Count Set Bits Brian Kernighan Algorithm in DSA Typescript - 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 number's binary form. This is useful in many areas like error detection and network data processing.

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

📋 What You'll Learn

Create a variable called num with the exact value 29

Create a variable called count and set it to 0

Use a while loop with the condition num > 0

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

Inside the loop, increment count by 1

Print the value of count using console.log(count)

💡 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 like Brian Kernighan's is valuable for software engineers working with low-level data manipulation and optimization.

1

Create the number variable

Create a variable called num and set it to the exact value 29.

DSA Typescript

# Your code here
// Create variable num with value 29

Hint

Use let num = 29; to create the variable.

2

Create the count variable

Create a variable called count and set it to 0.

DSA Typescript

let num = 29;
# Your code here
// Create variable count with value 0

Hint

Use let count = 0; to create the variable.

3

Implement the Brian Kernighan loop

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

DSA Typescript

let num = 29;
let count = 0;
# Your code here
// Use while loop to count set bits using Brian Kernighan algorithm

Hint

The loop runs while num is greater than 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.log(count).

DSA Typescript

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

Hint

Use console.log(count); to display the number of set bits.

Practice

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

easy

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

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

C. It shifts the number to the right until it becomes zero without checking bits.

D. It adds all bits of the number without any bitwise operation.

Solution

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

   The Brian Kernighan algorithm clears the least significant set bit in each iteration by doing n = n & (n-1).

2. Step 2: Effect of clearing bits

   Each clearing reduces the number of set bits by one until the number becomes zero, counting how many set bits were present.

3. Final Answer:

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

4. Quick Check:

   Clearing bits one by one counts set bits [OK]

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

Common Mistakes:

• Confusing bit count with digit count
• Using simple right shifts without bit checks
• Ignoring bitwise AND operation

2. Which of the following is the correct TypeScript syntax to clear the least significant set bit of a number n?

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 bitwise operation to clear least set bit

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

2. Step 2: Verify other options

   OR, XOR, and addition do not clear the least significant set bit correctly.

3. Final Answer:

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

4. Quick Check:

   AND with (n-1) clears least set bit [OK]

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

Common Mistakes:

• Using OR or XOR instead of AND
• Adding numbers instead of bitwise operations
• Missing parentheses around (n - 1)

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

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

console.log(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 (1,1,0,1).

2. Step 2: Apply Brian Kernighan algorithm steps

   Each iteration clears one set bit, so count increments 3 times until n becomes 0.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Number of 1s in 1101 = 3 [OK]

Hint: Count 1s in binary using n & (n-1) loop [OK]

Common Mistakes:

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

4. Identify the error in this TypeScript function that tries to count set bits using Brian Kernighan's algorithm:

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

medium

A. Return statement is missing.

B. Using != instead of > in the while condition.

C. Incorrect initialization of count variable.

D. Missing parentheses around (n - 1) in the expression.

Solution

1. Step 1: Analyze the expression inside the loop

   The expression n = n & n - 1 lacks parentheses, so it is evaluated as (n & n) - 1, which is incorrect.

2. Step 2: Correct expression

   It should be n = n & (n - 1) to correctly clear the least significant set bit.

3. Final Answer:

   Missing parentheses around (n - 1) in the expression. -> Option D

4. Quick Check:

   Parentheses ensure correct order of operations [OK]

Hint: Use parentheses: n = n & (n - 1) [OK]

Common Mistakes:

• Using != 0 causing potential infinite loop for negatives
• Assuming both conditions always equivalent
• Operator precedence confusion causing wrong calculation

5. Given an array of numbers [5, 7, 10], which TypeScript code correctly uses Brian Kernighan's algorithm to return an array of their set bit counts?

hard

A. const counts = arr.map(n => {
let count = 0;
while (n > 0) {
n = n >> 1;
count++;
}
return count;
});

B. const counts = arr.map(n => n.toString(2).length);

C. const counts = arr.map(n => {
let count = 0;
while (n > 0) {
n = n & (n - 1);
count++;
}
return count;
});

D. const counts = arr.map(n => {
let count = 0;
for (let i = 0; i < 32; i++) {
if ((n & (1 << i)) !== 0) count++;
}
return count;
});

Solution

1. Step 1: Understand Brian Kernighan's algorithm usage

   const counts = arr.map(n => { let count = 0; while (n > 0) { n = n & (n - 1); count++; } return count; }); uses the correct loop with n = n & (n - 1) to count set bits for each number.

2. Step 2: Check other options for correctness

   const counts = arr.map(n => n.toString(2).length); counts total binary digits, not set bits. const counts = arr.map(n => { let count = 0; while (n > 0) { n = n >> 1; count++; } return count; }); counts total bits by shifting, not set bits. const counts = arr.map(n => { let count = 0; for (let i = 0; i < 32; i++) { if ((n & (1 << i)) !== 0) count++; } return count; }); uses a loop checking each bit, which works but is not Brian Kernighan's algorithm.

3. Final Answer:

   const counts = arr.map(n => { let count = 0; while (n > 0) { n = n & (n - 1); count++; } return count; }); -> Option C

4. Quick Check:

   Use n & (n-1) loop inside map for set bits [OK]

Hint: Use map with n & (n-1) loop for each number [OK]

Common Mistakes:

• Counting binary string length instead of set bits
• Using right shift without bit check
• Confusing bitwise loop with simple iteration