Count Set Bits Brian Kernighan Algorithm in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the count variable to zero.

DSA C#

int count = [1];

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

An

B1

C-1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing count to 1 or n instead of 0.

We start counting set bits from zero, so count should be initialized to 0.

2fill in blank

medium

Complete the while loop condition to run until n becomes zero.

DSA C#

while ([1] != 0) {
    n = n & (n - 1);
    count++;
}

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An

Bcount

Ccount++

Dn & 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using count or n & 1 in the loop condition instead of n.

The loop runs while n is not zero, because each iteration removes one set bit.

3fill in blank

hard

Fix the error in the bit manipulation expression inside the loop.

DSA C#

n = n [1] (n - 1);

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

A&

B^

C|

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using | or ^ instead of & in the expression.

The correct operation is bitwise AND (&) between n and (n - 1) to clear the rightmost set bit.

4fill in blank

hard

Fill both blanks to complete the method signature and return statement.

DSA C#

public static int [1](int n) {
    int count = 0;
    while (n != 0) {
        n = n & (n - 1);
        count++;
    }
    return [2];
}

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ACountSetBits

Bcount

Cn

DSetBitsCount

Attempts:

3 left

💡 Hint

Common Mistakes

Returning n instead of count.

Using wrong method name.

The method name is CountSetBits and it returns the count variable.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps numbers to their set bit counts for 1 to 5.

DSA C#

var result = new Dictionary<int, int> {
    { [1], [2].[3](x) }
};

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

Ax

BCountSetBits

CInvoke

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of x as key.

Not calling the method correctly.

We map each number x to the result of CountSetBits.Invoke(x) in the dictionary.

Practice

1. What does the Brian Kernighan algorithm do when counting set bits in an integer?

easy

A. It converts the number to a string and counts characters.

B. It counts the total number of digits in the integer.

C. It shifts the bits to the right one by one and counts zeros.

D. It repeatedly clears the least significant set bit until the number becomes zero.

Solution

1. Step 1: Understand the algorithm's main operation

   The Brian Kernighan algorithm works by clearing the least significant set bit in each iteration.

2. Step 2: Effect of clearing bits on counting set bits

   Each time it clears a set bit, it increments the count until the number becomes zero.

3. Final Answer:

   It repeatedly clears the least significant set bit until the number becomes zero. -> Option D

4. Quick Check:

   Clearing bits counts set bits [OK]

Hint: Clear least set bit repeatedly to count ones [OK]

Common Mistakes:

• Counting zeros instead of ones
• Using string conversion to count bits
• Shifting bits without clearing

2. Which of the following is the correct syntax to clear the least significant set bit in C# using Brian Kernighan's method?

easy

A. n = n & (n - 1);

B. n = n | (n - 1);

C. n = n ^ (n + 1);

D. n = n << 1;

Solution

1. Step 1: Identify the bit clearing operation

   The expression n = n & (n - 1) clears the least significant set bit in n.

2. Step 2: Verify other options

   Other options perform different bitwise operations that do not clear the least significant set bit.

3. Final Answer:

   n = n & (n - 1); -> Option A

4. Quick Check:

   Use n & (n-1) to clear least set bit [OK]

Hint: Use n & (n-1) to clear least set bit [OK]

Common Mistakes:

• Using OR instead of AND
• Using XOR with n+1 incorrectly
• Using left shift which moves bits

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

int countSetBits(int n) {
    int count = 0;
    while (n > 0) {
        n = n & (n - 1);
        count++;
    }
    return count;
}

Console.WriteLine(countSetBits(13));

medium

A. 3

B. 4

C. 2

D. 5

Solution

1. Step 1: Convert 13 to binary and count set bits

   13 in binary is 1101, which has three set bits (1s).

2. Step 2: Apply Brian Kernighan's algorithm

   Each iteration clears one set bit, so the loop runs 3 times, incrementing count to 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Binary 1101 has 3 ones [OK]

Hint: Count 1s in binary of number [OK]

Common Mistakes:

• Counting total bits instead of set bits
• Misunderstanding bitwise AND operation
• Off-by-one errors in loop

4. Identify the error in the following C# code that attempts to count set bits using Brian Kernighan's algorithm:

int countSetBits(int n) {
    int count = 0;
    while (n != 0) {
        n = n & (n + 1);
        count++;
    }
    return count;
}

medium

A. Missing return statement

B. Using n & (n + 1) instead of n & (n - 1)

C. Count variable not initialized

D. Incorrect loop condition; should be n > 0

Solution

1. Step 1: Check the bit clearing expression

   The code uses n & (n + 1), which does not clear the least significant set bit correctly.

2. Step 2: Correct expression for clearing bits

   The correct expression is n & (n - 1) to clear the least significant set bit.

3. Final Answer:

   Using n & (n + 1) instead of n & (n - 1) -> Option B

4. Quick Check:

   Use n & (n-1) to clear bits [OK]

Hint: Always use n & (n-1) to clear least set bit [OK]

Common Mistakes:

• Using n & (n + 1) which is incorrect
• Confusing loop conditions
• Forgetting to initialize count

5. You want to count set bits in a large list of integers efficiently using Brian Kernighan's algorithm in C#. Which approach is best to optimize performance?

hard

A. Convert each integer to binary string and count '1' characters sequentially.

B. Use a simple for loop shifting bits right and counting set bits sequentially.

C. Use Brian Kernighan's algorithm inside a parallel loop to count bits for each integer concurrently.

D. Store all integers in a list and count set bits only for the first element.

Solution

1. Step 1: Understand the need for efficiency

   Counting set bits for many integers can be slow if done sequentially.

2. Step 2: Use parallel processing with Brian Kernighan's algorithm

   Running the efficient bit counting algorithm concurrently on multiple integers speeds up processing.

3. Final Answer:

   Use Brian Kernighan's algorithm inside a parallel loop to count bits for each integer concurrently. -> Option C

4. Quick Check:

   Parallel + efficient algorithm = best performance [OK]

Hint: Combine parallelism with Brian Kernighan's method [OK]

Common Mistakes:

• Using string conversion which is slow
• Sequential bit shifting which is less efficient
• Ignoring concurrency for large data