CS 173: Skills list for eleventh examlet

• Basic data structures
  • 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 (what's in x's connected component)
    • Towers of Hanoi solver
  • 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).