# shareoi | hzwer | Knowledge Base | Instagit 算法竞赛课件分享 GitHub Stars: 4.4k Repository: https://github.com/hzwer/shareoi --- ## Articles ### [Gaussian Elimination for Solving XOR Systems in Linear Algebra Problems](/hzwer/shareoi/gaussian-elimination-solving-xor-systems-linear-algebra-problems) Learn how Gaussian elimination solves XOR systems efficiently in linear algebra. Discover O(n*m) solutions over GF(2) by treating XOR as addition. Explore this powerful technique now. - Tags: deep-dive - Published: 2026-03-03 ### [Using Fourier Transforms for Polynomial Multiplication in Competitive Programming: A Complete Guide](/hzwer/shareoi/using-fourier-transforms-polynomial-multiplication-competitive-programming) Master polynomial multiplication with Fourier Transforms in competitive programming. Learn how FFT speeds up calculations from O(n^2) to O(n log n) with this guide. - Tags: tutorial - Published: 2026-03-03 ### [How to Solve Knapsack Problems Using Dynamic Programming: A Complete Guide](/hzwer/shareoi/how-to-solve-knapsack-problems-using-dynamic-programming) Master knapsack problems with dynamic programming. Discover how to define states and apply transitions to maximize value efficiently. Learn the complete guide now. - Tags: tutorial - Published: 2026-03-03 ### [Computational Geometry Primitives in ShareOI: Convex Hull and Rotating Calipers Resources](/hzwer/shareoi/implementation-computational-geometry-primitives-convex-hull-rotating-calipers) Explore computational geometry primitives like convex hull and rotating calipers in the hzwer/shareoi repository. Find lecture slides on theory but not direct code implementations. - Tags: tutorial - Published: 2026-03-03 ### [State Compression DP for Graph Connectivity Problems: Algorithms and Implementations](/hzwer/shareoi/using-state-compression-dp-graph-connectivity-problems) Learn state compression DP for graph connectivity. Encode vertex subsets with bitmasks to solve complex problems like Steiner trees efficiently. Explore algorithms and implementations. - Tags: tutorial - Published: 2026-03-03 ### [Applying Divide and Conquer on Trees: Centroid Decomposition Techniques from the shareOI Repository](/hzwer/shareoi/applying-divide-and-conquer-trees-problems-centroid-decomposition) Master tree divide and conquer with centroid decomposition from shareOI. Solve path and distance problems efficiently in O(N log N) time. Explore advanced algorithms today! - Tags: tutorial - Published: 2026-03-03 ### [Modeling Combinatorial Problems Using Flow Graphs: A Complete Guide](/hzwer/shareoi/modeling-combinatorial-problems-using-flow-graphs) Learn to model combinatorial problems with flow graphs. This guide explains how vertices, edges, and capacities unlock solutions with max flow and min cut algorithms. - Tags: tutorial - Published: 2026-03-03 ### [How to Implement Persistent Segment Trees for Versioned Data Queries](/hzwer/shareoi/how-to-implement-persistent-segment-trees-versioned-data-queries) Learn to implement persistent segment trees for efficient versioned data queries. Store historical array versions and query past states in O(log n) time. Master this advanced data structure. - Tags: how-to-guide - Published: 2026-03-03 ### [Link-Cut Trees (LCT): Key Operations and Applications for Dynamic Forests](/hzwer/shareoi/key-operations-applications-link-cut-trees-dynamic-trees) Explore Link-Cut Trees (LCT) for dynamic forests. Master key operations like link and cut in O(log N) time and discover their applications in graph algorithms. - Tags: deep-dive - Published: 2026-03-03 ### [Implementing Binary Lifting for LCA and Ancestor Queries on Trees](/hzwer/shareoi/implementing-binary-lifting-lca-ancestor-queries-trees) Implement binary lifting for efficient LCA and ancestor queries on trees. Preprocess in O(N log N) for O(log N) query time. - Tags: tutorial - Published: 2026-03-03 ### [Heavy-Light Decomposition vs Tree Chain Decomposition: Key Differences and Implementation Guide](/hzwer/shareoi/comparison-heavy-light-decomposition-tree-chain-decomposition) Explore heavy-light decomposition vs tree chain decomposition. Discover how HLD optimizes TCD for O(log N) path queries and learn implementation essentials. - Tags: deep-dive - Published: 2026-03-03 ### [Fundamentals of Combinatorial Game Theory Using SG Functions: A Complete Guide](/hzwer/shareoi/fundamentals-combinatorial-game-theory-sg-functions) Master combinatorial game theory with SG functions. Learn how the mex rule and XOR operations simplify complex impartial games into Nim heaps, making them solvable. Your complete guide. - Tags: tutorial - Published: 2026-03-03 ### [Spatial Partitioning with k-d Trees for Nearest Neighbor Queries: A Complete Guide to the shareOI Implementation](/hzwer/shareoi/spatial-partitioning-k-d-trees-nearest-neighbor-queries) Master spatial partitioning with k-d trees for fast nearest neighbor queries. Explore the hzwer shareOI implementation for efficient O(log n) searches. - Tags: deep-dive - Published: 2026-03-03 ### [Applying Möbius Inversion in Number Theory Problems for Competitive Programming: A Complete Guide](/hzwer/shareoi/applying-mobius-inversion-number-theory-problems-competitive-programming) Master Mobius inversion for competitive programming. Learn how this number theory technique transforms divisor sums into prefix sums for efficient O(sqrt N) queries. Optimize your algorithms today. - Tags: tutorial - Published: 2026-03-03 ### [Suffix Automaton Construction and Applications in String Matching](/hzwer/shareoi/suffix-automaton-construction-applications-string-matching) Learn suffix automaton construction for efficient string matching. Explore linear-time solutions for pattern matching and substring problems. - Tags: deep-dive - Published: 2026-03-03 ### [Splay Tree Amortized Analysis and Basic Rotation Operations: A Complete Guide](/hzwer/shareoi/splay-tree-amortized-analysis-basic-rotation-operations) Explore splay tree amortized analysis and basic rotation operations. Learn how zig zig-zig and zig-zag rotations achieve O(log n) performance with our comprehensive guide. - Tags: tutorial - Published: 2026-03-03 ### [Tree Chain Decomposition for Path Queries on Trees: A Complete Guide to Heavy-Light Decomposition](/hzwer/shareoi/understanding-applying-tree-chain-decomposition-path-queries-trees-competitive-programming) Master tree chain decomposition for efficient path queries on trees. Learn Heavy-Light Decomposition (HLD) for O(log N) segment tree operations. Essential for competitive programming. - Tags: tutorial - Published: 2026-03-03 ### [How to Implement Max Flow and Min Cut Algorithms in Competitive Programming](/hzwer/shareoi/how-to-implement-network-flow-algorithms-max-flow-min-cut-competitive-programming) Master max flow and min cut algorithms for competitive programming. Learn to build residual graphs, apply Dinic's algorithm, and find the min cut efficiently. Boost your problem-solving skills today. - Tags: how-to-guide - Published: 2026-03-03