Bit Manipulation
Here are some common approaches that can be used to solve problems related to bit manipulation in data structures and algorithms:
Bitwise AND, OR, XOR, NOT: These are the basic operations that can be performed on bits. They are used in a variety of problems, such as finding the unique number in an array where all numbers except one appear twice (XOR), or adding two numbers without using arithmetic operators (AND, XOR).
Bit Shifting: This involves shifting the bits of a number left or right.
Bit Masking: This involves using a “mask” to isolate certain bits of a number. This is often used in problems where you need to manipulate or test specific bits of a number.
Counting Set Bits: Several problems require counting the number of set bits (bits that are 1) in a number. This can be done using Brian Kernighan’s Algorithm, lookup table method, or even using built-in functions in some languages.
Finding the Rightmost Set Bit, Unset Bit, etc.: Some problems require finding or manipulating the rightmost set bit, the rightmost unset bit, or similar. This can be done using bitwise operations and bit manipulation tricks.
Two’s Complement and Signed Numbers: Understanding how negative numbers are represented in binary can be useful for certain problems, particularly those involving arithmetic and overflow.
Remember, bit manipulation problems can often be solved using a combination of these techniques. The key is to understand how binary numbers work and how different operations affect the bits.
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