joseph lindo recursion sir joseph lindo university of the cordilleras
TRANSCRIPT
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Joseph Lindo
Recursion
Sir Joseph LindoUniversity of the Cordilleras
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Joseph Lindo
Activity
Application
Definition
No Iteration
RecursionRecursionIt is a programming
technique in which a call to a method appears in that method’s body
Once you understand recursive methods, they are often simpler to write than their iterative equivalents
Definition
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Joseph Lindo
No Iteration
DefinitionActivity
Activity
Application
RecursionRecursion
vsIteration
Problem: Collect $1,000.00 for charity
Assumption: Everyone is willing to donate a penny
No Iteration
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Joseph Lindo
No Iteration
DefinitionActivity
Activity
Application
RecursionRecursion
vsIteration
Iterative SolutionVisit 100,000 people, asking each for a pennyRecursive SolutionIf you are asked to collect a penny, give a penny to the person who asked you for it
No Iteration
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Joseph Lindo
No Iteration
DefinitionActivity
Activity
Application
RecursionBasic
Applications
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Joseph Lindo
Application
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DefinitionActivity
Activity
RecursionGroup
ActivityCreate the flow chart of a
Fibonacci Sequence with the following conditions:
1 is always the startAccept the number of series
to be printed from the user.Activity
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Joseph Lindo
Application
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DefinitionActivity
Activity
Recursion
Assignment
Create the flow chart of a simple Factorial in a one whole yellow paper, wherein the number must come from the user and there is no negative number.
Activity
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Joseph Lindo
Recursion--end--
Sir Joseph LindoUniversity of the Cordilleras
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Joseph Lindo
Definition
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Factorial
A factorial is defined as follows:n! = n * (n-1) * (n-2) …. * 1;
For example:1! = 1 (Base Case)2! = 2 * 1 = 23! = 3 * 2 * 1 = 64! = 4 * 3 * 2 * 1 = 245! = 5 * 4 * 3 * 2 * 1 = 120
If you will study the examples you will
start to see a pattern
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Joseph Lindo
Definition
jo
Factorial
Example using the pattern
10 = 10 * 9!
5! = 5 * 4!
4! = 4 * 3!
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Joseph Lindo
Code
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Factorial
Iterative approach:
int factorial (int n){ int answer = 1; for (int i=1; i<=n; i++) answer *= i; return answer;}
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Joseph Lindo
Code
jo
Factorial
Recursive approach:
int factorial (int n){ if (n == 0) return 1; else return n * factorial(n-1);}
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Joseph Lindo
Definition
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Fibonacci Sequence
The sequence begins with one
Each subsequent number is the sum of the two preceding numbers
Fib(n) = Fib(n-1) + Fib(n-2) 1, 1, 2, 3, 5, 8, 13 . . .
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Joseph Lindo
Applications
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Fibonacci Sequence
Many aspects of nature are grouped in bunches equaling Fibonacci numbers.
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Joseph Lindo
Applications
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Fibonacci Sequence
Music involves several applications of Fibonacci numbers.
A full octave is composed of 13 total musical tones, 8 of which make up the actual musical octave.
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Joseph Lindo
Applications
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Fibonacci Sequence
Paintings
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Joseph Lindo
Applications
jo
Fibonacci Sequence
Human BodyThe lengths of bones in a hand are Fibonacci numbers.
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Joseph Lindo
Diagram
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Fibonacci Sequence
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Joseph Lindo
Diagram
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Fibonacci Sequence
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Joseph Lindo
Diagram
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Fibonacci Sequence