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Reverse Bits

Number: 190

Difficulty: Easy

Paid? No

Companies: Apple, Meta, Nvidia, Google, Qualcomm, Amazon, Airbnb

Problem Description

Given a 32-bit binary string representing an unsigned integer, reverse its bits and return the new integer. For example, given the input "00000010100101000001111010011100", the output should be 964176192 because the reversed binary is "00111001011110000010100101000000".

Key Insights

  • The input is a binary string of fixed length (32 bits).
  • Reversing the bits is equivalent to reversing the string.
  • The reversed binary string can be converted back into its integer representation.
  • Since the number of bits is constant (32), the solution can be achieved in constant time and constant space.
  • For performance optimization when this function is called many times, caching may be applied for common intermediate results.

Space and Time Complexity

Time Complexity: O(1) – We always process 32 bits regardless of the input. Space Complexity: O(1) – Only constant extra space is used.

Solution

We solve the problem by reversing the 32-character binary string representing the unsigned integer. Once reversed, the new binary string is converted into its integer value. An alternative solution involves using bitwise operations where you iterate over each bit, shift the result to the left, and add the current bit. This approach does the reversal one bit at a time. The chosen approach leverages string reversal which is straightforward to implement and understand.

Code Solutions

# Function to reverse bits of a 32-bit binary string.
def reverse_bits(n: str) -> int:
    # Reverse the binary string using slicing.
    reversed_binary = n[::-1]
    # Convert the reversed binary string to an integer.
    result = int(reversed_binary, 2)
    return result

# Example usage:
binary_input = "00000010100101000001111010011100"
print(reverse_bits(binary_input))  # Expected output: 964176192
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