Count Set Bits Brian Kernighan Algorithm in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the count variable to zero.

DSA Javascript

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

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

A1

B0

Cn

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing count to 1 instead of 0

Initializing count to n or -1

The count variable should start at 0 because we haven't counted any set bits yet.

2fill in blank

medium

Complete the code to update n by removing the rightmost set bit.

DSA Javascript

function countSetBits(n) {
  let count = 0;
  while (n > 0) {
    n = n [1] (n - 1);
    count++;
  }
  return count;
}

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

A&

B|

C^

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using bitwise OR (|) instead of AND (&)

Using XOR (^) or addition (+) which do not remove bits

Using bitwise AND (&) between n and (n-1) removes the rightmost set bit.

3fill in blank

hard

Fix the error in the loop condition to correctly count set bits.

DSA Javascript

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

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

A==

B<

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using n < 0 which never runs for positive integers

Using n == 0 which never enters the loop

The loop should continue while n is greater than zero to count all set bits.

4fill in blank

hard

Fill both blanks to complete the function that counts set bits using Brian Kernighan's algorithm.

DSA Javascript

function countSetBits(n) {
  let count = [1];
  while (n [2] 0) {
    n = n & (n - 1);
    count++;
  }
  return count;
}

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

A0

B>

C<

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing count to 1

Using '<' instead of '>' in the loop condition

Initialize count to 0 and loop while n is greater than 0 to count all set bits.

5fill in blank

hard

Fill all three blanks to create a function that returns the count of set bits in n using Brian Kernighan's algorithm.

DSA Javascript

function countSetBits(n) {
  let count = [1];
  while (n [2] 0) {
    n = n [3] (n - 1);
    count++;
  }
  return count;
}

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

A0

B>

C&

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect loop condition operators

Using bitwise OR or XOR instead of AND

Initialize count to 0, loop while n > 0, and update n with n & (n - 1) to remove the rightmost set bit.

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