tanvir002700/Algorithm ? reverse-engineered prompt

Build me a clean C++ algorithm library with a folder for common competitive programming routines and small examples for each one.

I want it to cover things like string matching, graph basics, trees, shortest paths, flows, union find, geometry, number theory, dynamic programming, and data structures like segment trees and sparse tables. Make each algorithm easy to copy and use, with simple function names, short comments, and a consistent style across the whole repo. Include a reusable template file too, and make sure the code is organized so I can quickly find each topic.

If you can, add a simple index or README that explains what each folder is for, and include a few notes for common tricks like modular arithmetic and fast exponentiation. Keep everything in standard C++, and look up current best practice docs online if you need to.