Senior Training Plan

This program is designed to deepen your mastery of advanced topics. Ideal for Div1 preparation and ICPC regionals.

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Senior

Data Structures Advanced query and tree-based structures

  • Range Queries: Segment Tree, Fenwick Tree (BIT), and Sparse Table.
  • Decomposition: Square Root Decomposition and Mo's Algorithm.
  • Advanced Techniques: CDQ Divide & Conquer, Persistent Segment Tree, and Augmented/Rollback DSU.
  • 2D Queries: 2D Segment/Sparse/BIT and Sparse Segment Trees.

Strings Hashing, tries, and suffix structures

  • Hashing: Rolling, XOR, Polynomial, 2D, and Double Hashing.
  • Classic Algorithms: KMP, Z-Algorithm, and Manacher's Algorithm.
  • Tree-based Structures: Trie (String/Bit-based) and Suffix Array.
  • Automata: Aho-Corasick Algorithm.

Graph Theory Flows, matching, and advanced connectivity

  • Connectivity: Strongly Connected Components (Tarjan's, Kosaraju's) and Bridge/DFS Trees.
  • Flows & Matching: Maximum Flow, Min-Cost Max-Flow, and Maximum Bipartite Matching.
  • Logic: 2-SAT problem-solving.

Dynamic Programming Advanced techniques and optimizations

  • Common Tricks: Presorting, Pre-calculation, Double DP, and State Elimination.
  • Masking: Broken Profile DP and Submask Enumeration.
  • Optimizations: Prefix Sum, Data Structures, Convex Hull Trick, D&C Optimization, and Knuth Optimization.

Trees Advanced traversals and decomposition

  • Ancestry & Traversal: Binary Lifting for LCA and Euler Tour for tree linearization.
  • DP & Tricks: DP on Trees, the "All Roots" problem-solving pattern, and Small to Large merging.
  • Decomposition: Heavy-Light Decomposition (HLD) and Centroid Decomposition.

Combinatorics Counting, probability, and sequences

  • Binomial Coefficients: Pascal's Triangle, Hockey Stick Identity, and Binomial/Multinomial Theorems.
  • Sequences & Techniques: Fibonacci, Stirling, Catalan numbers, Stars and Bars, and Inclusion-Exclusion.
  • Advanced Topics: Probability & Expectations, Matrix Exponentiation, and XOR Basis.

Computational Geometry Primitives and problem-solving

  • Fundamental geometric primitives and their applications.
  • Solving common geometry problems from contests (e.g., "Ahmed Elsayed Mood Problems").