Basic Algorithms, v22.0310, Fall'98: Homework 2

Due date: Wednesday, September 30, in class.

Hand in solution in hard copy, STAPLED together.

  1. Prove that (n+c)5 is O(n5), for any real constant c. Do not forget to consider the case where c is negative. NOTE: in showing Big-Oh claims, you need to explicitly show the constants C>0 and n0 of the Big-Oh definition.
  2. Prove parts 4 and 9 in Proposition 2.16 on page 49.
  3. Do Problem R-2.5 on page 58.
  4. Do Problem R-2.6 on page 58.