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

Time Complexity: Set Clear Toggle a Specific Bit

O(1)

Understanding Time Complexity

We want to understand how fast we can change a specific bit in a number.

How does the time to set, clear, or toggle a bit grow as the number size changes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def set_bit(num: int, pos: int) -> int:
    return num | (1 << pos)

def clear_bit(num: int, pos: int) -> int:
    return num & ~(1 << pos)

def toggle_bit(num: int, pos: int) -> int:
    return num ^ (1 << pos)

This code sets, clears, or toggles a bit at a given position in an integer.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Bitwise shift and bitwise AND, OR, XOR operations.
• How many times: Each operation runs once per function call, no loops or recursion.

How Execution Grows With Input

Each operation takes the same amount of time regardless of the number size.

Input Size (bits in number)	Approx. Operations
10	3 simple bitwise operations
100	3 simple bitwise operations
1000	3 simple bitwise operations

Pattern observation: The time stays constant no matter how big the number is.

Final Time Complexity

Time Complexity: O(1)

This means the time to set, clear, or toggle a bit does not grow with the size of the number.

Common Mistake

[X] Wrong: "Changing a bit takes longer for bigger numbers because they have more bits."

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

Interview Connect

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

Self-Check

"What if we had to set multiple bits one by one in a loop? How would the time complexity change?"

Practice

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

easy

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

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

C. Toggles the k-th bit of num

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 A

4. Quick Check:

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

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

Common Mistakes:

• Confusing OR with AND operation
• Thinking it clears or toggles the bit
• Misunderstanding bit positions starting at 0

2. Which of the following Python expressions correctly clears (sets to 0) the k-th bit of an integer 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 keep all bits except the k-th bit set to 0.

2. Step 2: Use AND with NOT mask

   The mask ~(1 << k) has all bits set to 1 except the k-th bit which is 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 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 code?

num = 42  # binary 101010
k = 1
result = num ^ (1 << k)
print(result)

medium

A. 40

B. 43

C. 44

D. 41

Solution

1. Step 1: Convert num and identify bit

   42 in binary is 101010. The bit positions (0-based) from right are: bit 0=0, bit 1=1, bit 2=0, bit 3=1, bit 4=0, bit 5=1.

2. Step 2: Toggle bit 1 using XOR

   1 << 1 is 2 (binary 10). XOR toggles bit 1: original bit 1 is 1, toggled to 0. So binary becomes 101000 which is 40 decimal.

3. Final Answer:

   40 -> Option A

4. Quick Check:

   XOR toggles bit 1 from 1 to 0 [OK]

Hint: XOR toggles bit; check original bit to find result [OK]

Common Mistakes:

• Confusing XOR with OR or AND
• Miscounting bit positions
• Forgetting bits are zero-indexed from right

4. The following code is intended to clear the 3rd bit (0-based) of num. What is the error?

num = 29  # binary 11101
k = 3
num = num | ~(1 << k)
print(num)

medium

A. Incorrect bit shift direction

B. Using OR instead of AND to clear the bit

C. Missing parentheses around bitwise NOT

D. No error, code works correctly

Solution

1. Step 1: Understand clearing bit logic

   To clear a bit, we must AND with the inverse mask, not OR.

2. Step 2: Identify incorrect operator usage

   The code uses OR (|) which sets bits, so it cannot clear the bit. It should use AND (&).

3. Final Answer:

   Using OR instead of AND to clear the bit -> Option B

4. Quick Check:

   Clear bit requires AND with NOT mask [OK]

Hint: Clear bit uses AND with NOT mask, not OR [OK]

Common Mistakes:

• Using OR instead of AND to clear bits
• Confusing bitwise NOT precedence
• Assuming code works without testing

5. You have a number num = 0. You want to toggle bits 0, 2, and 4 in sequence using the expression num = num ^ (1 << k). What is the final decimal value of num after toggling these bits?

hard

A. 15

B. 31

C. 21

D. 10

Solution

1. Step 1: Toggle bit 0 on num=0

   num = 0 ^ (1 << 0) = 0 ^ 1 = 1 (binary 00001)

2. Step 2: Toggle bit 2 on num=1

   num = 1 ^ (1 << 2) = 1 ^ 4 = 5 (binary 00101)

3. Step 3: Toggle bit 4 on num=5

   num = 5 ^ (1 << 4) = 5 ^ 16 = 21 (binary 10101)

4. Final Answer:

   21 -> Option C

5. Quick Check:

   Toggling bits 0,2,4 sets bits to 1, sum 1+4+16=21 [OK]

Hint: Toggle bits one by one with XOR, sum powers of two [OK]

Common Mistakes:

• Toggling bits in wrong order
• Miscounting bit positions
• Adding instead of XORing bits