Data Structures Ladders¶
These ladders connect reusable structures to focused practice.
Subtopic Ladders¶
- DSU
- DSU Rollback / Offline Dynamic Connectivity
- DSU On Tree / Small-To-Large
- Fenwick tree
- Monotonic stack / queue
- Binary Trie / XOR Queries
- PBDS / Order Statistics Tree
- Balanced BSTs For Contests
- B-Trees
- Skip Lists
- X-Fast / Y-Fast Tries
- Interval Trees
- Splay Tree
- Pairing Heap / Leftist Heap
- Persistent data structures
- Persistent Treap
- Treap / Implicit Treap
- Wavelet Tree
- Mo's algorithm
- Segment tree
- Lazy segment tree
- Segment Tree Beats
- ODT / Chtholly
- Sparse table
- Heaps and ordered sets
- Offline tricks
Representative Solved Note¶
- Dynamic Connectivity: exact rollback-DSU route for component counts under add/remove edge events
- Distinct Colors: exact first small-to-large subtree-container route for one answer per rooted subtree
- CVP00001: Fenwick-backed circular simulation with reset/capture logic
- Range Queries and Copies: exact first persistent segment-tree route for versioned point updates and old-version range sums
- Persistent List: exact first persistent split/merge treap route for branching list versions
- Nearest Smaller Values: exact first monotonic-stack route where one domination rule kills dead boundary candidates forever
- Salary Queries: exact key-based treap route for duplicate-safe rank differences under online updates
- Cut and Paste: exact first sequence-surgery route where split/merge by position replaces explicit index maintenance
- MKTHNUM - K-th Number: exact first static order-statistics route where one range is translated through value partitions
- Powerful Array: exact first
Moroute where one current range and one frequency-weighted score are the whole state - Vasiliy's Multiset: exact first binary-trie route for live xor-max queries with duplicates
- ORDERSET - Order Statistic Set: exact first PBDS route for online rank and
k-th queries on one changing ordered set - Balanced BSTs For Contests: compare-note track for AVL and the other textbook balancing families the repo intentionally does not treat as first-line contest retrieval
- B-Tree Dictionary: exact first high-fanout textbook dictionary route where split-full-child is the whole insert story
- Skiplist Dictionary: exact first probabilistic ordered-dictionary route where tower search and
update[]splicing are the whole state - X-Fast Dictionary: exact first bounded-universe predecessor route where binary-searching the deepest existing prefix is the real idea
- Reservation System: exact first augmented-BST route where subtree
max_ris enough to answer online half-open overlap queries on one live interval set - Ordinary Balanced Tree: exact first self-adjusting ordered-set route and the direct bridge into link-cut tree machinery
- Mergeable Heap 1: exact first meldable-heap route where singleton heaps keep unioning and delete-min names one item's current heap
- HORRIBLE: exact
range add + range sumlazy-propagation baseline - Range Chmin Chmax Add Range Sum: exact canonical verifier for
range chmin / chmax / add / sum - Willem, Chtholly and Seniorious: exact canonical ODT route where one
std::setinterval partition withsplit / assign / walkmatches the whole statement