hw1sol - CS 170 Fall 2009 Algorithms Christos Papadimitriou HW 1 Due September 4th 7pm Instructions Please write your name your TAs name your discussion

CS 170 Algorithms Fall 2009 Christos Papadimitriou HW 1 Due September 4th, 7pm Instructions: Please write your name, your TA’s name, your discussion section time (e.g., Fri 11am) prominently on the first page of your homework. Also list your study partners for this homework, or “none” if you had no partners. You are welcome to form small groups (up to four people) to work through the homework, but you must write up all your solutions strictly by yourself, and you must acknowledge any ideas you got from others (including from books, papers, web pages, etc.). Please read the collaboration policy on the course web page. This homework is due Friday, September 4th, at 7pm, in the homework drop box in 283 Soda. Unless indicated otherwise, all problems are from the Algorithms textbook by Dasgupta, Papadimitriou and Vazirani. 1. ( pts.) 0.1 (also give a one sentence justification for your answer) Answer: • a) f = Θ ( g ) ; both linear functions • b) f = O ( g ) ; 1 / 2 < 2 / 3 • c) f = Θ ( g ) ; both linear up to an aditive polylog term • d) f = Θ ( g ) ; aditive terms linear, grow much slower than n log n • e) f = Θ ( g ) ; both are linear in log n • f) f = Θ ( g ) ; both are linear in log n • g) f = Ω