Top 10 Algorithms and Data Structures for Competitive Programming Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report In this post, we will discuss Important top 10 algorithms and data structures for competitive coding.Topics : Graph algorithmsDynamic programmingSearching and Sorting:Number theory and Other MathematicalGeometrical and Network Flow AlgorithmsData StructuresThe links below cover most important algorithms and data structure topics:Best Algorithms and Data Structures for Competitive ProgrammingGraph AlgorithmsBreadth First Search (BFS)Depth First Search (DFS)Shortest Path from source to all vertices **Dijkstra**Shortest Path from every vertex to every other vertex **Floyd Warshall**Minimum Spanning tree **Prim**Minimum Spanning tree **Kruskal**Topological SortJohnson's algorithmArticulation Points (or Cut Vertices) in a GraphBridges in a graphAll Graph Algorithms Dynamic ProgrammingLongest Common SubsequenceLongest Increasing SubsequenceEdit DistanceMinimum PartitionWays to Cover a DistanceLongest Path In MatrixSubset Sum ProblemOptimal Strategy for a Game0-1 Knapsack ProblemAssembly Line SchedulingAll DP Algorithms Searching And SortingBinary SearchQuick SortMerge SortOrder StatisticsKMP algorithmRabin karpZ's algorithmAho Corasick String MatchingCounting SortManacher's algorithm: Part 1, Part 2 and Part 3All Articles on Searching, Sorting and Pattern Searching. Number theory and Other MathematicalPrime Numbers and Prime Factorization Primality Test | Set 1 (Introduction and School Method)Primality Test | Set 2 (Fermat Method)Primality Test | Set 3 (Miller–Rabin)Sieve of EratosthenesSegmented SieveWilson’s TheoremPrime FactorizationPollard's rho algorithmModulo Arithmetic Algorithms Basic and Extended Euclidean algorithmsEuler’s Totient FunctionModular ExponentiationModular Multiplicative InverseChinese remainder theorem IntroductionChinese remainder theorem and Modulo Inverse ImplementationnCr%m and this.Miscellaneous:Counting InversionsCounting Inversions using BITlogarithmic exponentiationSquare root of an integerHeavy light Decomposition , this and thisMatrix RankGaussian Elimination to Solve Linear EquationsHungarian algorithmLink cutMo's algorithm and thisFactorial of a large number in C++Factorial of a large number in Java+Russian Peasant MultiplicationCatalan NumberAll Articles on Mathematical Algorithms Geometrical and Network Flow AlgorithmsConvex HullGraham ScanLine IntersectionInterval TreeMatrix Exponentiation and thisMaxflow Ford Furkerson Algo and Edmond Karp ImplementationMin cutStable Marriage ProblemHopcroft–Karp Algorithm for Maximum MatchingDinic's algo and e-maxxAll Articles on Geometric Algorithms Data StructuresBinary Indexed Tree or Fenwick treeSegment Tree (RMQ, Range Sum and Lazy Propagation)K-D tree (See insert, minimum and delete)Union Find Disjoint Set (Cycle Detection and By Rank and Path Compression)TriesSuffix array (this, this and this)Sparse tableSuffix automataSuffix automata IILCA and RMQAll Articles on Advanced Data Structures. How to Begin? Please see How to begin with Competitive Programming? How to Practice? Please see https://www.geeksforgeeks.org/ What are top algorithms in Interview Questions? Top 10 algorithms in Interview Questions How to prepare for ACM – ICPC? How to prepare for ACM – ICPC? This is an initial draft. We will soon be adding more links and algorithms to this post. The biggest mistake programmers make is probably getting discouraged and not practicing enough. Or practicing only on problems they feel they're good at. - Derek Kisman, aka SnapDragon Related Courses Competitive Programming - Live CourseTaking the first step is always hard, isn’t it? But we say no, why? Because we’ve brought a course that will help you to top the charts of leading coding competitions and interviews. Great right? You can start your journey of being a Competitive Programmer now, but before you start know the basics of Data structures and algorithms and programming foundations. Enroll Today, we'll see you inside the course. Comment More infoAdvertise with us Next Article Must do Math for Competitive Programming K kartik Follow Improve Article Tags : GBlog BFS Segment-Tree Binary Indexed Tree sieve Modular Arithmetic DFS Topological Sorting BIT number-theory GBlog-Competitive-Programming +7 More Practice Tags : BFSBinary Indexed TreeDFSModular Arithmeticnumber-theorySegment-Treesieve +3 More Similar Reads Competitive Programming - A Complete Guide Competitive Programming is a mental sport that enables you to code a given problem under provided constraints. The purpose of this article is to guide every individual possessing a desire to excel in this sport. This article provides a detailed syllabus for Competitive Programming designed by indust 8 min read Competitive Programming (CP) Handbook with Complete Roadmap Welcome to the Competitive Programming Handbook or CP Handbook by GeeksforGeeks! This Competitive Programming Handbook is a go-to resource for individuals aiming to enhance their problem-solving skills and excel in coding competitions. This CP handbook provides a comprehensive guide, covering fundam 12 min read Mathematics for Competitive ProgrammingMust do Math for Competitive ProgrammingCompetitive Programming (CP) doesn’t typically require one to know high-level calculus or some rocket science. But there are some concepts and tricks which are sufficient most of the time. You can definitely start competitive coding without any mathematical background, but maths becomes essential as 15+ min read Pigeonhole Principle for CP | Identification, Approach & ProblemsIn competitive programming, where people solve tough problems with computer code, the Pigeonhole Principle is like a secret tool. Even though it's a simple idea, it helps programmers tackle complex challenges. This article is your guide to understanding how this principle works and why it's crucial 8 min read Euler Totient for Competitive ProgrammingWhat is Euler Totient function(ETF)?Euler Totient Function or Phi-function for 'n', gives the count of integers in range '1' to 'n' that are co-prime to 'n'. It is denoted by \phi(n) .For example the below table shows the ETF value of first 15 positive integers: 3 Important Properties of Euler Totie 8 min read Mathematics for Competitive Programming Course By GeeksforGeeksMathematics forms the foundation of problem-solving in Competitive Programming (CP). Mastering key mathematical concepts is crucial for approaching algorithmic challenges effectively. If you're an aspiring competitive programmer or someone who wishes to enhance your problem-solving skills, this Math 3 min read Number Theory for CPBinary Exponentiation for Competitive ProgrammingIn competitive programming, we often need to do a lot of big number calculations fast. Binary exponentiation is like a super shortcut for doing powers and can make programs faster. This article will show you how to use this powerful trick to enhance your coding skills. Table of ContentWhat is Binary 15+ min read GCD (Greatest Common Divisor) Practice Problems for Competitive ProgrammingGCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest positive integer that divides both of the numbers.GCD of Two NumbersFastest Way to Compute GCDThe fastest way to find the Greatest Common Divisor (GCD) of two numbers is by using the Euclidean algorithm. The E 4 min read Bit Manipulation for CPBit Manipulation for Competitive ProgrammingBit manipulation is a technique in competitive programming that involves the manipulation of individual bits in binary representations of numbers. It is a valuable technique in competitive programming because it allows you to solve problems efficiently, often reducing time complexity and memory usag 15+ min read Bit Tricks for Competitive ProgrammingIn competitive programming or in general, some problems seem difficult but can be solved very easily with little concepts of bit magic. We have discussed some tricks below in the previous post.Bitwise Hacks for Competitive Programming One-Liner Hacks of Bit Manipulation:One-Liner CodeFunctionx&1 7 min read Bitwise Hacks for Competitive ProgrammingPrerequisite: It is recommended to refer Interesting facts about Bitwise Operators How to set a bit in the number 'num': If we want to set a bit at nth position in the number 'num', it can be done using the 'OR' operator( | ).  First, we left shift '1' to n position via (1<<n)Then, use the 'O 14 min read Combinatorics for CPInclusion Exclusion principle for Competitive ProgrammingWhat is the Inclusion-Exclusion Principle?The inclusion-exclusion principle is a combinatoric way of computing the size of multiple intersecting sets or the probability of complex overlapping events. Generalised Inclusion-Exclusion over Set:For 2 Intersecting Set A and B: A\bigcup B= A + B - A\bigca 5 min read Greedy for CPBinary Search on Answer Tutorial with ProblemsBinary Search on Answer is the algorithm in which we are finding our answer with the help of some particular conditions. We have given a search space in which we take an element [mid] and check its validity as our answer, if it satisfies our given condition in the problem then we store its value and 15+ min read Ternary Search for Competitive ProgrammingTernary search is a powerful algorithmic technique that plays a crucial role in competitive programming. This article explores the fundamentals of ternary search, idea behind ternary search with its use cases that will help solving complex optimization problems efficiently. Table of Content What is 8 min read Array based concepts for CPWhat are Online and Offline query-based questions in Competitive ProgrammingThe query-based questions of competitive programming are mainly of two types: Offline Query.Online Query. Offline Query An offline algorithm allows us to manipulate the data to be queried before any answer is printed. This is usually only possible when the queries do not update the original element 4 min read Precomputation Techniques for Competitive ProgrammingWhat is the Pre-Computation Technique?Precomputation refers to the process of pre-calculating and storing the results of certain computations or data structures in advance, in order to speed up the execution time of a program. This can be useful in situations where the same calculations or data stru 15+ min read PreComputation Technique on ArraysPrecomputation refers to the process of pre-calculating and storing the results of certain computations or data structures(array in this case) in advance, in order to speed up the execution time of a program. This can be useful in situations where the same calculations are needed multiple times, as 15 min read Frequency Measuring Techniques for Competitive ProgrammingMeasuring the frequency of elements in an array is a really handy skill and is required a lot of competitive coding problems. We, in a lot of problems, are required to measure the frequency of various elements like numbers, alphabets, symbols, etc. as a part of our problem. Examples: Input: arr[] = 15+ min read Dynamic Programming (DP) for CPDP on Trees for Competitive ProgrammingDynamic Programming (DP) on trees is a powerful algorithmic technique commonly used in competitive programming. It involves solving various tree-related problems by efficiently calculating and storing intermediate results to optimize time complexity. By using the tree structure, DP on trees allows p 15+ min read Dynamic Programming in Game Theory for Competitive ProgrammingIn the fast-paced world of competitive programming, mastering dynamic programming in game theory is the key to solving complex strategic challenges. This article explores how dynamic programming in game theory can enhance your problem-solving skills and strategic insights, giving you a competitive e 15+ min read Game Theory for CPInteractive Problems in Competitive ProgrammingInteractive Problems are those problems in which our solution or code interacts with the judge in real time. When we develop a solution for an Interactive Problem then the input data given to our solution may not be predetermined but is built for that problem specifically. The solution performs a se 6 min read Mastering Bracket Problems for Competitive ProgrammingBracket problems in programming typically refer to problems that involve working with parentheses, and/or braces in expressions or sequences. It typically refers to problems related to the correct and balanced usage of parentheses, and braces in expressions or code. These problems often involve chec 4 min read MEX (Minimum Excluded) in Competitive ProgrammingMEX of a sequence or an array is the smallest non-negative integer that is not present in the sequence.Note: The MEX of an array of size N cannot be greater than N since the MEX of an array is the smallest non-negative integer not present in the array and array having size N can only cover integers 15+ min read Like