Algorithm Mastery Course 算法精通课程
From Basic Algorithms to Advanced Problem Solving 从基础算法到高级问题解决
🧮 Course Overview 🧮 课程概述
Master the art of algorithmic thinking and problem-solving in this comprehensive 60+ hour course. From fundamental sorting algorithms to advanced dynamic programming and graph theory, you'll gain the skills needed to excel in competitive programming (USACO, ACSL), technical interviews at top tech companies, and real-world software development. Our systematic approach ensures deep understanding of both theoretical concepts and practical implementations. 在这个60多小时的综合课程中掌握算法思维和问题解决的艺术。从基础排序算法到高级动态规划和图论， 您将获得在竞赛编程（USACO、ACSL）、顶级科技公司技术面试和实际软件开发中脱颖而出所需的技能。 我们的系统化方法确保深入理解理论概念和实际实现。
📚 Comprehensive Curriculum 📚 完整课程大纲
Basic Algorithms 基础算法
Master fundamental algorithmic techniques and concepts 掌握基础算法技术和概念
- Sorting Algorithms (Quick, Merge, Heap)
- Binary Search & Variations
- Two Pointer Technique
- Sliding Window Algorithm
- Bit Manipulation
- Prefix Sums & Differences
- Discretization
- Interval Merging
Advanced Data Structures 高级数据结构
Essential data structures for efficient problem solving 高效解决问题的基本数据结构
- Linked Lists (Single & Double)
- Stacks & Queues
- Monotonic Stack & Queue
- String Algorithms (KMP, Z-Algorithm)
- Trie (Prefix Tree)
- Union-Find (Disjoint Set)
- Heaps & Priority Queues
- Hash Tables & Rolling Hash
Graph Theory 图论
Graph algorithms and network analysis 图算法和网络分析
- DFS & BFS Traversal
- Topological Sorting
- Shortest Path (Dijkstra, Bellman-Ford)
- SPFA Algorithm
- All-Pairs Shortest Path (Floyd-Warshall)
- MST (Prim & Kruskal)
- Bipartite Graph Detection & Matching
- Network Flow & Hungarian Algorithm
Mathematical Foundations 数学基础
Mathematical concepts essential for algorithms 算法必需的数学概念
- Prime Numbers & Sieve of Eratosthenes
- GCD & Euler's Function
- Fast Exponentiation & Modular Arithmetic
- Extended Euclidean Algorithm
- Chinese Remainder Theorem
- Gaussian Elimination
- Combinatorics & Probability
- Inclusion-Exclusion Principle
- Game Theory & Nim
Dynamic Programming 动态规划
Optimization through state-based problem solving 通过状态优化问题解决
- Knapsack Problems (0/1, Unbounded, Multiple)
- Linear DP & LIS/LCS
- Interval DP
- Counting DP
- Digit DP
- State Compression DP
- Tree DP
- DP Optimization (Convex Hull, Monotone Queue)
Greedy & Advanced Topics 贪心与高级主题
Optimal strategies and advanced techniques 最优策略和高级技术
- Interval Scheduling Problems
- Huffman Coding
- Activity Selection
- Fractional Knapsack
- Exchange Arguments
- Segment Trees & Fenwick Trees
- Heavy-Light Decomposition
- Persistent Data Structures
📋 Prerequisites 📋 先修要求
- ✨ Proficiency in Python, Java, or C++ 精通Python、Java或C++
- ✨ Basic data structures knowledge 基础数据结构知识
- ✨ High school mathematics 高中数学
- ✨ Problem-solving mindset 问题解决思维