XOR Trick
Domain: Algorithms
🎯 Motivation
XOR (^) has special properties: a^a=0, a^0=a, and it is commutative. This enables elegant solutions for finding unique elements and swapping.
📋 Concrete Example
Array [2, 3, 2, 4, 4]: XOR all -> 2^3^2^4^4 = (2^2)^(4^4)^3 = 0^0^3 = 3. The unique element is 3, found without extra memory.
🔗 Analogy
A game where matching cards cancel each other out. After pairing all duplicates, the one card left face-up is the unique one. XOR does this cancellation automatically.