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My library of algorithms and topics focused on competitive programming

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# Ubiratan Correia Barbosa Neto - Competitive Programming Library

This repository contains algorithms that I learned through my journey on competitive programming:

* Data Structures
	* Segment Tree
	* Binary Indexed Tree
	* Dynamic/Persistent Segment Tree
	* Trie
	* Lichao Segment Tree (Online Convex Hull Trick)/ Integer and Float Version
	* Offline Convex Hull Trick
	* Ordered Set
	* Implicit Treap
	* Splay Tree
	
* Uncategorized
	* Longest Increase Subsequence
	* 2D Longest Increase Subsequence
	* Inversion Count Offline (Merge-Sort)
	* Mos Query Decomposition
	* Find kth permutation
	
* Basic 2D Geometry
  * Point/Vector Structure
  * Vector Structure
  * Line/Segment Structure
  * Distance from Point to Line
  * Distance from Point to Segment
  * Distance from Line to Segment
  * Distance from Point to Ray
  * Distance from Segment to Ray
  * Distance from Line to Ray
  * Distance between Segments
  * Distance between Rays
  * Distance between Lines
  * Line-Line Intersection
  * Segment-Segment Intersection
  * Line-Segment Intersection
  * Circle-Circle Intersection Area
  * Circle-Circle Intersection Points (NOT TESTED)
  * Tangent Line to a Circle Given a Point
  * Circle of Radius R Passing Through 2 Given Points
  * Barycenter, Circumcenter, Incenter, Excenter, Orthocenter, Centroid...
		
* 2D Geometry Algorithms
	* Closest Pair of Points
	* Convex Hull(Monotone Chain) + Perimeter/Area Calculation
	* Smallest Enclosing Circle Randomized Algorithm
	* Check if a Point Lies in Convex Hull
	* Largest quadrilater given a set of distinct points
	* Check if line intersects polygon
	* Maximum dot product queries
  
* Math and Number Theory
	* Binomial Coefficient
	* Euler Totient
	* Sieve of Erathostenes
	* Miller Rabin Primality Test
	* Count Primes/Divisors for Large Numbers + Sum Of Divisors of a Number
	* Matrix Exponentiation
	* Fast Fourier Transform (Iterative + Recursive)
	* Chinese Remainder Theorem
	* Diophantine Equations
	* Shank's Baby-Step Giant-Steps
	
* Strings
	* Knuth - Morris - Pratt (KMP)
	* Z-Function
	* Rolling Hash
	* Aho-Corasick
  * Suffix Array + Linear Sorting (O(nlogn) S.Array)

* Graphs
  * LCA
  * Max-Flow (Dinic's Algorithm)
  * Minimum Path Cover in Directed Acyclic Graphs
  * Minimum Edge Cover in Bipartite Graph
  * Minimum Cut in Flow Network
  * Minimum Vertex Cover in Bipartite Graph
  * Bellman Ford Shortest Path Algorithm
	* Dynammic Connectivity for connected(u,v) - query 
	* Eulerian Circuit Directed/Undirected Graphs
	* Tarjan Algorithm for Bridges/Articulation Points
	* Heavy-Light Decomposition
	* Centroid Decomposition
	* Kosaraju's Strong Connected Components Algorithm

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