Syllabus for CS218 - Midterm II exam

Topics and Sample Questions for Midterm II:
• 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 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 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 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 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...

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