Generate All Subsets Powerset in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of powerset generation with duplicates

What is the output of this code that generates all subsets (powerset) of the list [1, 2, 2]?

DSA Python

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

print(powerset([1, 2, 2]))

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

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

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

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

💡 Hint

Think about how duplicates in the input list affect the subsets generated.

The code adds each number to all existing subsets, so duplicates cause repeated subsets. The output includes duplicates subsets like [2] twice.

❓ Predict Output

intermediate

Number of subsets generated

How many subsets does the powerset function generate for the input list [3, 5, 7]?

DSA Python

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

print(len(powerset([3, 5, 7])))

A 8

B 7

C 6

D 9

💡 Hint

Number of subsets for a list of length n is 2^n.

For 3 elements, total subsets = 2^3 = 8.

🔧 Debug

advanced

Identify the error in this powerset code

What error does this code raise when run?

DSA Python

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

print(powerset([1, 2]))

A RuntimeError: maximum recursion depth exceeded

B IndexError: list index out of range

C TypeError: unsupported operand type(s) for +: 'int' and 'list'

D ValueError: too many values to unpack

💡 Hint

Look at the initial value of result and how list concatenation is used.

result starts as empty list, so list comprehension uses curr from empty list, causing error when adding int and list.

🧠 Conceptual

advanced

Why does the powerset size grow exponentially?

Why does the number of subsets in a powerset grow exponentially with the size of the input list?

A Because subsets are limited to half the size of the input list

B Because each element can either be included or excluded, doubling subsets each time

C Because the function uses recursion which multiplies subsets

D Because subsets are formed by adding elements in pairs only

💡 Hint

Think about choices for each element in subset formation.

Each element has two choices: include or exclude, so total subsets = 2^n.

🚀 Application

expert

Find subsets with sum equal to target

Given the powerset function below, which option correctly returns all subsets of [2, 4, 6] whose sum is 6?

DSA Python

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

nums = [2, 4, 6]
all_subsets = powerset(nums)

# Which option filters subsets with sum 6 correctly?

A [subset for subset in all_subsets if sum(subset) == 6]

B [subset for subset in all_subsets if sum(subset) != 6]

C [subset for subset in all_subsets if sum(subset) > 6]

D [subset for subset in all_subsets if sum(subset) >= 6]

💡 Hint

You want subsets whose sum is exactly 6.

Option A filters subsets whose sum equals 6 exactly, others do not.

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