Set Clear Toggle a Specific Bit in DSA Rust - 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 needed change when we work with bigger numbers or more bits?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn set_bit(num: u32, pos: u8) -> u32 {
    num | (1u32 << pos)
}

fn clear_bit(num: u32, pos: u8) -> u32 {
    num & !(1u32 << pos)
}

fn toggle_bit(num: u32, pos: u8) -> u32 {
    num ^ (1u32 << pos)
}
    

This code sets, clears, or toggles a bit at a given position in a 32-bit number.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Bitwise shift and bitwise logical operations.
• How many times: Each operation runs exactly once per function call.

How Execution Grows With Input

Each operation works on fixed-size 32-bit numbers, so the time does not grow with input size.

Input Size (n)	Approx. Operations
10	3 (shift, OR/AND/XOR)
100	3 (same fixed steps)
1000	3 (still same fixed steps)

Pattern observation: The number of steps stays the same no matter how big the number is.

Final Time Complexity

Time Complexity: O(1)

This means the operation takes the same amount of time regardless of input size.

Common Mistake

[X] Wrong: "Setting a bit takes longer if the number is bigger or has more bits."

[OK] Correct: Bitwise operations work on fixed-size numbers and do not depend on the number's value or size.

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 a bit in a very large number stored as an array of bits? How would the time complexity change?"

Practice

1. What does the operation num | (1 << pos) do to the bit at position pos in num?

easy

A. Sets the bit at position pos to 1

B. Clears the bit at position pos to 0

C. Toggles the bit at position pos

D. Checks if the bit at position pos is set

Solution

1. Step 1: Understand the bitwise OR with shifted 1

   The expression 1 << pos creates a number with only the bit at position pos set to 1, all others 0.

2. Step 2: Apply OR operation to set the bit

   Using num | (1 << pos) sets the bit at pos to 1 regardless of its previous value, leaving other bits unchanged.

3. Final Answer:

   Sets the bit at position pos to 1 -> Option A

4. Quick Check:

   OR with 1 at pos sets bit to 1 [OK]

Hint: OR with 1 at position sets that bit to 1 [OK]

Common Mistakes:

• Confusing OR with XOR for toggling
• Thinking it clears the bit instead of setting
• Assuming it checks the bit instead of modifying

2. Which of the following Rust code snippets correctly clears (sets to 0) the bit at position pos in num?

easy

A. num & (1 << pos)

B. num & !(1 << pos)

C. num | !(1 << pos)

D. num ^ (1 << pos)

Solution

1. Step 1: Create mask with 0 at pos and 1 elsewhere

   The expression !(1 << pos) creates a mask with all bits 1 except bit pos which is 0.

2. Step 2: AND operation clears bit at pos

   Using num & !(1 << pos) clears the bit at pos to 0, keeping other bits unchanged.

3. Final Answer:

   num & !(1 << pos) -> Option B

4. Quick Check:

   AND with inverted mask clears bit [OK]

Hint: AND with NOT mask clears bit at position [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 Rust code?

let mut num = 0b1010; // binary 10
let pos = 1;
num ^= 1 << pos;
println!("{:04b}", num);

medium

A. 1000

B. 1010

C. 1011

D. 1110

Solution

1. Step 1: Understand initial value and bit position

   Initial num is binary 1010 (decimal 10). Position pos is 1 (counting from 0 at right).

2. Step 2: Toggle bit at position 1 using XOR

   1 << pos is 0010. XOR toggles bit 1: 1010 XOR 0010 = 1000 (decimal 8).

3. Final Answer:

   1000 -> Option A

4. Quick Check:

   XOR toggles bit 1: 1010 -> 1000 [OK]

Hint: XOR with 1 toggles the bit at position [OK]

Common Mistakes:

• Confusing XOR with OR or AND
• Miscounting bit positions
• Printing decimal instead of binary

4. Identify the error in this Rust code that tries to toggle the bit at position pos in num:

let mut num = 0b1001;
let pos = 2;
num = num | (1 << pos);
num = num ^ (1 << pos);
println!("{:04b}", num);

medium

A. The code will cause a compile error

B. The bit position is out of range

C. The bit is toggled twice, so no change occurs

D. The OR operator should be AND to toggle

Solution

1. Step 1: Analyze the first operation (OR)

   num | (1 << pos) sets bit 2 to 1. Bit 2 was 0 in 1001, so num becomes 1101.

2. Step 2: Analyze the second operation (XOR)

   num ^ (1 << pos) toggles bit 2 from 1 back to 0, resulting in 1001.

3. Step 3: Check final output

   After both operations, bit 2 was set then toggled back, so no net change occurs.

4. Final Answer:

   The bit is toggled twice, so no change occurs -> Option C

5. Quick Check:

   Setting then toggling same bit cancels out [OK]

Hint: Setting then toggling same bit cancels effect [OK]

Common Mistakes:

• Assuming OR then XOR always toggles bit
• Ignoring bit position indexing
• Expecting compile error where none exists

5. Given a 8-bit number num = 0b11001100, write the result after toggling bits at positions 2, 3, and 7 in sequence using Rust bitwise operations. What is the final binary value?

hard

A. 10001100

B. 01001100

C. 11001100

D. 01000000

Solution

1. Step 1: Initial value and bit positions

   Initial num is 11001100 (bits 7 to 0). Positions to toggle: 2, 3, 7.

2. Step 2: Toggle bit 2

   Bit 2 is 1 (counting from 0 rightmost). Toggle flips it to 0: 11001100 -> 11001000.

3. Step 3: Toggle bit 3

   Bit 3 is 1. Toggle flips it to 0: 11001000 -> 11000000.

4. Step 4: Toggle bit 7

   Bit 7 is 1. Toggle flips it to 0: 11000000 -> 01000000.

5. Step 5: Final binary value

   Final value is 01000000 in binary (bits 7,3,2 toggled to 0, others unchanged).

6. Final Answer:

   01000000 -> Option D

7. Quick Check:

   Toggle bits 2,3,7 flips those bits [OK]

Hint: Toggle bits one by one with XOR [OK]

Common Mistakes:

• Miscounting bit positions from right
• Forgetting to toggle bits in sequence
• Confusing toggle with set or clear