X-Fast / Y-Fast Hot Sheet¶
Use this page when the real lesson is bounded-universe predecessor / successor through prefix hashing, not one ordinary ordered set and not xor greediness.
Do Not Use When¶
- the task is max-xor against one stored value -> Binary Trie hot sheet
- online rank /
k-th is the actual invariant -> Order Statistics Tree hot sheet - one ordinary contest ordered set is enough ->
setor PBDS / Order Statistics Tree
Choose By Signal¶
- fixed-width bounded integer universe + predecessor / successor ->
X-Fast Trie - same job, but you now care about fixing x-fast's space / update cost ->
Y-Fast Trie - fixed-width integer universe + xor-max objective ->
Binary Trie
Core Invariants¶
- every existing prefix is stored in exactly one hash table for its depth
- leaves stay linked in sorted order
- one-child internal nodes carry a jump to the nearest surviving leaf on that side
- all keys use one fixed bit width
Main Traps¶
- forgetting that x-fast is
O(nw)space, not one magical contest default - mixing predecessor / successor logic with xor-greedy trie walks
- claiming y-fast when only x-fast machinery is implemented
Exact Starter Route¶
- exact starter ->
x-fast-trie.cpp - flagship rep -> X-Fast Dictionary
- compare route -> Binary Trie / XOR Queries
- compare route -> Skip Lists
Reopen Paths¶
- full lesson -> X-Fast / Y-Fast Tries
- xor-bit route -> Binary Trie hot sheet
- ordered-set fallback -> Order Statistics Tree hot sheet
- textbook breadth sibling -> Skiplist hot sheet