{"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": "2025-06-28T20:13:26+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/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": "2025-05-31T23:35:19+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}, {"id": "https://cp-algorithms.com/string/manacher.html", "url": "https://cp-algorithms.com/string/manacher.html", "title": "Manacher's Algorithm - Finding all sub-palindromes in O(N)", "content_html": "<h1>Manacher's Algorithm - Finding all sub-palindromes in $O(N)$</h1>\n<h2>Statement</h2>\n<p>Given string $s$ with length $n$. Find all the pairs $(i, j)$ such that substri...</p>", "image": null, "date_modified": "2025-05-24T18:58:13+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/num_methods/simulated_annealing.html", "url": "https://cp-algorithms.com/num_methods/simulated_annealing.html", "title": "Simulated Annealing", "content_html": "<h1>Simulated Annealing</h1>\n<p><strong>Simulated Annealing (SA)</strong> is a randomized algorithm, which approximates the global optimum of a function. It's called a randomized ...</p>", "image": null, "date_modified": "2025-05-21T11:11:00+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/sequences/longest_increasing_subsequence.html", "url": "https://cp-algorithms.com/sequences/longest_increasing_subsequence.html", "title": "Longest increasing subsequence", "content_html": "<h1>Longest increasing subsequence</h1>\n<p>We are given an array with $n$ numbers: $a[0 \\dots n-1]$.\nThe task is to find the longest, strictly increasing, subsequence...</p>", "image": null, "date_modified": "2025-05-21T09:00:17+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/fibonacci-numbers.html", "url": "https://cp-algorithms.com/algebra/fibonacci-numbers.html", "title": "Fibonacci Numbers", "content_html": "<h1>Fibonacci Numbers</h1>\n<p>The Fibonacci sequence is defined as follows:</p>\n<p>$$F_0 = 0, F_1 = 1, F_n = F_{n-1} + F_{n-2}$$</p>\n<p>The first elements of the sequence ([OEIS ...</p>", "image": null, "date_modified": "2025-04-22T03:58:03+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/graph/edmonds_karp.html", "url": "https://cp-algorithms.com/graph/edmonds_karp.html", "title": "Maximum flow - Ford-Fulkerson and Edmonds-Karp", "content_html": "<h1>Maximum flow - Ford-Fulkerson and Edmonds-Karp</h1>\n<p>The Edmonds-Karp algorithm is an implementation of the Ford-Fulkerson method for computing a maximal flow i...</p>", "image": null, "date_modified": "2025-04-22T02:45:52+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/graph/second_best_mst.html", "url": "https://cp-algorithms.com/graph/second_best_mst.html", "title": "Second best Minimum Spanning Tree - Using Kruskal and Lowest Common Ancestor", "content_html": "<h1>Second Best Minimum Spanning Tree</h1>\n<p>A Minimum Spanning Tree $T$ is a tree for the given graph $G$ which spans over all vertices of the given graph and has t...</p>", "image": null, "date_modified": "2025-04-22T02:26:46+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/graph/topological-sort.html", "url": "https://cp-algorithms.com/graph/topological-sort.html", "title": "Topological Sorting", "content_html": "<h1>Topological Sorting</h1>\n<p>You are given a directed graph with $n$ vertices and $m$ edges.\nYou have to find an <strong>order of the vertices</strong>, so that every edge lead...</p>", "image": null, "date_modified": "2025-04-22T02:26:46+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": "2025-04-22T02:22:24+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": "2025-04-22T02:11:52+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/string/aho_corasick.html", "url": "https://cp-algorithms.com/string/aho_corasick.html", "title": "Aho-Corasick algorithm", "content_html": "<h1>Aho-Corasick algorithm</h1>\n<p>The Aho-Corasick algorithm allows us to quickly search for multiple patterns in a text.\nThe set of pattern strings is also called a...</p>", "image": null, "date_modified": "2025-04-18T21:47:45+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/graph/finding-negative-cycle-in-graph.html", "url": "https://cp-algorithms.com/graph/finding-negative-cycle-in-graph.html", "title": "Finding a Negative Cycle in the Graph", "content_html": "<h1>Finding a negative cycle in the graph</h1>\n<p>You are given a directed weighted graph $G$ with $N$ vertices and $M$ edges. Find any cycle of negative weight in it...</p>", "image": null, "date_modified": "2025-04-16T00:46:24+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/sequences/k-th.html", "url": "https://cp-algorithms.com/sequences/k-th.html", "title": "K-th order statistic in O(N)", "content_html": "<h1>$K$th order statistic in $O(N)$</h1>\n<p>Given an array $A$ of size $N$ and a number $K$. The problem is to find $K$-th largest number in the array, i.e., $K$-th o...</p>", "image": null, "date_modified": "2025-04-16T00:31:59+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/algebra/sieve-of-eratosthenes.html", "url": "https://cp-algorithms.com/algebra/sieve-of-eratosthenes.html", "title": "Sieve of Eratosthenes", "content_html": "<h1>Sieve of Eratosthenes</h1>\n<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>\n<p>T...</p>", "image": null, "date_modified": "2025-04-15T02:32:08+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/data_structures/fenwick.html", "url": "https://cp-algorithms.com/data_structures/fenwick.html", "title": "Fenwick Tree", "content_html": "<h1>Fenwick Tree</h1>\n<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>", "image": null, "date_modified": "2025-04-15T02:32:08+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": "2025-04-15T02:32:08+00:00", "authors": [], "tags": null}, {"id": "https://cp-algorithms.com/geometry/convex_hull_trick.html", "url": "https://cp-algorithms.com/geometry/convex_hull_trick.html", "title": "Convex hull trick and Li Chao tree", "content_html": "<h1>Convex hull trick and Li Chao tree</h1>\n<p>Consider the following problem. There are $n$ cities. You want to travel from city $1$ to city $n$ by car. To do this y...</p>", "image": null, "date_modified": "2025-04-15T02:32:08+00:00", "authors": [], "tags": null}]}