Syllabus for CS218 - FINAL exam

- Concept of worst-case time-complexity
- Asymptotic notations: big-Oh, big-Theta, big-Omega and their properties
- prove or disprove that the following function is big-Oh, big-Theta, big-Omega of ...

- Worst-case analysis of (purely) iterative code
- Lower bound on comparison-based sorting
- Deriving and solving recurrence relations
- derive a recurrence relation from the following pseudo-code ...
- solve the following recurrence relation by iterative substitution ...
- solve the following recurrence relation by Master Theorem ...
- prove by induction the correctness of the solution of the following recurrence relation ...

- Amortized analysis
- Derive a upper bound for the total work required for the following sequence
of
*n*operations ... - String Matching (Brute force, KMP, tries, suffix tries)
- questions (correctness, pseudocode, time complexity) on the algorithms/data structures mentioned in parenthesis (or about the corresponding problems)
- design an efficient algorithm that determines whether a string x ...
- KMP: compute the failure function on the following string ...
- compute the suffix trie of the following string ...

- Greedy method (activity selection, fractional knapsack, Huffman coding, Dijkstra, Prim, Kruskal)
- questions (correctness, pseudocode, time complexity) on the algorithms mentioned in parenthesis (or about the corresponding problems)
- build the optimal huffman tree for the following string ...
- run Dijkstra algorithm on the following graph ...
- run Kruskal algorithm on the following graph ...
- run Prim algorithm on the following graph ...
- devise a greedy algorithm for the following problem ...
- prove that the following algorithm has the greedy-choice property ...
- prove that the following problem has the optimal substructure property ...
- show why greedy is a bad choice for the following problem ...

- Union-Find
- run the following set of operations (Make-Set, Find-Set, Union) using both union by rank and path compression. Show the final trees ...
- prove the following property about Union-Find ...

- Divide and Conquer method (linear time selection, Karatsuba's integer multiplication, Strassen's matrix multiplication, polynomial multiplication and FFT, FFT-based integer multiplication)
- questions (correctness, pseudocode, time complexity) on the algorithms mentioned in parenthesis (or about the corresponding problems)
- questions on the complex roots of unity and their properties
- devise a divide and conquer algorithm for the following problem ...

- Dynamic Programming method (01-knapsack, LCS, matrix chain product, Bellman-Ford, Floyd-Warshall)
- questions (correctness, pseudocode, time complexity) on the algorithms mentioned in parenthesis (or about the corresponding problems)
- devise a dynamic programming algorithm for the following problem ...
- compute the maximum profit for the following 01-knapsack assignment ...
- compute the longest common subsequence for the following two strings ...
- run Bellman-Ford algorithm on the following (small) graph ...
- run Floyd-Warshall algorithm on the following (very small) graph ...
- given the final table for a dynamic programming algorithm, trace back all the optimal solutions...

- Network Flow (Ford-Fulkerson, Edmonds-Karp, max bipartite matching)
- questions (correctness, pseudocode, time complexity) on the methods/algorithms mentioned in parenthesis (or about the corresponding problem)
- run Edmonds-Karp algorithm on the following flow network ...
- find the maximum matching on the following bipartite graph ...

**NOTE:** The list above is representative of the problems that could be on the
exam, but not necessarly exhaustive