Subsets Generation Using Bitmask in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind generating subsets using bitmask?

Each subset corresponds to a binary number where each bit represents whether an element is included (1) or excluded (0) from the subset.

beginner

How many subsets can be generated from a set of size n using bitmask?

There are 2^n subsets because each element can either be included or excluded independently.

intermediate

In C, how do you check if the i-th element is included in the subset represented by bitmask m?

Use the expression (m & (1 << i)) != 0 to check if the i-th bit is set, meaning the element is included.

intermediate

Why is bitmasking an efficient way to generate subsets compared to recursion?

Bitmasking uses simple bit operations and loops, avoiding function call overhead and making it easy to generate all subsets iteratively.

beginner

What is the output of subsets generated by bitmask for the set {a, b}?

The subsets are: {}, {a}, {b}, {a, b} corresponding to bitmasks 00, 01, 10, 11 respectively.

How many subsets does a set with 3 elements have?

A 8

B 6

C 3

D 9

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

What does the bitmask 101 represent for a set {x, y, z}?

A {x, z}

B {y}

C {x, y, z}

D {z}

Bitmask 101 means bits 0 and 2 are set, so elements x and z are included.

Which operation checks if the i-th bit is set in a bitmask m?

A m ^ (1 << i)

B m | (1 << i)

C m & (1 << i)

D m << i

The bitwise AND with (1 << i) checks if the i-th bit is set.

What is the total number of subsets for an empty set?

A 0

B 1

C 2

D Undefined

An empty set has exactly one subset: the empty subset.

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

A {1, 2}

B {1}

C {}

D {2, 3}

{2, 3} is not a subset because 3 is not in the original set.

Explain how bitmasking helps generate all subsets of a set.

Think about how binary numbers can represent choices for each element.

Describe the steps to generate subsets of a set of size n using bitmask in C.

Focus on the loop and bit checking process.

Practice

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

easy

A. All possible subsets of the set

B. Only the largest subset of the set

C. Only subsets with even number of elements

D. Only subsets with odd number of elements

Solution

1. Step 1: Understand bitmask representation

   Each bit in the 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, all combinations of included/excluded elements are covered, producing all subsets.

3. Final Answer:

   All possible subsets of the set -> Option A

4. Quick Check:

   Bitmask = All subsets [OK]

Hint: Bitmask from 0 to 2^n-1 covers all subsets [OK]

Common Mistakes:

• Thinking bitmask generates only largest subsets
• Confusing bitmask with subsets of fixed size
• Assuming bitmask excludes empty subset

2. Which of the following C code snippets correctly initializes the loop to generate all subsets of an array of size n using bitmask?

easy

A. for (int mask = 0; mask < n; mask++)

B. for (int mask = 0; mask < (1 << n); mask++)

C. for (int mask = 0; mask <= n; mask++)

D. for (int mask = 1; mask <= n; mask++)

Solution

1. Step 1: Understand bitmask range

   Bitmask must cover all numbers from 0 to 2^n - 1, which is (1 << n) in C.

2. Step 2: Check loop conditions

   Loop from 0 to less than (1 << n) correctly iterates all subsets.

3. Final Answer:

   for (int mask = 0; mask < (1 << n); mask++) -> Option B

4. Quick Check:

   Loop from 0 to 2^n-1 [OK]

Hint: Use (1 << n) for 2^n in bitmask loops [OK]

Common Mistakes:

• Using mask <= n instead of mask < 2^n
• Starting loop from 1 excludes empty subset
• Using mask < n only covers n subsets

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

int arr[] = {1, 2};
int n = 2;
for (int mask = 0; mask < (1 << n); mask++) {
    printf("{");
    for (int i = 0; i < n; i++) {
        if (mask & (1 << i)) {
            printf("%d", arr[i]);
        }
    }
    printf("}\n");
}

medium

A. {}
{1}
{2}
{1, 2}

B. {}
{1}
{2}
{1 2}

C. {}
{1}
{2}
{12}

D. {}
{1}
{2}
{1}{2}

Solution

1. Step 1: Understand bitmask iterations

   mask goes from 0 to 3 (binary 00 to 11), representing subsets: empty, {1}, {2}, {1,2}.

2. Step 2: Trace output formatting

   Elements printed without spaces or commas, so subsets print as {}, {1}, {2}, {12}.

3. Final Answer:

   {} {1} {2} {12} -> Option C

4. Quick Check:

   Bitmask subsets printed without separators [OK]

Hint: Check print format carefully for separators [OK]

Common Mistakes:

• Assuming spaces or commas between elements
• Confusing bitmask order of elements
• Missing empty subset output

4. Identify the error in the following C code that attempts to generate subsets using bitmask:

int arr[] = {1, 2, 3};
int n = 3;
for (int mask = 0; mask <= (1 << n); mask++) {
    for (int i = 0; i < n; i++) {
        if (mask & (1 << i)) {
            printf("%d ", arr[i]);
        }
    }
    printf("\n");
}

medium

A. Loop condition should be mask < (1 << n), not <=

B. Bitwise AND operator is incorrect

C. Loop should start from 0 to include empty subset

D. Array indexing is out of bounds

Solution

1. Step 1: Check loop range correctness

   Loop runs from 0 to (1 << n) inclusive, which is 0 to 8 for n=3, but max mask should be 7 (0 to 7).

2. Step 2: Identify off-by-one error

   Using mask <= (1 << n) causes mask=8, which is out of valid subset range, causing incorrect behavior.

3. Final Answer:

   Loop condition should be mask < (1 << n), not <= -> Option A

4. Quick Check:

   Loop must run from 0 to 2^n - 1 [OK]

Hint: Use mask < (1 << n), not <= [OK]

Common Mistakes:

• Starting loop from 1 excludes empty subset
• Using <= causes out-of-range mask
• Misunderstanding bitwise AND usage

5. Given an array arr = {1, 2, 3, 4}, how many subsets generated by bitmask will have exactly two elements?

medium

A. 12

B. 4

C. 8

D. 6

Solution

1. Step 1: Calculate total subsets of size 2

   Number of subsets with exactly 2 elements from 4 elements is combination 4 choose 2 = 6.

2. Step 2: Understand bitmask filtering

   Among all 2^4=16 subsets, exactly 6 have two bits set in their bitmask representing two elements included.

3. Final Answer:

   6 -> Option D

4. Quick Check:

   Combination(4,2) = 6 [OK]

Hint: Count subsets with 2 bits set = C(n,2) [OK]

Common Mistakes:

• Counting total subsets instead of size 2
• Confusing subsets with permutations
• Miscounting bitmask bits set