Count Set Bits Brian Kernighan Algorithm in DSA C# - Build from Scratch

Count Set Bits using Brian Kernighan Algorithm

📖 Scenario: Imagine you are working with binary numbers in a computer system. You want to count how many bits are set to 1 in a given number. This is useful in many areas like error detection, cryptography, and optimization.

🎯 Goal: You will build a program that counts the number of set bits (1s) in an integer using the Brian Kernighan algorithm, which efficiently reduces the number of operations by turning off the rightmost set bit in each step.

📋 What You'll Learn

Create an integer variable named number with the value 29

Create an integer variable named count and initialize it to 0

Use a while loop with the condition number != 0

Inside the loop, update number using number = number & (number - 1)

Increment count by 1 inside the loop

Print the value of count after the loop ends

💡 Why This Matters

🌍 Real World

Counting set bits is useful in network masks, cryptography, and optimizing algorithms that depend on bit manipulation.

💼 Career

Understanding bitwise operations and efficient algorithms is important for software developers working in systems programming, embedded systems, and performance-critical applications.

1

Create the initial number variable

Create an integer variable called number and set it to 29.

DSA C#

# Create an integer variable called number and set it to 29
# Your code here

Hint

Use int number = 29; to create the variable.

2

Initialize the count variable

Create an integer variable called count and set it to 0.

DSA C#

int number = 29;
# Create an integer variable called count and set it to 0
# Your code here

Hint

Use int count = 0; to start counting from zero.

3

Implement the Brian Kernighan loop

Use a while loop with the condition number != 0. Inside the loop, update number with number = number & (number - 1) and increment count by 1.

DSA C#

int number = 29;
int count = 0;
# Use a while loop with condition number != 0
# Inside the loop, update number and increment count
# Your code here

Hint

The loop runs until number becomes zero. Each time, it removes the rightmost set bit and increases count.

4

Print the count of set bits

Print the value of count using Console.WriteLine(count);.

DSA C#

int number = 29;
int count = 0;
while (number != 0)
{
    number = number & (number - 1);
    count++;
}
# Print the count variable
# Your code here

Hint

Use Console.WriteLine(count); to display the number of set bits.

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