{"version": "https://jsonfeed.org/version/1", "title": "Algorithms for Competitive Programming", "home_page_url": "https://cp-algorithms.com/", "feed_url": "https://cp-algorithms.com/feed_json_updated.json", "description": "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.", "icon": null, "authors": [], "language": "en", "items": [{"id": "https://cp-algorithms.com/geometry/nearest_points.html", "url": "https://cp-algorithms.com/geometry/nearest_points.html", "title": "Finding the nearest pair of points", "content_html": "<h1>Finding the nearest pair of points</h1>\n<h2>Problem statement</h2>\n<p>Given $n$ points on the plane. Each point $p_i$ is defined by its coordinates $(x_i,y_i)$. It is ...</p>", "image": null, "date_modified": "2025-08-23T13:27:11+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/num_methods/binary_search.html", "url": "https://cp-algorithms.com/num_methods/binary_search.html", "title": "Binary Search", "content_html": "<h1>Binary search</h1>\n<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>", "image": null, "date_modified": "2025-08-19T18:20:25+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/discrete-log.html", "url": "https://cp-algorithms.com/algebra/discrete-log.html", "title": "Discrete Log", "content_html": "<h1>Discrete Logarithm</h1>\n<p>The discrete logarithm is an integer $x$ satisfying the equation</p>\n<p>$$a^x \\equiv b \\pmod m$$</p>\n<p>for given integers $a$, $b$ and $m$.</p>\n<p>The d...</p>", "image": null, "date_modified": "2025-08-19T18:12:53+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/navigation.html", "url": "https://cp-algorithms.com/navigation.html", "title": "Navigation", "content_html": "<ul>\n<li>Home<ul>\n<li><a href=\"index.md\">Main Page</a></li>\n<li><a href=\"navigation.md\">Navigation</a></li>\n<li><a href=\"tags.md\">Tag index</a></li>\n<li><a href=\"contrib.md\">How to Contribute</a></li>\n<li>[Code of conduct]...</li>\n</ul>\n</li>\n</ul>", "image": null, "date_modified": "2025-08-19T15:59:22+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/geometry/enclosing-circle.html", "url": "https://cp-algorithms.com/geometry/enclosing-circle.html", "title": "Minimum Enclosing Circle", "content_html": "<h1>Minimum Enclosing Circle</h1>\n<p>Consider the following problem:</p>\n<p>!!! example \"[Library Checker - Minimum Enclosing Circle](https://judge.yosupo.jp/problem/minimu...</p>", "image": null, "date_modified": "2025-08-19T15:59:22+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/combinatorics/burnside.html", "url": "https://cp-algorithms.com/combinatorics/burnside.html", "title": "Burnside's lemma / P\u00f3lya enumeration theorem", "content_html": "<h1>Burnside's lemma / P\u00f3lya enumeration theorem</h1>\n<h2>Burnside's lemma</h2>\n<p><strong>Burnside's lemma</strong> was formulated and proven by <strong>Burnside</strong> in 1897, but historically...</p>", "image": null, "date_modified": "2025-08-17T19:18:12+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/linear-diophantine-equation.html", "url": "https://cp-algorithms.com/algebra/linear-diophantine-equation.html", "title": "Linear Diophantine Equations", "content_html": "<h1>Linear Diophantine Equation</h1>\n<p>A Linear Diophantine Equation (in two variables) is an equation of the general form:</p>\n<p>$$ax + by = c$$</p>\n<p>where $a$, $b$, $c$ are...</p>", "image": null, "date_modified": "2025-08-15T21:04:35+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/geometry/manhattan-distance.html", "url": "https://cp-algorithms.com/geometry/manhattan-distance.html", "title": "Manhattan Distance", "content_html": "<h1>Manhattan Distance</h1>\n<h2>Definition</h2>\n<p>For points $p$ and $q$ on a plane, we can define the distance between them as the sum of the differences between their $...</p>", "image": null, "date_modified": "2025-08-11T08:42:20+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/data_structures/stack_queue_modification.html", "url": "https://cp-algorithms.com/data_structures/stack_queue_modification.html", "title": "Minimum Stack / Minimum Queue", "content_html": "<h1>Minimum stack / Minimum queue</h1>\n<p>In this article we will consider three problems: \nfirst we will modify a stack in a way that allows us to find the smallest ...</p>", "image": null, "date_modified": "2025-08-09T09:10:30+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/geometry/basic-geometry.html", "url": "https://cp-algorithms.com/geometry/basic-geometry.html", "title": "Basic Geometry", "content_html": "<h1>Basic Geometry</h1>\n<p>In this article we will consider basic operations on points in Euclidean space which maintains the foundation of the whole analytical geome...</p>", "image": null, "date_modified": "2025-08-09T09:05:50+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/polynomial.html", "url": "https://cp-algorithms.com/algebra/polynomial.html", "title": "Operations on polynomials and series", "content_html": "<h1>Operations on polynomials and series</h1>\n<p>Problems in competitive programming, especially the ones involving enumeration some kind, are often solved by reducin...</p>", "image": null, "date_modified": "2025-08-07T06:04:38+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/linear_algebra/linear-system-gauss.html", "url": "https://cp-algorithms.com/linear_algebra/linear-system-gauss.html", "title": "Gauss & System of Linear Equations", "content_html": "<h1>Gauss method for solving system of linear equations</h1>\n<p>Given a system of $n$ linear algebraic equations (SLAE) with $m$ unknowns. You are asked to solve the ...</p>", "image": null, "date_modified": "2025-07-31T08:48:33+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/chinese-remainder-theorem.html", "url": "https://cp-algorithms.com/algebra/chinese-remainder-theorem.html", "title": "Chinese Remainder Theorem", "content_html": "<h1>Chinese Remainder Theorem</h1>\n<p>The Chinese Remainder Theorem (which will be referred to as CRT in the rest of this article) was discovered by Chinese mathemati...</p>", "image": null, "date_modified": "2025-07-29T01:26:09+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/binary-exp.html", "url": "https://cp-algorithms.com/algebra/binary-exp.html", "title": "Binary Exponentiation", "content_html": "<h1>Binary Exponentiation</h1>\n<p>Binary exponentiation (also known as exponentiation by squaring) is a trick which allows to calculate $a^n$ using only $O(\\log n)$ m...</p>", "image": null, "date_modified": "2025-07-27T06:10:49+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/graph/bridge-searching-online.html", "url": "https://cp-algorithms.com/graph/bridge-searching-online.html", "title": "Finding Bridges Online", "content_html": "<h1>Finding Bridges Online</h1>\n<p>We are given an undirected graph.\nA bridge is an edge whose removal makes the graph disconnected (or, more precisely, increases the...</p>", "image": null, "date_modified": "2025-07-26T20:01:08+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/big-integer.html", "url": "https://cp-algorithms.com/algebra/big-integer.html", "title": "Arbitrary-Precision Arithmetic", "content_html": "<h1>Arbitrary-Precision Arithmetic</h1>\n<p>Arbitrary-Precision arithmetic, also known as \"bignum\" or simply \"long arithmetic\" is a set of data structures and algorith...</p>", "image": null, "date_modified": "2025-07-12T15:11:52+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/data_structures/treap.html", "url": "https://cp-algorithms.com/data_structures/treap.html", "title": "Treap", "content_html": "<h1>Treap (Cartesian tree)</h1>\n<p>A treap is a data structure which combines binary tree and binary heap (hence the name: tree + heap $\\Rightarrow$ Treap).</p>\n<p>More spe...</p>", "image": null, "date_modified": "2025-07-03T15:57:46+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/graph/mst_prim.html", "url": "https://cp-algorithms.com/graph/mst_prim.html", "title": "Minimum Spanning Tree - Prim's Algorithm", "content_html": "<h1>Minimum spanning tree - Prim's algorithm</h1>\n<p>Given a weighted, undirected graph $G$ with $n$ vertices and $m$ edges.\nYou want to find a spanning tree of this ...</p>", "image": null, "date_modified": "2025-06-30T19:15:08+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/graph/fixed_length_paths.html", "url": "https://cp-algorithms.com/graph/fixed_length_paths.html", "title": "Number of paths of fixed length / Shortest paths of fixed length", "content_html": "<h1>Number of paths of fixed length / Shortest paths of fixed length</h1>\n<p>The following article describes solutions to these two problems built on the same idea:\nr...</p>", "image": null, "date_modified": "2025-06-14T10:11:52+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/factorization.html", "url": "https://cp-algorithms.com/algebra/factorization.html", "title": "Integer factorization", "content_html": "<h1>Integer factorization</h1>\n<p>In this article we list several algorithms for the factorization of integers, each of which can be either fast or varying levels of ...</p>", "image": null, "date_modified": "2025-05-29T05:50:00+00:00", "authors": [], "tags": null}]}