"随机搜索与回溯法：设计与分析"

Design and Analysis of Algorithms, taught by Professor Xu Yun in the fall of 2018 at USTC, covers various algorithms and their analysis. Chapter 2 focuses on backtracking, a method used for solving combinatorial problems. The backtracking method involves selecting rules randomly from available nodes, allowing for the analysis of search performance from a statistical perspective. One successful example of random search is provided to illustrate its effectiveness. Chapter 2.1 provides an overview of the backtracking method, while chapter 2.2 discusses tree and graph traversal. Chapter 2.3 delves into the n-queens problem, while chapter 2.4 tackles permutation generation problems. The Traveling Salesman Problem (TSP) is explored in chapter 2.5, and the 0-1 knapsack problem is covered in chapter 2.6. The lecture introduces search algorithms, backtracking, and related terminology. The basic steps of backtracking algorithms are outlined, followed by a detailed analysis of examples. Exhaustive search, a method of exploring all possible solutions, is also discussed. Overall, the course provides a comprehensive understanding of algorithm design and analysis, with a specific focus on backtracking methods for combinatorial problems. Professor Xu Yun's expertise and guidance ensure that students gain a deep knowledge of various algorithms and their applications.