CS 173: Skills list for eleventh examlet

• Basic data structures
  • Be able to read code that uses basic linked list operations (first, rest, cons).
  • Know the big-O running times of basic operations on linked lists and arrays. These include reading/writing values, adding/removing elements, and dividing the list/array at locations at/near the start, in the middle, and at the end.
• Algorithms
  • Be familiar with the overall structure and big-O running times of the following algorithms.
    • merge two sorted lists
    • binary search
    • merge sort
    • graph reachability
    • Towers of Hanoi solver
  • Know that Karatsuba's algorithm divides a size n multiplication problem into 3 (better than 4!) half-size sub-problems. And that its running time is O(n^{log ₂ 3}), which is about O(n^1.6) and thus better than the O(n²) you get by dividing a multiplication into 4 half-size sub-problems. You aren't expected to reproduce the details.
  • Find a big-O solution for slightly harder recursive definitions than the ones for examlet 10, e.g. requiring use of the change of base formula.
  • Given an unfamiliar but fairly simple function in pseudo-code, analyze how long it takes using big-O notation. You should be able to analyze nested for loops, recursive functions, and simple examples of while loops.
  • For an algorithm involving loops (perhaps nested), express its running time using summations.
  • Given a recursive algorithm (familiar or unfamiliar) express its running time as a recursive definition.
• NP
  • Know that certain classes of sentences have exponentially many parse trees. (And thus producing all parses of a sentence requires exponential time.)
  • Know that the Towers of Hanoi puzzle has been proved to require exponential time.
  • Know that NP is the set of problems for which we can quickly (polynomial time) justify "yes" answers.
  • Know that co-NP is the set of problems for which we can quickly (polynomial time) justify "no" answers.
  • Know that problems in NP can be solved in exponential time, but it's not known whether they can be solved in polynomial time.
  • Know what an NP-complete problem is: a problem in NP for which a polynomial-time algorithm would imply that any problem in NP can be solved in polynomial time.
  • Know some examples of NP-complete problems: graph colorability, circuit satisfiability (Circuit SAT), propositional logic satisfiability, marker making, the travelling salesman problem.
  • Know that you can decide in polynomial time whether a graph is 2-colorable (aka bipartite).