Recurrence Relations
Chapter 7
(7.1 Introduction)
October 30, 2009
So far …
• Sets
Sets
•
Logic, Proof
•
Functions, Sequences, Relations
• Algorithms
Algorithms
•
(Number theory)
•
Counting Methods
– … Pigeonhole Principle
… Pigeonhole Principle
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CS204 Discrete Math (Fall 2009)
2
sequence
{ C }
{ C
n
}
1,
1,
2,
5,
14, 42, 132, 429,
1430, 4862, 19796
…
C
…
A
i l t
f f
ti
i
hi h th
d
i
…
n
…
•
A special type of function in which the domain
consists of a set of consecutive integers.
–
D = {0,1,2,3,4,5,6,7,8,9,10}
– C
0
= 1, C
1
=1, C
2
= 2, … , C
10
= 19796,
… , C
n
= ?
n
0
1
2
3
4
5
6
7
8
9
10
C
1
1
2
5
14
42
132
429
1430
4862
16796
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CS204 Discrete Math (Fall 2009)
3
n
Recurrence Relations
•
Advanced Counting Technique
• Recursion
•
Recursive algorithms
P
id
th
l ti
f
bl
f
i
i
t
– Provide the solution of a problem of size n in terms
of the solutions of one or more instances of the
same problem of smaller size
– To analyze its complexity
•
Obtain a recurrence relation
that expresses the number of
operations required to solve a problem of size n in terms of the
number of operations required to solve the problem for one or
more instances of smaller size.
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 Spring '08
 Unkown
 Algorithms, Recursion, CN, Recurrence relation, Fibonacci number

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