The goal of this project is to translate the wonderful resource http://e-maxx.ru/algo which provides descriptions of many algorithms and data structures especially popular in field of competitive programming. Moreover we want to improve the collected knowledge by extending the articles and adding new articles to the collection.https://cp-algorithms.com/ https://github.com/cp-algorithms/cp-algorithmsen Sat, 17 Oct 2026 19:32:59 -0000 Sat, 17 Oct 2026 19:32:59 -0000 1440 MkDocs RSS plugin - v1.19.0 None https://cp-algorithms.com/ <h1>Gray code</h1> <p>Gray code is a binary numeral system where two successive values differ in only one bit. </p> <p>Denote by $G(n)$ the representation of the number $n$...</p> https://cp-algorithms.com/algebra/gray-code.html Sat, 17 Oct 2026 04:36:28 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/algebra/gray-code.html <h1>Segment Tree</h1> <p>A Segment Tree is a data structure that stores information about array intervals as a tree. This allows answering range queries over an array...</p> https://cp-algorithms.com/data_structures/segment_tree.html Sun, 04 Oct 2026 19:00:33 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/data_structures/segment_tree.html <h1>Disjoint Set Union</h1> <p>This article discusses the data structure <strong>Disjoint Set Union</strong> or <strong>DSU</strong>. Often it is also called <strong>Union Find</strong> because of its two ...</p> https://cp-algorithms.com/data_structures/disjoint_set_union.html Sat, 19 Sep 2026 12:39:39 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/data_structures/disjoint_set_union.html <h1>Binary search</h1> <p><strong>Binary search</strong> is a method that allows for quicker search of something by splitting the search interval into two. Its most common applica...</p> https://cp-algorithms.com/num_methods/binary_search.html Sat, 19 Sep 2026 11:59:27 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/num_methods/binary_search.html <h1>0-1 BFS</h1> <p>It is well-known, that you can find the shortest paths between a single source and all other vertices in $O(|E|)$ using [Breadth First Search](bre...</p> https://cp-algorithms.com/graph/01_bfs.html Sat, 19 Sep 2026 11:15:44 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/graph/01_bfs.html <h1>Convex Hull construction</h1> <p>In this article we will discuss the problem of constructing a convex hull from a set of points.</p> <p>Consider $N$ points given on a p...</p> https://cp-algorithms.com/geometry/convex-hull.html Sat, 19 Sep 2026 10:34:59 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/geometry/convex-hull.html <h1>Lowest Common Ancestor - Binary Lifting</h1> <p>Let $G$ be a tree. For every query of the form <code>(u, v)</code> we want to find the lowest common ancestor of the nodes `u...</p> https://cp-algorithms.com/graph/lca_binary_lifting.html Sat, 19 Sep 2026 10:31:06 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/graph/lca_binary_lifting.html <h1>Knapsack Problem</h1> <p>Prerequisite knowledge: <a href="https://cp-algorithms.com/dynamic_programming/intro-to-dp.html">Introduction to Dynamic Programming</a></p> <h2>Introduc...</h2> https://cp-algorithms.com/dynamic_programming/knapsack.html Fri, 18 Sep 2026 21:47:54 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/dynamic_programming/knapsack.html <h1>Primality tests</h1> <p>This article describes multiple algorithms to determine if a number is prime or not.</p> <h2>Trial division</h2> <p>By definition a prime number does...</p> https://cp-algorithms.com/algebra/primality_tests.html Fri, 18 Sep 2026 21:24:31 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/algebra/primality_tests.html <h1>Bit manipulation</h1> <h2>Binary number</h2> <p>A <strong>binary number</strong> is a number expressed in the base-2 numeral system or binary numeral system, it is a method of math...</p> https://cp-algorithms.com/algebra/bit-manipulation.html Fri, 18 Sep 2026 19:35:15 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/algebra/bit-manipulation.html <h1>Longest increasing subsequence</h1> <p>We are given an array with $n$ numbers: $a[0 \dots n-1]$. The task is to find the longest, strictly increasing, subsequence...</p> https://cp-algorithms.com/dynamic_programming/longest_increasing_subsequence.html Fri, 18 Sep 2026 19:17:46 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/dynamic_programming/longest_increasing_subsequence.html <h1>Knuth's Optimization</h1> <p>Knuth's optimization, also known as the Knuth-Yao Speedup, is a special case of dynamic programming on ranges, that can optimize the ...</p> https://cp-algorithms.com/dynamic_programming/knuth-optimization.html Fri, 18 Sep 2026 18:39:58 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/dynamic_programming/knuth-optimization.html <h1>Bellman-Ford Algorithm</h1> <p><strong>Single source shortest path with negative weight edges</strong></p> <p>Suppose that we are given a weighted directed graph $G$ with $n$ vertic...</p> https://cp-algorithms.com/graph/bellman_ford.html Fri, 18 Sep 2026 18:36:06 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/graph/bellman_ford.html <h1>Check if point belongs to the convex polygon in $O(\log N)$</h1> <p>Consider the following problem: you are given a convex polygon with integer vertices and a lot...</p> https://cp-algorithms.com/geometry/point-in-convex-polygon.html Fri, 18 Sep 2026 18:17:04 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/geometry/point-in-convex-polygon.html <h1>Sieve of Eratosthenes</h1> <p>Sieve of Eratosthenes is an algorithm for finding all the prime numbers in a segment $[1;n]$ using $O(n \log \log n)$ operations.</p> <p>T...</p> https://cp-algorithms.com/algebra/sieve-of-eratosthenes.html Fri, 18 Sep 2026 18:10:07 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/algebra/sieve-of-eratosthenes.html <h1>Finding Power of Factorial Divisor</h1> <p>You are given two numbers $n$ and $k$. Find the largest integer $x$ such that $k^x$ divides $n!$.</p> <h2>Prime $k$ {data-t...</h2> https://cp-algorithms.com/algebra/factorial-divisors.html Fri, 18 Sep 2026 18:03:40 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/algebra/factorial-divisors.html <h1>Factorial modulo $p$</h1> <p>In some cases it is necessary to consider complex formulas modulo some prime $p$, containing factorials in both numerator and denomin...</p> https://cp-algorithms.com/algebra/factorial-modulo.html Fri, 18 Sep 2026 18:03:40 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/algebra/factorial-modulo.html <h1>Catalan Numbers</h1> <p>Catalan numbers form a number sequence which is useful in a number of combinatorial problems, often involving recursively-defined objects. ...</p> https://cp-algorithms.com/combinatorics/catalan-numbers.html Fri, 18 Sep 2026 17:59:44 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/combinatorics/catalan-numbers.html <h1>The Inclusion-Exclusion Principle</h1> <p>The inclusion-exclusion principle is an important combinatorial way to compute the size of a set or the probability of c...</p> https://cp-algorithms.com/combinatorics/inclusion-exclusion.html Fri, 18 Sep 2026 17:59:44 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/combinatorics/inclusion-exclusion.html <h1>Newton's method for finding roots</h1> <p>This is an iterative method invented by Isaac Newton around 1664. However, this method is also sometimes called the Rap...</p> https://cp-algorithms.com/num_methods/roots_newton.html Fri, 18 Sep 2026 17:30:18 +0000 Algorithms for Competitive Programminghttps://cp-algorithms.com/num_methods/roots_newton.html