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.