Topics for CS4102, Exam 1, Spring 2010

• Terms and concepts: feasible, tractable, intractable, brute-force, what's an algorithm?
• Total execution time and counting basic operations
• Worst-case, average-case, best-case
• Counting operations, using summations
• Asymptotic growth rate; order classes; BigTheta and all the others
  • Definitions and their conceptual meaning
  • Limit definitions for BigTheta and the others
  • Proof that a function belongs to an order class: use limit definitions, proof by induction
• Lower bounds, optimal algorithms
• Searching: sequential, modified sequential, binary search
  • Decision trees for searching
  • Lower bound argument for searching, and why binary search is optimal

• Definition of divide and conquer design strategy (D&C)
  • Writing simple recursive divide and conquer algorithms
• Writing recurrence relations for D&C algorithms
• Reducing recurrences to closed form using the substitution method
• Using the Main and Master theorems (I'll give you the 3 cases for each one)
• Examples: mergesort; finding max and min; binary search; quicksort; Towers of Hanoi
• Trominos: example of D&C; the analysis doesn't require a recurrence
• Nothing on closest-pair of points problem
  
• Strassens' matrix mult., just know the general ideas that make this algorithms interesting. (No details on implementation.)

• Insertion sort: worst-case complexity; what's its advantages
  • What is the Lower Bound argument about sorts that just swap adjacent keys?
• Quicksort:
  • What's the overall D&C strategy?
  • Partition: only do the one in the book (the first one in the slides). (This is not Hoare's partition; it's called Lomuto's partition). W(n) = n-1 for this Partition
  • For Quicksort, what's the recurrence of the worst-case? the best-case?
  • What leads to the worst-case? How can we prevent this? (randomized choice of pivot element at start of partition code)
  • Average case for QS: know the rationale behind the initial recurrence. But no need to solve this. Know the bottom line.
• Space complexities of sorts: insertion sort, quicksort, mergesort. (General questions on these.)
• This will not be covered on Exam 1.  (This is slides 31 onwards in that set.) Decision tree and lower-bound arguments for optimal sorting.