**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.