Why Count Set Bits Brian Kernighan Algorithm in DSA Javascript?

The Big Idea

What if you could count all the 1s in a number's binary form without checking every single bit?

The Scenario

Imagine you have a long list of numbers, and you want to know how many 1s are in their binary forms. Doing this by checking each bit one by one feels like counting grains of sand on a beach.

The Problem

Checking every bit manually means going through all bits even if most are zeros. This takes a lot of time and can be very slow for big numbers. It's easy to make mistakes and lose patience.

The Solution

The Brian Kernighan Algorithm smartly jumps from one 1-bit to the next by turning off the rightmost 1-bit each time. This way, it only counts the actual 1s, skipping all zeros quickly and saving time.

Before vs After

✗ Before

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

✓ After

function countSetBits(number) {
  let count = 0;
  while (number > 0) {
    number &= (number - 1);
    count++;
  }
  return count;
}

What It Enables

This algorithm makes counting 1s in binary fast and efficient, even for very large numbers.

Real Life Example

In networking, counting set bits helps quickly find how many devices are active in a network mask, speeding up network management.

Key Takeaways

Manual bit checking is slow and error-prone.

Brian Kernighan Algorithm skips zeros and counts only 1s efficiently.

It makes bit counting fast and practical for big numbers.

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