Bit Manipulation: The Binary Tricks

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Bit manipulation can feel like magic - a few XORs here, some shifts there, and suddenly you've solved a problem in O(1) space that would otherwise require O(n). While not every interview includes bit manipulation, knowing these techniques gives you elegant solutions to certain problems and demonstrates low-level thinking that impresses interviewers.

Before diving into tricks, let's review the fundamental bitwise operators.

Count the number of 1 bits in a number. This is a classic interview question with multiple solutions.

XOR has special properties that make it incredibly useful:

a ^ a = 0 (number XOR itself is 0)
a ^ 0 = a (number XOR 0 is itself)
a ^ b ^ a = b (XOR is reversible)
XOR is commutative and associative

Bit masks use binary numbers to represent sets or flags efficiently. Each bit position represents whether an element is included.

ASCII characters have useful bit patterns that enable clever tricks.

Operator precedence: Bitwise operators have lower precedence than comparison. Use parentheses: (n & 1) == 0, not n & 1 == 0.
Signed vs unsigned: Python integers have arbitrary precision. Use masks (like 0xFFFFFFFF) when you need fixed-width behavior.
Shifting negative numbers: Right-shifting negative numbers is arithmetic (preserves sign) in Python, which may not be what you expect.
Off-by-one in bit positions: Remember bit positions are 0-indexed from the right.

Try these problems to solidify your understanding:Easy:

Medium:

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Bit Manipulation: The Binary Tricks

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