CS 173: Skills list for Examlet 6

• (Recap) Earlier algorithms and big-O content
• Recursion Trees
  • Given a recursively defined function, find its closed form by drawing a recursion tree and adding up the work at all levels. (Examples would look like those presented in the textbook, e.g. the level sums are constant or increase in a pattern based on the key summations given above.)
  • Find a big-O solution for a simple recursive definition, of the types that we've seen as examples of unrolling and recursion trees.
• Algorithms
  • Be familiar with the overall structure and big-O running times of the following algorithms.
    • Towers of Hanoi solver
    • Karatsuba's algorithm (you won't have to reproduce all 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).