COMP3010: Algorithm Theory and Design

Daniel Sutantyo, Department of Computing, Macquarie University

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List of Topics

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1. Complexity
2. Correctness
3. Brute Force
4. Dynamic Programming
5. Greedy 
6. Divide and Conquer (Recursion Tree)
7. Strings
8. Graphs
9. Probabilistic Methods
10. P vs NP (Reduction)
11. P vs NP (Approximation Algorithms)

Class Test 2

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1. Complexity
2. Correctness
3. Brute Force
4. Dynamic Programming
5. Greedy
6. Divide and Conquer (Recursion Tree)
7. Strings
8. Graphs
9. Probabilistic Methods
10. P vs NP (Reduction)
11. P vs NP (Approximation Algorithms)

Final Exam

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1. Complexity
2. Correctness
3. Brute Force
4. Dynamic Programming
5. Greedy
6. Divide and Conquer (Recursion Tree)
7. Strings
8. Graphs
9. Probabilistic Methods
10. P vs NP (Reduction)
11. P vs NP (Approximation Algorithms)

Final Exam

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1. Complexity
2. Correctness
3. Brute Force
4. Dynamic Programming (25 marks ~ 14%)
5. Greedy (30 marks ~ 16%)
6. Divide and Conquer (Recursion Tree) 
7. Strings
8. Graphs (35 marks ~ 19%)
9. Probabilistic Methods
10. P vs NP (Reduction) (25 marks ~ 14%)
11. P vs NP (Approximation Algorithms) (45 marks ~ 25%)

Class Test 2

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1. Complexity
2. Correctness
3. Brute Force
4. Dynamic Programming
5. Greedy
6. Divide and Conquer (Recursion Tree)
7. Strings
8. Graphs
9. Probabilistic Methods
10. P vs NP (Reduction)
11. P vs NP (Approximation Algorithms)

Major Topics not in the Final Exam:

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1. String Algorithms (Huffman Coding, Edit Distance)
   • as in you would not be required to do them, but you may still need to know the basic principles
2. Substitution method
   • as above

Week 1-3, 6: Complexity, Correctness, Brute Force

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• induction
• complexity notation (\(O\)-notation, \(\Theta\)-notation, \(\Omega\)-notation)
• recursion-tree method, master-method
• permutations and combinations for brute force
  • \(O(2^n)\) and \(O(n!)\)
• recursive backtracking

Week 4-5: Greedy and Dynamic Programming

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• recursive relation (recursion tree)
  • decompose problems into subproblems
• optimal substructure, cut and paste technique
• dynamic programming:
  • overlapping subproblems
  • no need for bottom-up if you cannot spot it
• greedy algorithm:
  • greedy choice, explain why it is safe
• time complexities

Week 8: Graph Algorithms

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• mostly straightforward
• make sure you understand the algorithms:
  • Bellman-Ford
  • Matrix Multiplication Method
  • Floyd-Warshall

Week 11-12: P vs NP

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• may have some brute-force questions 
• understand what reductions are
• understand how to do approximation algorithms

Extra Support Sessions

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• Can organise a zoom class on Tuesday or Wednesday, Q&A session
  • but please don't use this to ask questions about the assignment ...
• Discord