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🗂️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

Centroid Decomposition - Distance Queries

Centroid decomposition splits a tree into levels by repeatedly removing a centroid so that each remaining component is at most half the size.

#centroid decomposition

#tree distance queries

#nearest red node

+12

🗂️Data StructureAdvanced

Centroid Decomposition

Centroid decomposition splits a tree around a special node (centroid) so that every remaining component has at most half the nodes.

#centroid decomposition#centroid tree#tree algorithms+11

🗂️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

Wavelet Tree

A wavelet tree is a recursive data structure built over a sequence’s alphabet that answers rank, select, and quantile (k-th smallest) queries in O(log σ) time, where σ is the number of distinct values.

#wavelet tree#wavelet matrix#rank select+11

🗂️Data StructureAdvanced

Heavy-Light Decomposition

Heavy-Light Decomposition (HLD) breaks a tree into O(n) disjoint chains so that any root-to-node path crosses only O(log n) chains.

#heavy light decomposition#hld c++#segment tree on tree+10

🗂️Data StructureAdvanced

Persistent Array and Treap

Persistence lets you keep every past version of a data structure while making O(log n) updates and queries on any version.

#persistent array#persistent segment tree#treap+12

🗂️Data StructureAdvanced

Splay Tree

A splay tree is a self-adjusting binary search tree that moves the most recently accessed node to the root with rotations.

#splay tree#self-adjusting bst#zig+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

Persistent Segment Tree

A persistent segment tree stores every historical version of an array-like data while supporting queries and updates in O(log n) time.

#persistent segment tree#path copying#kth smallest+12

🗂️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

Merge Sort Tree

A Merge Sort Tree is a segment tree where every node stores the sorted list of values in its segment.

#merge sort tree#segment tree#range query+12