts of the comprehension

Using the wrong variable in the condition

We iterate over each subset in subsets and select those with length greater than 1.

Practice

1. What does the powerset of a set represent in terms of subsets?

easy

A. Only subsets with even number of elements

B. Only the full set itself

C. Only subsets with odd number of elements

D. All possible subsets including empty and full set

Solution

1. Step 1: Understand the definition of powerset

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

2. Step 2: Compare options with definition

   All possible subsets including empty and full set correctly states all possible subsets are included. Other options limit subsets incorrectly.

3. Final Answer:

   All possible subsets including empty and full set -> Option D

4. Quick Check:

   Powerset = All subsets [OK]

Hint: Remember powerset means every subset possible [OK]

Common Mistakes:

• Thinking powerset excludes empty set
• Confusing powerset with subsets of certain size
• Assuming powerset only includes full set

2. Which of the following Python code snippets correctly initializes an empty list to store subsets for generating a powerset?

easy

A. subsets = set()

B. subsets = {}

C. subsets = []

D. subsets = ()

Solution

1. Step 1: Identify the correct data structure for storing subsets

   Subsets are typically stored in a list because order and duplicates matter for powerset generation.

2. Step 2: Analyze each option

   subsets = [] uses an empty list []. subsets = {} uses a dictionary {}, which is incorrect. subsets = () uses a tuple (), which is immutable. subsets = set() uses a set(), which cannot store duplicates or ordered subsets.

3. Final Answer:

   subsets = [] -> Option C

4. Quick Check:

   Use list [] for subsets storage [OK]

Hint: Use list [] to store multiple subsets [OK]

Common Mistakes:

• Using {} which creates a dictionary, not a list
• Using () which is immutable tuple
• Using set() which loses order and duplicates

3. What is the output of the following code?

def powerset(nums):
    result = [[]]
    for num in nums:
        result += [curr + [num] for curr in result]
    return result

print(powerset([1, 2]))

medium

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

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

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

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

Solution

1. Step 1: Trace initial result and loop iterations

   Start with result = [[]]. For num=1, add subsets: [] + [1] = [1], so result = [[], [1]]. For num=2, add subsets: [] + [2] = [2], [1] + [2] = [1, 2], so result = [[], [1], [2], [1, 2]].

2. Step 2: Confirm final output list

   The final list contains all subsets: empty, single elements, and full set.

3. Final Answer:

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

4. Quick Check:

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

Hint: Add new element to all existing subsets each loop [OK]

Common Mistakes:

• Missing empty subset [] in output
• Not combining previous subsets with new element
• Confusing order of subsets

4. Find the error in this powerset generation code:

def powerset(nums):
    result = []
    for num in nums:
        for curr in result:
            result.append(curr + [num])
    return result

print(powerset([1, 2]))

medium

A. result list is empty initially, so loop never runs

B. Appending inside loop modifies list during iteration

C. Missing return statement

D. Using list instead of set causes duplicates

Solution

1. Step 1: Check initial value of result

   result is initialized as empty list []. The inner loop for curr in result will not run because result is empty.

2. Step 2: Understand consequence on output

   Since inner loop never runs, no subsets are added. The function returns empty list [].

3. Final Answer:

   result list is empty initially, so loop never runs -> Option A

4. Quick Check:

   Empty result means no subsets generated [OK]

Hint: Initialize result with [[]] to start with empty subset [OK]

Common Mistakes:

• Not initializing result with [[]]
• Modifying list while iterating (can cause bugs)
• Forgetting to add empty subset initially

5. Given a list nums = [1, 2, 2], which code modification correctly generates the powerset without duplicate subsets?

hard

A. Sort nums and skip duplicates during subset generation

B. Use a set to store tuples of subsets to avoid duplicates

C. Use list comprehension without any checks

D. Remove duplicates from nums before generating subsets

Solution

1. Step 1: Understand the problem with duplicates

   Input has duplicates (2 appears twice). Powerset generation can create duplicate subsets if duplicates are not handled.

2. Step 2: Analyze options for handling duplicates

   Use a set to store tuples of subsets to avoid duplicates uses a set of tuples which works but changes data type and order. Sort nums and skip duplicates during subset generation sorts nums and skips duplicates during recursion, which is standard and efficient. Use list comprehension without any checks ignores duplicates. Remove duplicates from nums before generating subsets removes duplicates, which changes the original set.

3. Final Answer:

   Sort nums and skip duplicates during subset generation -> Option A

4. Quick Check:

   Sort and skip duplicates to avoid repeated subsets [OK]

Hint: Sort input and skip duplicates while building subsets [OK]

Common Mistakes:

• Removing duplicates changes original data meaning
• Using sets loses subset order
• Ignoring duplicates causes repeated subsets