190. Reverse Bits

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.

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

• cache can be solution but not perfect
• input range is [0 … 2^32-1] so it’s too much data for caching
  • we need 2^32 - 1 * uint32_t memory in case
• we can use cache with lru or something else..
  • but worst!!
  • in this case average cache hit rate wold be memory size / 2^32 - 1
  • and also we know we have to use hash funtions
    • when we use hash funtions, we have to make hash key, so have to iterate all bits o(n)
  • in below solution, we iterate half of n

class Solution {
public:
    uint32_t reverseBits(uint32_t n) {
        for(int i = 0; i < 16; i++) {
            int left = (1<<(31 - i)) & n;
            int right = (1<<i) & n;
            if((!left and right) or (left and !right)) {
                n ^= (1<<(31 - i)) ^ (1<<i);
            }
        }
        return n;
    }
};