Fibonacci Sequences-Advance Analysis Design-Lecture Slides, Slides for Advance Analysis Design. Bengal Engineering & Science University

Advance Analysis Design

Description: This course object is to design and analysis of modern algorithms, different variants, accuracy, efficiency, comparing efficiencies, advance designing techniques. In this course algorithm will be analyse using real world examples. This lecture includes: Fibonacci, Sequences, Natural, Model, Construction, Explicit, Formula, Recursive, Algorithm, Applications, Model
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Lecture No. 6
Fibonacci Sequences
(Natural Models)
Dr Nazir A. Zafar Advanced Algorithms Analysis and Design
In this lecture we will cover the following:
Fibonacci Problem and its Sequence
Construction of Mathematical Model
Explicit Formula Computing Fibonacci
Recursive Algorithms
Generalizations of Rabbits Problem and
Constructing its Mathematical Models
Applications of Fibonacci Sequences
Dr Nazir A. Zafar Advanced Algorithms Analysis and Design
Today Covered
By studying Fibonacci numbers and constructing
Fibonacci sequence we can imagine how
mathematics is connected to apparently unrelated
things in this universe.
Even though these numbers were introduced in
1202 in Fibonacci’s book Liber abaci, but these
numbers and sequence are still fascinating and
mysterious to people of today.
Fibonacci, who was born Leonardo da Pisa gave a
problem in his book whose solution was the
Fibonacci sequence as we will discuss it today.
Fibonacci Sequence
Dr Nazir A. Zafar Advanced Algorithms Analysis and Design
Start with a pair of rabbits, one male and one female,
born on January 1.
Assume that all months are of equal length and that
rabbits begin to produce two months after their own birth.
After reaching age of two months, each pair produces
another mixed pair, one male and one female, and then
another mixed pair each month, and no rabbit dies.
How many pairs of rabbits will there be after one year?
Answer: The Fibonacci Sequence!
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
Fibonacci’s Problem
Dr Nazir A. Zafar Advanced Algorithms Analysis and Design
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University: Bengal Engineering & Science University
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