Concepts5

Sqrt Decomposition on Queries

Sqrt decomposition on queries (time blocking) processes Q operations in blocks of size about \(\sqrt{Q}\) to balance per-query overhead and rebuild cost.

#sqrt decomposition#time blocking#query blocking+12

⚙️AlgorithmAdvanced

Convex Hull Trick (CHT)

The Convex Hull Trick (CHT) speeds up dynamic programs where each state is a minimum over linear functions, such as dp[i] = min_j (dp[j] + b[j] × a[i]).

#convex hull trick#cht#dynamic programming optimization+12

🗂️Data StructureAdvanced

Palindromic Tree (Eertree)

A Palindromic Tree (Eertree) stores every distinct palindromic substring of a string as a node and can be built online in linear time.

#palindromic tree#eertree#palindromic substrings+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

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