CS 332: Algorithms

Homework #1

Assigned: Monday, Jan 21

Due: Monday, Jan 28

CLRS = Cormen, Leiserson, Rivest, and Stein (the text book).

(1) CLRS 2.1-3

(2) CLRS 2.3-5

(3) CLRS 2.3-4. To what, asymptotically, does the recurrence evaluate?

(4) CLRS 2.3-6

(5) A graph T is said to be a tree if T is connected and has no cycles. Show by induction that if T is a tree with n vertices, then T has exactly n-1 edges.
Caution: When proving the induction step (if true for a tree of n nodes then true for a tree of n+1nodes), make sure to argue that your proof will work for an arbitrary tree of n+1 nodes.