Subsets Generation Using Bitmask in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to generate all subsets of a list using bitmask.

DSA Python

nums = [1, 2, 3]
subsets = []
n = len(nums)
for mask in range(1 << n):
    subset = []
    for i in range(n):
        if mask & (1 << [1]):
            subset.append(nums[i])
    subsets.append(subset)
print(subsets)

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

Ai

Bsubset

Cn

Dmask

Attempts:

3 left

💡 Hint

Common Mistakes

Using mask instead of i in the bit shift.

Using n or subset instead of i for the bit position.

We use 'i' to check each bit position in the mask to decide if nums[i] is included in the subset.

2fill in blank

medium

Complete the code to calculate the total number of subsets using bitmask.

DSA Python

nums = [4, 5, 6, 7]
n = len(nums)
total_subsets = [1]
print(total_subsets)

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

A2 * n

Bn * 2

C1 << n

Dn ** 2

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of bit shift.

Using n squared instead of 2 to the power n.

Total subsets of a set with n elements is 2^n, which is 1 shifted left by n bits.

3fill in blank

hard

Fix the error in the code to correctly generate subsets using bitmask.

DSA Python

nums = [8, 9]
n = len(nums)
subsets = []
for mask in range(1 << n):
    subset = []
    for i in range(n):
        if mask & (1 << i):
            subset.append(nums[[1]])
    subsets.append(subset)
print(subsets)

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

Amask

Bi

Cn

Dsubset

Attempts:

3 left

💡 Hint

Common Mistakes

Appending nums[mask] instead of nums[i].

Using wrong variable in bit shift.

We must use 'i' to index nums, not 'mask', to get the correct element for the subset.

4fill in blank

hard

Fill both blanks to create a list of subsets with their sums using bitmask.

DSA Python

nums = [1, 2, 3]
n = len(nums)
subsets_with_sum = []
for mask in range(1 << n):
    subset = []
    for i in range(n):
        if mask & (1 << [1]):
            subset.append(nums[i])
    subsets_with_sum.append((subset, sum([2])))
print(subsets_with_sum)

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

Ai

Bsubset

Cnums

Dmask

Attempts:

3 left

💡 Hint

Common Mistakes

Using nums instead of subset for sum.

Using mask or i instead of subset for sum.

Use 'i' to check bits and 'subset' to calculate the sum of elements included.

5fill in blank

hard

Fill all three blanks to create a dictionary mapping subsets (as tuples) to their sums using bitmask.

DSA Python

nums = [2, 4]
n = len(nums)
subset_sum_map = {}
for mask in range(1 << n):
    subset = []
    for i in range(n):
        if mask & (1 << [1]):
            subset.append(nums[i])
    subset_sum_map[tuple([2])] = [3]
print(subset_sum_map)

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

Ai

Bsubset

Csum(subset)

Dnums

Attempts:

3 left

💡 Hint

Common Mistakes

Using nums instead of subset for key.

Using subset instead of sum(subset) for value.

Using wrong variable for bit check.

Use 'i' for bit check, 'subset' as key (converted to tuple), and sum(subset) as value.

Practice

1. What does the bitmask technique help to generate when applied to a set of elements?

easy

A. Only subsets with odd number of elements

B. Only the largest subset of the set

C. Only subsets with even number of elements

D. All possible subsets of the set

Solution

1. Step 1: Understand bitmask representation

   Each bit in a bitmask represents whether an element is included (1) or excluded (0) in a subset.

2. Step 2: Generate subsets using bitmask

   By iterating from 0 to 2^n - 1 (where n is number of elements), all combinations of included/excluded elements are covered, producing all subsets.

3. Final Answer:

   All possible subsets of the set -> Option D

4. Quick Check:

   Bitmask = subsets generator [OK]

Hint: Bitmask bits map directly to subset inclusion [OK]

Common Mistakes:

• Thinking bitmask generates only large subsets
• Confusing bitmask with sorting or filtering
• Assuming bitmask generates only even or odd subsets

2. Which of the following is the correct Python syntax to iterate over all bitmasks for a set of size n?

easy

A. for mask in range(1 << n):

B. for mask in range(n << 1):

C. for mask in range(2 * n):

D. for mask in range(n ** 2):

Solution

1. Step 1: Understand bit shift for 2^n

   Using 1 << n shifts 1 left by n bits, which equals 2 to the power n.

2. Step 2: Use range to cover all bitmasks

   Iterating from 0 to 1 << n - 1 covers all subsets represented by bitmasks.

3. Final Answer:

   for mask in range(1 << n): -> Option A

4. Quick Check:

   1 << n = 2^n range [OK]

Hint: Use 1 << n for 2^n subsets [OK]

Common Mistakes:

• Using multiplication instead of bit shift
• Using n squared or doubled incorrectly
• Confusing range limits

3. What is the output of the following code?

arr = ["a", "b"]
subsets = []
for mask in range(1 << len(arr)):
    subset = []
    for i in range(len(arr)):
        if mask & (1 << i):
            subset.append(arr[i])
    subsets.append(subset)
print(subsets)

medium

A. [['a', 'b'], ['a'], ['b'], []]

B. [[], ['a'], ['b'], ['a', 'b']]

C. [[], ['b'], ['a'], ['b', 'a']]

D. [['a'], ['b'], ['a', 'b'], []]

Solution

1. Step 1: Understand bitmask iteration

   For arr of length 2, masks go from 0 to 3 (00, 01, 10, 11 in binary).

2. Step 2: Map bits to elements

   Mask 0 (00) -> no elements -> [] Mask 1 (01) -> include arr[0] -> ['a'] Mask 2 (10) -> include arr[1] -> ['b'] Mask 3 (11) -> include arr[0], arr[1] -> ['a', 'b']

3. Final Answer:

   [[], ['a'], ['b'], ['a', 'b']] -> Option B

4. Quick Check:

   Bitmask subsets match output [OK]

Hint: Trace bitmask bits to elements included [OK]

Common Mistakes:

• Mixing order of subsets
• Appending elements incorrectly
• Confusing bit positions

4. Identify the error in the following code snippet for generating subsets using bitmask:

arr = [1, 2, 3]
subsets = []
for mask in range(1 << len(arr)):
    subset = []
    for i in range(len(arr)):
        if mask & i:
            subset.append(arr[i])
    subsets.append(subset)
print(subsets)

medium

A. The subset list should be initialized outside the loop

B. The range should be 'range(len(arr))' instead of 'range(1 << len(arr))'

C. The condition should be 'mask & (1 << i)' instead of 'mask & i'

D. The print statement should be inside the inner loop

Solution

1. Step 1: Analyze bitmask condition

   The condition 'mask & i' incorrectly checks bits; it should check if the i-th bit is set using 'mask & (1 << i)'.

2. Step 2: Correct bit checking

   Using 'mask & (1 << i)' correctly tests if the bit at position i is 1, indicating inclusion of arr[i].

3. Final Answer:

   The condition should be 'mask & (1 << i)' instead of 'mask & i' -> Option C

4. Quick Check:

   Bit check needs shift [OK]

Hint: Use bit shift to check bits, not index alone [OK]

Common Mistakes:

• Using 'mask & i' instead of 'mask & (1 << i)'
• Initializing subset outside loop causing accumulation
• Misplacing print inside loops

5. Given a list arr = [1, 2, 2], what is the output of the following code that generates subsets using bitmask?

arr = [1, 2, 2]
subsets = []
for mask in range(1 << len(arr)):
    subset = []
    for i in range(len(arr)):
        if mask & (1 << i):
            subset.append(arr[i])
    subsets.append(subset)
print(subsets)

hard

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

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

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

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

Solution

1. Step 1: Calculate total subsets

   For 3 elements, total subsets = 2^3 = 8, masks from 0 to 7.

2. Step 2: Map each mask to subset

   Mask 0 (000): [] Mask 1 (001): [1] Mask 2 (010): [2] (second element) Mask 3 (011): [1, 2] Mask 4 (100): [2] (third element) Mask 5 (101): [1, 2] Mask 6 (110): [2, 2] Mask 7 (111): [1, 2, 2]

3. Final Answer:

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

4. Quick Check:

   Duplicates appear as separate elements [OK]

Hint: Duplicates create repeated subsets with same elements [OK]

Common Mistakes:

• Assuming duplicates merge subsets
• Missing subsets with repeated elements
• Incorrect mask to subset mapping