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://paulofilipe.com/cp-algorithms/https://github.com/filipemsilv4/cp-algorithmsen Sun, 13 Oct 2024 16:28:34 -0000 Sun, 13 Oct 2024 16:28:34 -0000 1440 MkDocs RSS plugin - v1.15.0 <p>Artigos com a bandeira 🇺🇸 estão em inglês. Artigos com a bandeira 🇧🇷 já foram traduzidos para o português.</p><ul><li>Página Inicial<ul><li>[🇧🇷 Página Inicial](index....</li></ul></li></ul>https://paulofilipe.com/cp-algorithms/navigation.html Sun, 13 Oct 2024 13:27:34 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/navigation.html <h1>Função de Prefixo. Algoritmo de Knuth–Morris–Pratt</h1><h2>Definição da função de prefixo</h2><p>Dada uma string $s$ de comprimento $n$.A <strong>função de prefixo</strong> para...</p>https://paulofilipe.com/cp-algorithms/string/prefix-function.html Sun, 13 Oct 2024 13:27:34 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/string/prefix-function.html <h1>Algoritmo de Rabin-Karp para busca de padrões em strings</h1><p>Este algoritmo é baseado no conceito de hashing, então se você não estiver familiarizado com hash...</p>https://paulofilipe.com/cp-algorithms/string/rabin-karp.html Sat, 12 Oct 2024 20:28:33 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/string/rabin-karp.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://paulofilipe.com/cp-algorithms/data_structures/disjoint_set_union.html Sat, 12 Oct 2024 07:13:20 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/data_structures/disjoint_set_union.html <h1>The Stern-Brocot tree and Farey sequences</h1><h2>Stern-Brocot tree</h2><p>The Stern-Brocot tree is an elegant construction to represent the set of all positive frac...</p>https://paulofilipe.com/cp-algorithms/others/stern_brocot_tree_farey_sequences.html Sat, 12 Oct 2024 07:12:15 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/others/stern_brocot_tree_farey_sequences.html <h1>Sprague-Grundy theorem. Nim</h1><h2>Introduction</h2><p>This theorem describes the so-called <strong>impartial</strong> two-player game,i.e. those in which the available moves a...</p>https://paulofilipe.com/cp-algorithms/game_theory/sprague-grundy-nim.html Fri, 11 Oct 2024 21:42:54 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/game_theory/sprague-grundy-nim.html <h1>Strongly connected components and the condensation graph</h1><h2>Definitions</h2><p>Let $G=(V,E)$ be a directed graph with vertices $V$ and edges $E \subseteq V \time...</p>https://paulofilipe.com/cp-algorithms/graph/strongly-connected-components.html Fri, 11 Oct 2024 21:27:41 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/graph/strongly-connected-components.html <h1>Introduction to Dynamic Programming</h1><p>The essence of dynamic programming is to avoid repeated calculation. Often, dynamic programming problems are naturall...</p>https://paulofilipe.com/cp-algorithms/dynamic_programming/intro-to-dp.html Fri, 11 Oct 2024 21:14:52 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/dynamic_programming/intro-to-dp.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://paulofilipe.com/cp-algorithms/graph/bellman_ford.html Fri, 11 Oct 2024 21:11:42 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/graph/bellman_ford.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://paulofilipe.com/cp-algorithms/algebra/sieve-of-eratosthenes.html Fri, 11 Oct 2024 07:03:16 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/algebra/sieve-of-eratosthenes.html <h1>Busca em Largura (BFS)</h1><p>A busca em largura (BFS - Breadth First Search) é um dos algoritmos de busca mais básicos e essenciais em grafos.</p><p>Como resultado d...</p>https://paulofilipe.com/cp-algorithms/graph/breadth-first-search.html Thu, 10 Oct 2024 17:59:56 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/graph/breadth-first-search.html <h1>Hashing de Strings</h1><p>Algoritmos de hashing são úteis na resolução de diversos problemas.</p><p>Queremos resolver o problema de comparar strings eficientemente.A...</p>https://paulofilipe.com/cp-algorithms/string/string-hashing.html Thu, 10 Oct 2024 15:31:24 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/string/string-hashing.html <h1>Sqrt Decomposition</h1><p>Sqrt Decomposition is a method (or a data structure) that allows you to perform some common operations (finding sum of the elements of ...</p>https://paulofilipe.com/cp-algorithms/data_structures/sqrt_decomposition.html Tue, 01 Oct 2024 02:06:32 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/data_structures/sqrt_decomposition.html <h1>Finding the Eulerian path in $O(M)$</h1><p>A Eulerian path is a path in a graph that passes through all of its edges exactly once.A Eulerian cycle is a Eulerian...</p>https://paulofilipe.com/cp-algorithms/graph/euler_path.html Sat, 14 Sep 2024 02:18:10 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/graph/euler_path.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://paulofilipe.com/cp-algorithms/algebra/factorial-modulo.html Sun, 25 Aug 2024 06:11:12 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/algebra/factorial-modulo.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://paulofilipe.com/cp-algorithms/dynamic_programming/knapsack.html Thu, 15 Aug 2024 23:48:29 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/dynamic_programming/knapsack.html <h1>Extended Euclidean Algorithm</h1><p>While the <a href="euclid-algorithm.md">Euclidean algorithm</a> calculates only the greatest common divisor (GCD) of two integers $a$ an...</p>https://paulofilipe.com/cp-algorithms/algebra/extended-euclid-algorithm.html Thu, 15 Aug 2024 07:16:54 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/algebra/extended-euclid-algorithm.html <h1>Suffix Array</h1><h2>Definition</h2><p>Let $s$ be a string of length $n$. The $i$-th suffix of $s$ is the substring $s[i \ldots n - 1]$.</p><p>A <strong>suffix array</strong> will con...</p>https://paulofilipe.com/cp-algorithms/string/suffix-array.html Fri, 02 Aug 2024 19:45:41 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/string/suffix-array.html <h1>Fenwick Tree</h1><p>Let $f$ be some group operation (a binary associative function over a set with an identity element and inverse elements) and $A$ be an array ...</p>https://paulofilipe.com/cp-algorithms/data_structures/fenwick.html Wed, 31 Jul 2024 11:14:13 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/data_structures/fenwick.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://paulofilipe.com/cp-algorithms/graph/01_bfs.html Sun, 28 Jul 2024 21:47:47 +0000Algoritmos para Programação Competitivahttps://paulofilipe.com/cp-algorithms/graph/01_bfs.html