Generate All Subsets Powerset in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to start the recursive function call for generating all subsets.

DSA C++

void generateSubsets(vector<int>& nums, vector<int>& current, int index, vector<vector<int>>& result) {
    if (index == nums.size()) {
        result.push_back(current);
        return;
    }
    // Include nums[index]
    current.push_back(nums[index]);
    generateSubsets(nums, current, [1], result);
    current.pop_back();
    // Exclude nums[index]
    generateSubsets(nums, current, index + 1, result);
}

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

Aindex - 1

Bindex + 1

C0

Dnums.size()

Attempts:

3 left

💡 Hint

Common Mistakes

Using index - 1 causes infinite recursion or wrong subsets.

Using 0 resets the index and causes infinite loops.

We move to the next index by adding 1 to the current index to explore subsets including the current element.

2fill in blank

medium

Complete the code to initialize the subsets generation and return the result.

DSA C++

vector<vector<int>> subsets(vector<int>& nums) {
    vector<vector<int>> result;
    vector<int> current;
    generateSubsets(nums, current, [1], result);
    return result;
}

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

A0

B1

Cnums.size()

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Starting from 1 skips the first element.

Starting from nums.size() means starting beyond the last element.

We start from index 0 to include or exclude elements from the beginning.

3fill in blank

hard

Fix the error in the base case condition to stop recursion correctly.

DSA C++

void generateSubsets(vector<int>& nums, vector<int>& current, int index, vector<vector<int>>& result) {
    if (index [1] nums.size()) {
        result.push_back(current);
        return;
    }
    current.push_back(nums[index]);
    generateSubsets(nums, current, index + 1, result);
    current.pop_back();
    generateSubsets(nums, current, index + 1, result);
}

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

A<=

B<

C>

D==

Attempts:

3 left

💡 Hint

Common Mistakes

Using < causes recursion to stop too early.

Using <= or > causes out-of-bound errors.

The recursion stops when index equals the size of nums, meaning all elements are processed.

4fill in blank

hard

Fill both blanks to create a loop that generates subsets iteratively.

DSA C++

vector<vector<int>> subsetsIterative(vector<int>& nums) {
    vector<vector<int>> result = [1];
    for (int num : nums) {
        int n = result.size();
        for (int i = 0; i < n; i++) {
            vector<int> subset = result[i];
            subset.push_back(num);
            result.[2](subset);
        }
    }
    return result;
}

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

A{{}}

Bpush_back

Cinsert

Dpop_back

Attempts:

3 left

💡 Hint

Common Mistakes

Using insert instead of push_back causes wrong insertion.

Starting with an empty vector instead of a vector containing an empty vector misses the empty subset.

Start with an empty subset represented by an empty vector inside result, and add new subsets using push_back.

5fill in blank

hard

Fill all three blanks to create a recursive function that generates subsets and uses backtracking.

DSA C++

void backtrack(vector<int>& nums, int [1], vector<int>& tempList, vector<vector<int>>& result) {
    result.push_back(tempList);
    for (int i = [2]; i < nums.size(); i++) {
        tempList.push_back(nums[i]);
        backtrack(nums, i + [3], tempList, result);
        tempList.pop_back();
    }
}

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

Astart

B0

C1

Dindex

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 in the loop start causes repeated subsets.

Using start instead of index causes undefined variable errors.

Using i + 0 in recursion causes infinite loops.

Use 'index' as the starting point, loop from index, and recurse with i + 1 to move forward.

Practice

1. What does the "Generate All Subsets (Powerset)" algorithm produce when given a set {1, 2}?

easy

A. Only subsets with two elements: {1, 2}

B. All possible subsets including empty set: {}, {1}, {2}, {1, 2}

C. Only subsets with one element: {1}, {2}

D. Only the empty set: {}

Solution

1. Step 1: Understand what subsets mean

   Subsets include all combinations of elements, from empty to full set.

2. Step 2: List all subsets of {1, 2}

   They are {}, {1}, {2}, and {1, 2}.

3. Final Answer:

   All possible subsets including empty set: {}, {1}, {2}, {1, 2} -> Option B

4. Quick Check:

   Subsets = all combinations [OK]

Hint: Remember powerset includes empty and full sets [OK]

Common Mistakes:

• Thinking subsets only have full or single elements
• Ignoring the empty subset
• Confusing subsets with permutations

2. Which of the following C++ code snippets correctly initializes an empty vector of vectors to store subsets?

easy

A. std::vector<int> subsets;

B. std::vector subsets = {{}};

C. std::vector subsets;

D. std::vector subsets<int>;

Solution

1. Step 1: Identify correct vector declaration

   We need a vector of vectors of int to store subsets.

2. Step 2: Check syntax correctness

   std::vector subsets; uses correct syntax: std::vector subsets; initializes empty vector of vectors.

3. Final Answer:

   std::vector subsets; -> Option C

4. Quick Check:

   Correct vector of vectors syntax [OK]

Hint: Use vector for subsets storage [OK]

Common Mistakes:

• Using vector<int> instead of vector
• Incorrect template syntax like vector subsets<int>
• Trying to initialize with empty braces incorrectly

3. What is the output of the following C++ code snippet?

std::vector<int> nums = {1, 2};
std::vector subsets = {{}};
for (int num : nums) {
    int n = subsets.size();
    for (int i = 0; i < n; i++) {
        std::vector<int> newSubset = subsets[i];
        newSubset.push_back(num);
        subsets.push_back(newSubset);
    }
}
for (auto &subset : subsets) {
    for (int x : subset) std::cout << x << " ";
    std::cout << "| ";
}

medium

A. | | 1 | 2 | 1 2 |

B. | | 1 2 | 1 | 2 |

C. | 1 | 2 | 1 2 |

D. | 1 2 | 1 | 2 |

Solution

1. Step 1: Understand initial subsets and loop

   Initially subsets = {{}}, empty subset only. For each num, we add new subsets by adding num to existing subsets.

2. Step 2: Trace iterations

   For num=1: subsets become {}, {1}. For num=2: subsets become {}, {1}, {2}, {1, 2}.

3. Final Answer:

   | | 1 | 2 | 1 2 | -> Option A

4. Quick Check:

   All subsets printed with spaces and separators [OK]

Hint: Start with empty subset and add elements iteratively [OK]

Common Mistakes:

• Missing the empty subset in output
• Printing subsets in wrong order
• Confusing push_back inside loop

4. Identify the error in this C++ code snippet for generating subsets:

std::vector<int> nums = {1, 2};
std::vector subsets;
for (int num : nums) {
    int n = subsets.size();
    for (int i = 0; i < n; i++) {
        std::vector<int> newSubset = subsets[i];
        newSubset.push_back(num);
        subsets.push_back(newSubset);
    }
}

medium

A. subsets vector is not initialized with empty subset before loop

B. Loop variable i should start from 1, not 0

C. newSubset.push_back(num) should be outside inner loop

D. nums vector should be empty to generate subsets

Solution

1. Step 1: Check initialization of subsets

   subsets is empty initially, so subsets.size() is 0, inner loop never runs.

2. Step 2: Identify missing empty subset

   We must start subsets with empty subset {{}} to build new subsets correctly.

3. Final Answer:

   subsets vector is not initialized with empty subset before loop -> Option A

4. Quick Check:

   Empty subset needed to start building subsets [OK]

Hint: Always start subsets with empty subset {{}} [OK]

Common Mistakes:

• Not initializing subsets with empty subset
• Changing loop start index incorrectly
• Misplacing push_back calls

5. Given a vector nums = {1, 2, 2}, which code modification ensures the generated subsets contain no duplicate subsets?

hard

A. Generate subsets normally; duplicates are impossible with vector<int>.

B. Use a set to store subsets after generation to remove duplicates.

C. Ignore duplicate elements in nums vector before generating subsets.

D. Sort nums first and skip adding duplicates during subset generation.

Solution

1. Step 1: Understand duplicates in input

   Input has duplicate 2's, so subsets like {2} can appear multiple times.

2. Step 2: Use sorting and skip duplicates

   Sorting nums helps detect duplicates; skip adding subsets with same element consecutively to avoid duplicates.

3. Final Answer:

   Sort nums first and skip adding duplicates during subset generation. -> Option D

4. Quick Check:

   Sorting + skipping duplicates avoids repeated subsets [OK]

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

Common Mistakes:

• Assuming duplicates never occur
• Removing duplicates from input loses valid subsets
• Using set after generation is less efficient