CS 151: Algorithms and Data Structures II

Course modules

• Module 1: Introduction
• Module 2: Sorting
  • Quicksort, quicksort optimizations.
  • Mergesort, mergesort optimizations.
  • Heaps and heapsort.
  • Bucketsort.

• Module 3: Ordered Search
  • Review of binary search trees.
  • Deletion from a binary search tree.
  • AVL trees.
  • Multiway trees.
  • Self-adjusting binary search trees.

• Module 4: Equality Search, Tries
  • Key signatures and addressing.
  • Open-chain hashing.
  • 2D hashing.
  • Digital search trees.
  • Tries

• Module 5: Pattern Search
  • The string search problem.
  • The Rabin-Karp algorithm.
  • The Knuth-Pratt-Morris algorithm
  • Finite-automaton search.
  • Wildcards, regular expressions and non-deterministic finite automata.
  • Web search engines.

• Module 6: Performance testing
  • Performance testing and profiling.
  • Code tuning in Java.
  • Stepwise refinement in problem-solving.
  • Tough programming problems.

• Module 7: Graphs, part I
  • Definitions, key ideas, applications.
  • Data structures for graphs.
  • Breadth-first search.
  • Depth-first search.
  • Applications of depth-first search.
  • Topological sort in DAG's.

• Module 8: Graphs, part II
  • On-line vs. off-line problems.
  • On-line equivalence-class problem and union-find.
  • Minimum spanning trees: Kruskal's algorithm with union-find.
  • Priority queues.
  • Prim's spanning tree algorithm.
  • Dijkstra's shortest-path algorithm.

• Module 9: Shortest Paths and Dynamic Programming
  • Assorted topics in Shortest-Paths: negative weights, DAG's.
  • All-pairs shortest paths: Floyd-Warshall algorithm.
  • Distributed routing: RIP, OSPF.
  • Dynamic programming: Load balancing problem.
  • Dynamic programming: Floyd-Warshall algorithm.
  • Dynamic programming: Optimal binary search trees.

• Module 10: Problems, solution spaces and local search
  • Combinatorial optimization problems.
  • Solution spaces, local neighborhood, walking around solution space.
  • Greedy local search.
  • Simulated annealing.

• Module 11: Problem complexity and NP-Completeness
  • Problem complexity.
  • Some well-known combinatorial problems.
  • Problem transformations.
  • NP-complete problems, reducibility.
  • Approximations.
  • Exhaustive Enumeration

• Module 12: Bio-inspired problems and algorithms
  • Molecular biology primer.
  • DNA sequencing problems.
  • Cellular automata and Von Neumann's Quandary.
  • Computing with DNA.
  • Genetic algorithms.

• Module 13: Probability and Algorithms
  • Simple Estimation.
  • Estimation accuracy: confidence intervals.
  • Histograms.
  • Monte Carlo estimation.
  • Evaluating average-case complexity of algorithms.

• Module 14: Scientific computation
  • Bisection algorithm.
  • Nonlinear iterative optimization
  • Fourier transform.