Computers operate on bits. Bit manipulation involves using bitwise operators like AND, OR, XOR, and shifts to perform tasks at lightning speed, often in O(1).
The Power of XOR
XOR has the unique property that `X ^ X = 0` and `X ^ 0 = X`. This makes it incredibly useful for finding the unique element in an array where every other element appears twice.
Setting and Clearing Bits
Learn how to use masks to check if a specific bit is set, or to set/clear bits without affecting others. This is essential for memory-efficient state representation (bitmasks).
Shift Operators and Powers of Two
Left shifting by K is equivalent to multiplying by 2^K, and right shifting is like dividing. These operations are handled directly at the CPU level, making them faster than standard arithmetic.