Reverse Bits of a Number in DSA C# - Time & Space Complexity

Time Complexity: Reverse Bits of a Number

O(1)

Understanding Time Complexity

We want to understand how the time needed to reverse bits changes as the number size grows.

How does the number of steps grow when we reverse bits of a number?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public int ReverseBits(int n) {
    int result = 0;
    for (int i = 0; i < 32; i++) {
        result <<= 1;
        result |= (n & 1);
        n >>= 1;
    }
    return result;
}
    

This code reverses the bits of a 32-bit integer by shifting and combining bits one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop runs 32 times, shifting and combining bits each time.
• How many times: Exactly 32 times, once for each bit in the integer.

How Execution Grows With Input

Since the loop always runs 32 times, the number of operations stays the same no matter the input number.

Input Size (bits)	Approx. Operations
10	32
100	32
1000	32

Pattern observation: The operations count does not grow with input size because the bit length is fixed.

Final Time Complexity

Time Complexity: O(1)

This means the time to reverse bits is constant and does not change with the input number.

Common Mistake

[X] Wrong: "The time to reverse bits grows with the value of the number."

[OK] Correct: The loop runs a fixed number of times (32), regardless of the number's value.

Interview Connect

Understanding fixed-time operations like bit reversal helps you explain efficiency clearly and confidently in interviews.

Self-Check

"What if we changed the input to a 64-bit number? How would the time complexity change?"

Practice

1. What does the operation of reversing bits of a number mean in simple terms?

easy

A. Adding 1 to the binary number

B. Changing all 0s to 1s and 1s to 0s

C. Shifting bits to the left by one position

D. Flipping the order of bits from left to right

Solution

1. Step 1: Understand bit order

   Bits are arranged from left (most significant) to right (least significant).

2. Step 2: Reverse means flip order

   Reversing bits means the leftmost bit becomes rightmost and vice versa.

3. Final Answer:

   Flipping the order of bits from left to right -> Option D

4. Quick Check:

   Reverse bits = flip order [OK]

Hint: Reverse bits means flip their order, not invert values [OK]

Common Mistakes:

• Confusing reversing bits with bitwise NOT (inverting bits)
• Thinking reversing means shifting bits
• Assuming reversing adds or subtracts from the number

2. Which of the following C# code snippets correctly reverses the bits of a 4-bit number stored in an integer variable n?

easy

A. int reversed = 0; for(int i=0; i<4; i++) { reversed <<= 1; reversed |= (n & 1); n >>= 1; }

B. int reversed = 0; for(int i=0; i<4; i++) { reversed |= (n & 1) << i; n >>= 1; }

C. int reversed = n << 4;

D. int reversed = ~n;

Solution

1. Step 1: Analyze the loop logic in int reversed = 0; for(int i=0; i<4; i++) { reversed <<= 1; reversed |= (n & 1); n >>= 1; }

   It shifts reversed left by 1, adds least bit of n, then shifts n right by 1, effectively reversing bits.

2. Step 2: Check other options

   int reversed = 0; for(int i=0; i<4; i++) { reversed |= (n & 1) << i; n >>= 1; } does not reverse bits, it copies bits in same order. int reversed = n << 4; shifts bits left, not reverse. int reversed = ~n; inverts bits, not reverse.

3. Final Answer:

   Option A code correctly reverses bits -> Option A

4. Quick Check:

   Shift left + OR + shift right = reverse bits [OK]

Hint: Shift reversed left, OR with last bit, shift input right [OK]

Common Mistakes:

• Using bitwise NOT (~) instead of reversing bits
• Shifting bits without combining properly
• Not updating reversed variable inside loop

3. What is the output of the following C# code snippet?

int n = 13; // binary 1101
int reversed = 0;
for (int i = 0; i < 4; i++) {
  reversed <<= 1;
  reversed |= (n & 1);
  n >>= 1;
}
Console.WriteLine(reversed);

medium

A. 11

B. 7

C. 13

D. 14

Solution

1. Step 1: Convert 13 to 4-bit binary

   13 in binary (4 bits) is 1101.

2. Step 2: Reverse bits step-by-step

   Bits: 1 1 0 1 reversed: 1 0 1 1 which is binary 1011 = decimal 11.

3. Final Answer:

   11 -> Option A

4. Quick Check:

   1101 reversed = 1011 = 11 [OK]

Hint: Reverse bits manually and convert to decimal [OK]

Common Mistakes:

• Not limiting to 4 bits, causing wrong output
• Confusing bit order when reversing
• Assuming reversed number equals original

4. Identify the error in the following C# code that attempts to reverse bits of an 8-bit number:

int ReverseBits(int n) {
  int reversed = 0;
  for (int i = 0; i < 8; i++) {
    reversed |= (n & 1) << i;
    n >>= 1;
  }
  return reversed;
}

medium

A. The variable reversed should be initialized to 1

B. The loop should run 16 times for 8-bit numbers

C. The bits are not reversed; they are copied in the same order

D. The shift operator << is used incorrectly

Solution

1. Step 1: Analyze bit placement in loop

   The code places bits at increasing positions without reversing order.

2. Step 2: Understand reversing bits logic

   Reversing requires shifting reversed left and OR with last bit, not shifting bits by i.

3. Final Answer:

   The bits are not reversed; they are copied in the same order -> Option C

4. Quick Check:

   Shifting bits by i copies order, not reverse [OK]

Hint: Reversing needs shifting reversed left each step, not shifting bits by i [OK]

Common Mistakes:

• Using bit shift by loop index instead of shifting reversed
• Incorrect loop count for bit size
• Initializing reversed incorrectly

5. You want to reverse the bits of a 16-bit unsigned integer and then check if the reversed number is a palindrome in binary (reads the same forwards and backwards). Which approach correctly combines reversing bits and palindrome check?

hard

A. Invert bits using bitwise NOT, then check if inverted equals original

B. Reverse bits using a loop shifting reversed left and OR with last bit, then compare reversed with original

C. Shift original number left by 16 bits, then compare with original

D. Reverse bits by shifting bits by index, then check if reversed equals original

Solution

1. Step 1: Reverse bits correctly

   Use loop to shift reversed left, OR with last bit of original, shift original right.

2. Step 2: Check palindrome by comparing reversed and original

   If reversed equals original, bits form a palindrome.

3. Final Answer:

   Reverse bits using a loop shifting reversed left and OR with last bit, then compare reversed with original -> Option B

4. Quick Check:

   Reverse bits + compare = palindrome check [OK]

Hint: Reverse bits properly, then compare to original for palindrome [OK]

Common Mistakes:

• Using bitwise NOT instead of reversing bits
• Shifting bits incorrectly causing wrong reverse
• Comparing inverted bits instead of reversed bits