Reverse Bits.py

'''
Reverse bits of a given 32 bits unsigned integer.

Example 1:
Input: 00000010100101000001111010011100
Output: 00111001011110000010100101000000
Explanation: The input binary string 00000010100101000001111010011100 represents the unsigned integer 43261596, 
so return 964176192 which its binary representation is 00111001011110000010100101000000.

Example 2:
Input: 11111111111111111111111111111101
Output: 10111111111111111111111111111111
Explanation: The input binary string 11111111111111111111111111111101 represents the unsigned integer 4294967293, 
so return 3221225471 which its binary representation is 10111111111111111111111111111111.

Note that in some languages such as Java, there is no unsigned integer type. In this case, both input and output will be given as 
signed integer type and should not affect your implementation, as the internal binary representation of the integer is the same whether it is signed or unsigned.
In Java, the compiler represents the signed integers using 2's complement notation. Therefore, in Example 2 above the input represents 
the signed integer -3 and the output represents the signed integer -1073741825.
 
Follow up:
If this function is called many times, how would you optimize it?
'''
'''
Solution:
The key idea is that for a bit that is situated at the index i, after the reversion, its position should be 31-i (note: the index starts from zero).

1. We iterate through the bit string of the input integer, from right to left (i.e. n = n >> 1). 
To retrieve the right-most bit of an integer, we apply the bit AND operation (n & 1).

2. For each bit, we reverse it to the correct position (i.e. (n & 1) << power). Then we accumulate this reversed bit to the final result.

3. When there is no more bits of one left (i.e. n == 0), we terminate the iteration.
'''
class Solution:
    def reverseBits(self, n: int) -> int:
        res, p = 0, 31
        while n:
            res += (n & 1) << p
            n = n >> 1
            p -= 1
        return res