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Concepts22

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🗂️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
🗂️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
12
Advanced
#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 StructureIntermediate

Binary Trie for XOR

A binary trie (also called a bitwise trie) stores numbers by their binary bits, branching on 0/1 at each level.

#binary trie#bitwise trie#xor+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 StructureIntermediate

Trie (Prefix Tree)

A trie (prefix tree) stores strings or bit-sequences so that common prefixes share nodes, making operations depend on the key length L rather than the set size.

#trie#prefix tree#autocomplete+12
🗂️Data StructureIntermediate

Segment Tree Basics

A segment tree is a complete binary tree that stores information about array intervals to answer range queries and support point updates in O(log n).

#segment tree#range query#point update+11
🗂️Data StructureIntermediate

2D Fenwick Tree

A 2D Fenwick Tree (Binary Indexed Tree) supports point updates and rectangle sum queries in O(log n × log m) time.

#2d fenwick tree#binary indexed tree 2d#bit 2d+12
🗂️Data StructureIntermediate

Fenwick Tree - Range Update Range Query

A Fenwick Tree (Binary Indexed Tree) can support range additions and range sum queries by maintaining two trees, often called B1 and B2.

#fenwick tree#binary indexed tree#range add+12
🗂️Data StructureIntermediate

Fenwick Tree (Binary Indexed Tree)

A Fenwick Tree (Binary Indexed Tree) maintains prefix sums so you can update a single position and query a prefix in O(\log n) time with a tiny constant factor.

#fenwick tree#binary indexed tree#prefix sum+11
🗂️Data StructureIntermediate

Sparse Table

A Sparse Table is a static range-query data structure that preprocesses an array in O(n \log n) time and answers many queries in O(1) time.

#sparse table#range minimum query#rmq+12
🗂️Data StructureIntermediate

Rollback DSU

Rollback DSU (Disjoint Set Union with undo) lets you union sets and later revert to any previous state in LIFO order.

#rollback dsu#dsu with undo#union find+11