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🗂️Data StructureAdvanced

Segment Tree with Range Affine Transformation

A segment tree with lazy propagation can support range updates of the form x → a·x + b (affine transformations) and range-sum queries in O(log n) per operation.

#segment tree#lazy propagation#affine update+12
🗂️Data StructureAdvanced

Top Tree

Top trees are dynamic tree data structures that represent a forest as a hierarchy of clusters, allowing O(log n) amortized time for link, cut, path queries/updates, and many subtree queries.

#top tree
12
Advanced
Filtering by:
#lazy propagation
#dynamic tree
#link cut
+12
🗂️Data StructureAdvanced

Link-Cut Tree

A Link-Cut Tree (LCT) maintains a dynamic forest and supports link, cut, and path queries in O(log n) amortized time.

#link-cut tree#dynamic tree#splay tree+12
🗂️Data StructureAdvanced

HLD - Path Queries and Updates

Heavy-Light Decomposition (HLD) breaks a tree into a small number of vertical chains so any path (u,v) becomes O(log n) contiguous segments in an array.

#heavy light decomposition#hld#path query+12
🗂️Data StructureAdvanced

Implicit Treap

An implicit treap is a randomized balanced binary tree that treats array positions as keys without storing them explicitly.

#implicit treap#treap#split and merge+11
🗂️Data StructureAdvanced

Treap

A treap is a binary search tree on keys combined with a heap on random priorities, which keeps the tree balanced in expectation.

#treap#randomized bst#fhq treap+12
🗂️Data StructureIntermediate

Sqrt Decomposition

Sqrt decomposition partitions an array into about \(\sqrt{n}\) blocks, each of size about \(\sqrt{n}\), to speed up range queries and updates.

#sqrt decomposition#block decomposition#bucket decomposition+11
🗂️Data StructureIntermediate

Iterative Segment Tree

An iterative segment tree stores all leaves in tree[n..2n-1] and internal nodes in tree[1..n-1], enabling O(\log n) point updates and range queries without recursion.

#iterative segment tree#segment tree#non-recursive+12
🗂️Data StructureAdvanced

Segment Tree Beats

Segment Tree Beats is a segment tree variant that supports range chmin/chmax (clamping) together with queries like range sum, min, and max in amortized logarithmic time.

#segment tree beats#range chmin#range chmax+12
🗂️Data StructureAdvanced

Segment Tree - Handling Multiple Lazy Operations

When a segment tree supports multiple range updates, you must define how lazy tags compose, because the order of operations matters and composition is not commutative.

#segment tree#lazy propagation#range add+12
🗂️Data StructureIntermediate

Segment Tree with Lazy Propagation

A segment tree with lazy propagation supports fast range updates and range queries in O(\log n) time.

#segment tree#lazy propagation#range update+12
🗂️Data StructureAdvanced

Dynamic Segment Tree

A dynamic segment tree stores values over a huge coordinate range by creating nodes only when an operation touches their interval.

#dynamic segment tree#sparse segment tree#lazy propagation+12