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

Count Set Bits using Brian Kernighan Algorithm

📖 Scenario: You are working on a simple program that counts how many bits are set to 1 in a binary number. This is useful in many areas like error detection and network data processing.

🎯 Goal: Build a program that counts the number of set bits (1s) in a given positive integer using the Brian Kernighan algorithm.

📋 What You'll Learn

Create a variable to hold the number to check

Create a variable to count the set bits

Use a loop with Brian Kernighan's method to count set bits

Print the final count of set bits

💡 Why This Matters

🌍 Real World

Counting set bits is useful in network programming, cryptography, and error detection where binary data is processed.

💼 Career

Understanding bitwise operations and efficient algorithms is important for software engineers working with low-level data or performance-critical applications.

1

Create the number variable

Create a variable called num and set it to 29.

DSA Javascript

// Your code here

Hint

Use let num = 29; to create the number variable.

2

Create the count variable

Create a variable called count and set it to 0.

DSA Javascript

let num = 29;
// Your code here

Hint

Use let count = 0; to start counting set bits.

3

Use Brian Kernighan's algorithm to count set bits

Use a while loop with the condition num > 0. Inside the loop, update num to num & (num - 1) and increase count by 1.

DSA Javascript

let num = 29;
let count = 0;
// Your code here

Hint

Use num = num & (num - 1); inside the loop to remove the rightmost set bit.

4

Print the count of set bits

Write console.log(count); to print the number of set bits.

DSA Javascript

let num = 29;
let count = 0;
while (num > 0) {
    num = num & (num - 1);
    count += 1;
}
// Your code here

Hint

The number 29 in binary is 11101, which has 4 set bits.

Practice

1. What does the Brian Kernighan algorithm do when counting set bits in a number?

easy

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

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

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

D. It shifts the number to the right and counts zeros

Solution

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

   The algorithm clears the least significant set bit by doing n = n & (n-1) repeatedly.

2. Step 2: Effect of clearing bits

   Each operation removes one set bit, counting how many times this happens gives the total set bits.

3. Final Answer:

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

4. Quick Check:

   Clearing bits counts set bits [OK]

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

Common Mistakes:

• Counting total digits instead of set bits
• Counting zeros instead of ones
• Using string length instead of bit operations

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

easy

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

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

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

D. n = n ^ (n - 1);

Solution

1. Step 1: Identify the bit clearing operation

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

2. Step 2: Verify other options

   Other options do not clear the least significant set bit correctly.

3. Final Answer:

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

4. Quick Check:

   Use AND with (n-1) to clear bit [OK]

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

Common Mistakes:

• Using OR or XOR instead of AND
• Adding instead of subtracting 1
• Confusing bitwise operators

3. What is the output of the following JavaScript code?

function countSetBits(n) {
  let count = 0;
  while (n > 0) {
    n = n & (n - 1);
    count++;
  }
  return count;
}
console.log(countSetBits(13));

medium

A. 3

B. 2

C. 4

D. 5

Solution

1. Step 1: Convert 13 to binary

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

2. Step 2: Apply Brian Kernighan's algorithm

   Each loop clears one set bit, so count increments 3 times before n becomes 0.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   13 (1101) has 3 set bits [OK]

Hint: Count set bits by clearing one bit each loop [OK]

Common Mistakes:

• Counting total bits instead of set bits
• Miscounting binary representation
• Off-by-one errors in loop

4. Identify the error in the following code snippet that uses Brian Kernighan's algorithm:

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

medium

A. Not initializing count to 1

B. Using while loop instead of for loop

C. Missing return statement

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

Solution

1. Step 1: Check the bit clearing operation

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

2. Step 2: Correct operation

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

3. Final Answer:

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

4. Quick Check:

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

Hint: Use n & (n-1), not n & (n+1) [OK]

Common Mistakes:

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

5. Given an array of integers, which code snippet correctly uses Brian Kernighan's algorithm to find the total count of set bits in all elements?

const arr = [3, 5, 7];
// Choose the correct code to count all set bits

A) let total = 0;
for(let n of arr) {
  while(n > 0) {
    n = n & (n - 1);
    total++;
  }
}
console.log(total);

B) let total = 0;
for(let n of arr) {
  total += n.toString(2).length;
}
console.log(total);

C) let total = 0;
for(let n of arr) {
  while(n > 0) {
    n = n | (n - 1);
    total++;
  }
}
console.log(total);

D) let total = 0;
for(let n of arr) {
  total += n & (n - 1);
}
console.log(total);

hard

A. Correctly counts set bits using Brian Kernighan's method

B. Counts total binary digits, not set bits

C. Uses OR instead of AND, incorrect bit clearing

D. Adds bitwise AND result directly, incorrect counting

Solution

1. Step 1: Identify the correct implementation

   The implementation using while(n > 0) { n = n & (n - 1); total++; } correctly applies Brian Kernighan's algorithm by clearing the least significant set bit repeatedly for each array element and incrementing the total count each time.

2. Step 2: Eliminate incorrect options

   The option using n.toString(2).length counts all bits including zeros; using n | (n - 1) does not clear set bits correctly; adding n & (n - 1) directly does not count the number of set bits.

3. Final Answer:

   Correctly counts set bits using Brian Kernighan's method -> Option A

4. Quick Check:

   Clear bits and count in loop [OK]

Hint: Loop clearing bits per number to sum counts [OK]

Common Mistakes:

• Counting total binary length instead of set bits
• Using OR instead of AND for clearing bits
• Adding bitwise results instead of counts