Course Notes: Algorithms

Author: Liang Huang

This book is intended for an introductory course on the design and analysis of algorithms, assuming that students have already taken a data structures course and are comfortable with recursion and big-\(O\) notations. We also assume that students are fluent in at least one of the three major languages: C/C++, Java, and Python. All coding examples are given in Python.

• Chapter 1: Data Structures
  • 1.1: Quicksort and Binary Search Tree
  • 1.2: Average-Case Analysis of Quicksort
  • 1.3: Quickselect
  • 1.4: Mergesort
  • 1.5: Advanced Divide-n-Conquer: Recursion with byproduct
  • 1.6: Priority queue and Binary Heap
  • 1.7: Applications of Heap
  • 1.8: Lowerbound of Sorting
• Chapter 2: Dynamic Programming
  • 2.1: From Fibonacci to Bitstrings to Max Independent Set
  • 2.2: Interpretations of DP: divide-n-conquer, graph, and semiring
  • 2.3: DP beyond graphs; further interpretations of DP
  • 2.4: Knapsack: Unbounded, 0-1, and Bounded
  • 2.5: RNA Folding
• Chapter 3: Graph Algorithms
  • 3.1: Graph Classifications and Representations
  • 3.2: BFS & DFS
  • 3.3: Topological Sort
  • 3.4: Viterbi algorithm and General DP
  • 3.5: Dijkstra’s algorithm for shortest-path
  • 3.6: Prim’s algorithm for minimum spanning-tree