XOR Optimization Patterns

XOR is self-inverse (x ^ a ^ a == x), which cancels paired updates—great for prefix “toggle” stories and single missing element puzzles.

Try this in Python

from functools import reduce
from operator import xor

nums = [4, 1, 2, 1, 2]
print(reduce(xor, nums))

Key takeaways

• Associative and commutative—order does not matter in XOR-sum.
• Duplicate values cancel in pairs.
• Combine with prefix XOR for paths.