36 docs tagged with "competitive-programming"

Extend the Prefix Sum technique to two dimensions — efficiently answer rectangular range sum queries on a 2D grid in O(1) after O(m×n) preprocessing. Includes intuition, dry runs, and multi-language implementations.

An efficient algorithm for multiple pattern matching using a trie and failure links.

Combinatorics is a branch of mathematics dealing with combinations, arrangements, and counting of objects.

Combinatorics is a branch of mathematics dealing with combinations, arrangements, and counting of objects.

Learn the Difference Array technique — a complement to Prefix Sum that enables O(1) range updates and O(n) reconstruction. Includes core concepts, dry runs, step-by-step examples, and multi-language implementations.

An overview of the Discrete Logarithm problem and its applications in cryptography.

A comprehensive guide to Disjoint Set Union (DSU) with visual diagrams, Path Compression, Union by Rank optimizations, step-by-step dry-runs, code templates in Python, Java, and C++, and practice problems.

A detailed guide to understanding and implementing the Divisibility and Prime Numbers.

A detailed guide to understanding and implementing the GCD (Greatest Common Divisor) Algorithm in Number Theory.

Greedy algorithms are a class of algorithms that make the optimal choice at each step with the hope of finding the global optimum

Heaps are commonly used to implement priority queues and ensure efficient retrieval of the minimum or maximum element.

Heaps are commonly used to implement priority queues and ensure efficient retrieval of the minimum or maximum element.

Heaps are commonly used to implement priority queues and ensure efficient retrieval of the minimum or maximum element.

Heaps are useful for merging multiple sorted lists efficiently and solving problems related to merging sorted sequences.

Heaps provide an efficient way to manage and retrieve median values from a stream of data by balancing two heaps.

Mathematical algorithms are essential for solving various computational problems and are widely used in both theoretical computer science and practical applications. They underpin many algorithms used in competitive programming and other fields.

The Two Pointers technique is an efficient algorithmic strategy used to solve various problems involving arrays or lists by utilizing two indices.

Learn how to prevent TLE (Time Limit Exceeded) errors by using BufferedReader and PrintWriter in Java.

A comprehensive guide to using the KMP Algorithm for efficient pattern matching.

Find the Kth largest element in an array using a heap data structure.

A detailed guide to understanding and implementing the LCM (Least Common Multiple) Algorithm in Number Theory.

An architectural guide to the Longest Increasing Subsequence (LIS) problem—covering combinatorial brute force foundations, the standard quadratic Dynamic Programming model, and the optimal log-linear Binary Search technique. Includes structural dry runs, complexity proofs, and robust multi-language implementations.

Learn Mo's Algorithm for offline range queries with block decomposition, dry runs, complexity analysis, and implementations in C++, Java, Python, and JavaScript.

A detailed guide to understanding and implementing the Modular Arithmetic in Number Theory.

A basic string-search algorithm that checks every position in the text for a match with the pattern.

Curated practice problems for mastering Prefix Sum and Difference Array techniques. Problems are organized by difficulty with hints and approach guidance.

Learn the Prefix Sum technique — a powerful range-query optimization that answers range sum queries in O(1) after O(n) preprocessing. Includes dry runs, complexity analysis, common mistakes, and multi-language implementations.

A comprehensive guide to using the Rabin-Karp Algorithm for efficient pattern matching.

A comprehensive guide to Segment Trees with visual diagrams, build/query/update operations, lazy propagation, code templates in Python, Java, and C++, and practice problems.

A comprehensive guide to Segment Tree with Lazy Propagation, including concept explanation, implementations in C++, Java, and Python, complexity analysis, and practice problems.

A complete guide to understanding and implementing the Sieve of Eratosthenes for finding prime numbers.

Directed Acyclic Word Graph (DAWG) for linear time substring operations.

A comprehensive guide to understanding and implementing the sweep line algorithm for computational geometry.

A comprehensive guide to the Trie (Prefix Tree) data structure with visual diagrams, Insert, Search, Delete, and AutoComplete implementations in Python, Java, and C++, and practice problems.

Mathematical Algorithms play a crucial role in solving complex problems efficiently in both DSA and competitive programming.

A comprehensive guide to using the Z-Algorithm for efficient pattern matching.