Set Clear Toggle a Specific Bit in DSA Javascript - Time & Space Complexity

Time Complexity: Set Clear Toggle a Specific Bit

O(1)

Understanding Time Complexity

We want to understand how fast operations like setting, clearing, or toggling a specific bit run.

How does the time to change one bit grow as the number size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function setBit(num, pos) {
  return num | (1 << pos);
}

function clearBit(num, pos) {
  return num & ~(1 << pos);
}

function toggleBit(num, pos) {
  return num ^ (1 << pos);
}
    

This code sets, clears, or toggles a bit at a given position in a number using bitwise operations.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single bitwise operation per function call.
• How many times: Exactly once per call, no loops or recursion.

How Execution Grows With Input

Changing one bit takes the same steps no matter how big the number is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The operation count stays constant regardless of input size.

Final Time Complexity

Time Complexity: O(1)

This means the time to set, clear, or toggle a bit does not change as the number gets bigger.

Common Mistake

[X] Wrong: "Changing a bit takes longer if the number is bigger because there are more bits."

[OK] Correct: Bitwise operations directly access the bit position without checking others, so time stays the same.

Interview Connect

Knowing that bit operations run in constant time helps you write efficient low-level code and answer questions confidently.

Self-Check

"What if we tried to set multiple bits at once? How would the time complexity change?"

Practice

1. What does the operation num | (1 << k) do to the number num in terms of bits?

easy

A. Toggles the k-th bit of num

B. Sets the k-th bit of num to 1

C. Clears the k-th bit of num to 0

D. Checks if the k-th bit of num is set

Solution

1. Step 1: Understand bitwise OR with shifted 1

   The expression 1 << k creates a number with only the k-th bit set to 1.

2. Step 2: Apply OR operation to set bit

   Using num | (1 << k) sets the k-th bit of num to 1 without changing other bits.

3. Final Answer:

   Sets the k-th bit of num to 1 -> Option B

4. Quick Check:

   Bitwise OR with 1 at position k sets that bit [OK]

Hint: Use OR with shifted 1 to set a bit [OK]

Common Mistakes:

• Confusing set with clear operation
• Thinking it toggles the bit
• Assuming it checks the bit instead

2. Which of the following JavaScript expressions correctly clears the k-th bit of a number num?

easy

A. num ^ (1 << k)

B. num | ~(1 << k)

C. num & (1 << k)

D. num & ~(1 << k)

Solution

1. Step 1: Understand clearing a bit

   To clear the k-th bit, we want to set it to 0 while keeping others unchanged.

2. Step 2: Use AND with NOT mask

   The mask ~(1 << k) has all bits 1 except the k-th bit 0. ANDing with this clears the k-th bit.

3. Final Answer:

   num & ~(1 << k) -> Option D

4. Quick Check:

   AND with inverted mask clears bit [OK]

Hint: AND with NOT of shifted 1 clears a bit [OK]

Common Mistakes:

• Using OR instead of AND to clear bits
• Forgetting to invert the mask
• Using XOR which toggles instead of clears

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

let num = 10; // binary 1010
let k = 1;
num = num ^ (1 << k);
console.log(num);

medium

A. 8

B. 10

C. 12

D. 14

Solution

1. Step 1: Understand initial values and bit positions

   num = 10 (binary 1010), k = 1 means second bit from right (0-based).

2. Step 2: Apply XOR to toggle k-th bit

   1 << 1 = 2 (binary 0010). XOR toggles bit 1: 1010 ^ 0010 = 1000 (binary), which is 8 decimal.

3. Final Answer:

   8 -> Option A

4. Quick Check:

   XOR toggles bit 1: 10 -> 8 [OK]

Hint: XOR toggles the bit at position k [OK]

Common Mistakes:

• Confusing XOR with OR or AND
• Miscounting bit positions (0-based)
• Not converting binary to decimal correctly

4. The following code is intended to toggle the k-th bit of num. What is the error?

function toggleBit(num, k) {
  return num & (1 << k);
}
console.log(toggleBit(5, 0));

medium

A. Function does not return a number

B. Incorrect bit shift direction

C. Using AND instead of XOR to toggle the bit

D. Missing parentheses around bit shift

Solution

1. Step 1: Identify intended toggle operation

   Toggling a bit requires flipping it: 0 to 1 or 1 to 0.

2. Step 2: Check the operator used

   The code uses AND (&) which masks bits, not toggles. XOR (^) is needed to toggle bits.

3. Final Answer:

   Using AND instead of XOR to toggle the bit -> Option C

4. Quick Check:

   Toggle needs XOR, not AND [OK]

Hint: Toggle bits with XOR, not AND [OK]

Common Mistakes:

• Using AND or OR instead of XOR for toggle
• Confusing toggle with set or clear
• Ignoring operator precedence

5. You want to write a function updateBit(num, k, bitValue) that sets the k-th bit of num to bitValue (0 or 1). Which of the following implementations is correct?

hard

A. return (num & ~(1 << k)) | (bitValue << k);

B. return (num | (bitValue << k)) & ~(bitValue << k);

C. return num ^ (bitValue << k);

D. return num & (bitValue << k);

Solution

1. Step 1: Clear the k-th bit first

   Use num & ~(1 << k) to clear the k-th bit regardless of its current value.

2. Step 2: Set the k-th bit to bitValue

   Shift bitValue to k-th position and OR it with cleared number to set the bit correctly.

3. Final Answer:

   return (num & ~(1 << k)) | (bitValue << k); -> Option A

4. Quick Check:

   Clear then set bit with OR [OK]

Hint: Clear bit then OR with shifted bitValue to update [OK]

Common Mistakes:

• Using XOR which toggles instead of sets
• Not clearing bit before setting
• Using AND which masks bits incorrectly