dsa5 min read
Bit Manipulation — Complete Guide
Master bit manipulation: XOR tricks, counting bits, bitmask DP, Brian Kernighan, two's complement, and 5-language operators.
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Xor
8 articles
dsa1 min read
Single Number — XOR Cancellation
Every element appears twice except one. XOR all numbers: duplicates cancel (a^a=0), single number remains.
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Single Number III — XOR Partition
Two numbers appear once, rest appear twice. XOR all to get a^b, then use any set bit to partition numbers into two groups.
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Missing Number — XOR or Gauss Formula
Find missing number in 0..n array. XOR approach: XOR all indices with all values, duplicate indices cancel. Or math: n*(n+1)/2 - sum.
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dsa1 min read
Maximum XOR of Two Numbers — Binary Trie
Find maximum XOR of any two numbers in array. Binary trie (bit by bit from MSB): for each number greedily choose opposite bit to maximize XOR.
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Maximum XOR With an Element — Offline Trie
For each query (xi, mi), find max xi XOR with element ≤ mi. Offline: sort queries and elements by value, add elements up to mi, query trie.
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dsa3 min read
Bit Manipulation: XOR Tricks and Bitmasking
Master bitwise operations for DSA: XOR tricks, Brian Kernighan bit counting, subset enumeration, and bitmask DP.
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dsa2 min read
Advanced Trie Applications — XOR, Palindrome Pairs, Stream Search
Advanced trie applications beyond basic insert/search: binary trie for XOR maximization, palindrome pairs detection, and stream search using Aho-Corasick automaton concept.
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