A well-structured segment tree implementation with lazy propagation, supporting range add and range sum queries. The code uses iterative segment tree sizing, clear operator functions (modify_op, cal_op), and a propagate method that applies pending updates to children. It is written with modern C++ practices, uses long long for overflow safety, and includes a full test harness from a Codeforces problem. This component is self-contained and could be extracted for any project requiring efficient range updates and queries on an array.

A merge sort tree implementation that builds a segment tree where each node stores a sorted vector of elements in its range. It supports queries that count elements ≤ x in a given interval using binary search on each relevant node. The code is cleanly structured with class encapsulation, recursive build and query methods, and clear comments. This pattern is reusable for any problem requiring range counting of ordered elements, such as finding number of elements greater than a threshold in a subarray.

An implementation of the palindrome pairs problem using a trie with a clever addition of palindrome index lists at each node. The algorithm inserts words in reverse order and, during search, checks for palindromic suffixes/prefixes to find all pairs that form palindromes when concatenated. The code demonstrates non-trivial use of a trie for a complex string problem and is well-organized with private helper functions (isPalindrome, add). This component can be extracted and reused for any problem involving palindrome pairing or advanced trie traversal.

A classic KMP (Knuth-Morris-Pratt) pattern matching implementation in C++. The code includes functions for computing the longest prefix-suffix (LPS) array and performing the search in O(n+m) time. Although the file extension is missing, the code is complete and self-contained with proper variable names and comments. KMP is a fundamental algorithm for substring search, and this implementation is clean enough to be reused directly in any project that needs efficient pattern matching without external libraries.