Reverse bits of a given 32 bits unsigned integer.

**Note:**

- 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 a signed integer type. They should not affect your implementation, as the integer’s internal binary representation 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`

.

**Example 1:**

`Input: n = 00000010100101000001111010011100`

Output: 964176192 (00111001011110000010100101000000)

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

**Example 2:**

`Input: n = 11111111111111111111111111111101`

Output: 3221225471 (10111111111111111111111111111111)

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

**Constraints:**

- The input must be a
**binary string**of length`32`

**Follow up:** If this function is called many times, how would you optimize it?

Solution:

Time complexity: O(N)

Space complexity: O(N)