Algorithms: Correctness and Complexity (Engi-5892) 2020

Notes

Course introduction

• Course introduction

Unit 0 Notations and math review

• Some programming notations.
• Discrete Math Review alg-co-co-notes-000-discrete-math-review

Unit 1 Correctness of algorithms and code

• Reading: Proof Outline Logic (sequential edition)
• Gapped notes 1 on proof outlines. alg-co-co-notes-010-proof-outlines
  • Revised 2020-Jan-12
• Notes (no gaps) 1.5 on improving the rules to prevent errors alg-co-co-notes-015-improving-our-rules
  • Revised 2020-Jan-12
• Gapped notes 2 on summing an array alg-co-co-notes-020-summing-an-array
• Notes 3 on binary search of an array alg-co-co-notes-030-binary-search
• Notes 4. Iteration checklist and finding invariants. Slide set 4
• Notes 5. Data refinement. Slide set 5
• Notes 6. Object invariants and class refinement Slide set 6
• Notes 7. More examples of object invariants and class refinement Slide set 7
• Dafny Notes 0. Verification of methods. Dafny Notes 0.
  • Binary searches in Dafny.
• Dafny Notes 1. Functions, predicates, and lemmas. Dafny Notes 1.
  • Russian peasant multiplication and exponentiation in Dafny.
• Dafny Notes 2. Arrays, sequences, and side effects. Dafny Notes 2.
  • Selection sort in Dafny.

Unit 2 Recursion, context-free grammars, and parsing

• Reading: Chapters 2 (especially 2.3) and 7.
• Notes 8.0. Procedure specification and recursion. Slide set 8.0
• [Optional Notes 8.3. Tail call optimization and eliminating arbitrary recursion. Optional slide set 8.3.]
• Notes 8.5. Top-down and bottom-up algorithms. Slide set 8.5
• Notes 9.0 Designing loops by reasoning recursively alg-co-co-notes-090-loops-as-recursion
• Notes 10.0. Languages and Grammars alg-co-co-notes-100-cfgs (Slide 8 updated 2020 Mar 5).
• Notes 10.5. Recursive-Descent Parsing alg-co-co-notes-105-parsing

Unit 3 Complexity

• Reading Chapters 3, 7, 8
• Notes 11. Time Complexity alg-co-co-notes-110-complexity
• Notes 12. Lower Bounds and the complexity of sorting. alg-co-co-notes-120-more-complexity (Updated 2020 March 19).
• Boun notes 12.5 Demystifying complexity with the help of some Dachshund's.

Unit 4 Graph Search

• Reading: Chapters 22 and 24 (especially 24.3)
• Notes 13. Graph search alg-co-co-notes-130-graph-search
• Algorithms Animated(Unless you use Internet Explorer, this is just not going to work.)
• Notes 14 [Not covered] A*alg-co-co-notes-140-a-star
• Notes 15. Depth-first search and Kosaraju's strongly connected components algorithm. alg-co-co-notes-150-more-graph-searching

Unit 5 Greedy Algorithms and Dynamic Programming

• Reading: Chapters 15 and 16.
• Notes 16. Greedy Algorithmsalg-co-co-notes-160-greedy-algorithms
• Notes 17 Recursive search of optimal solutions. alg-co-co-notes-170-recursive-search (Updated 2020 April 6 -- only page 9)
• Notes 18 Dynamic Programming alg-co-co-notes-180-dynamic-programming
  • Java code for MED. (Updated 2020 April 6 -- only page 15)

Unit 6 Limitations

• Reading: Chapter 34
• Notes 19: Intractability alg-co-co-notes-190-intractability
• Notes 20 Uncomputability alg-co-co-notes-200-incomputabilty

Summary

• Summary for units 1 and 2.alg-co-co-notes-210-summary

(c) Theodore Norvell