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Exploring Tree Recursion with Fibonacci Numbers and Microsoft Agents

This article delves into the concept of tree recursion, particularly through the lens of computing Fibonacci numbers. We begin with the classic Fibonacci sequence defined recursively, illustrating the computation process for `fib(n)` with an example where `n=5`. The recursive method leads to multiple calls, showcasing the importance of understanding tree structure in recursion. Additionally, we explore integrating Microsoft Agents to make learning more interactive, enhancing understanding through voice commands and user interactions. Inquire about further resources to dive deeper into MS Agents and their applications.

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Exploring Tree Recursion with Fibonacci Numbers and Microsoft Agents

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  1. Tree Recursion Traditional Approach

  2. Tree Recursion • Consider the Fibonacci Number Sequence: Time: 0 1 2 3 4 5 6 7 80, 1, 1, 2, 3, 5, 8, 13, 21, ... /0when n = 0fib(n)= |1 when n = 1\fib(n - 1) + fib(n - 2)otherwise

  3. Tree Recursion(cont.) • As code this is: int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

  4. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

  5. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4)

  6. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4)

  7. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4) fib(3) fib(2)

  8. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4) fib(3) fib(2)

  9. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4) fib(3) fib(2) fib(2) fib(1)

  10. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4) fib(3) fib(2) fib(2) fib(1)

  11. What happens when computing fib(5)? 5 2 3 2 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 0

  12. What is the Problem? • I am explaining everything! • Why not make this more interesting by using MS Agents • Agents are helpers like the paper clip in Word • But they are much more: • They talk to you • And can, in some cases, understand voice commands

  13. Tree Recursion MS Agent Approach

  14. Tree Recursion • Consider the Fibonacci Number Sequence: Time: 0 1 2 3 4 5 6 7 8 0, 1, 1, 2, 3, 5, 8, 13, 21, ... • This sequence is defined by the rule: /0when n = 0 fib(n)= |1 when n = 1 \fib(n - 1) + fib(n - 2)otherwise

  15. Tree Recursion(cont.) • As code this is: int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

  16. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

  17. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4)

  18. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4)

  19. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4) fib(3) fib(2)

  20. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4) fib(3) fib(2)

  21. What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; } fib(3) fib(4) fib(3) fib(2) fib(2) fib(1)

  22. MASH: Microsoft Agent Scripting Helper MASH is an editor that allows you to construct the scripts that you can then embed in other applications MASH

  23. Where to Learn More • MS Agent Page:http://msdn.microsoft.com/workshop/imedia/agent/default.asp • Sunfires MS Agent Page:http://www.angelfire.com/il2/sunfire/index.html • Uniquities MS Agent Planet:http://www.uniquities.co.uk/whatsnew.htm • Presentation Narrator: http://msdn.microsoft.com/workshop/imedia/agent/sampleoffice.asp • Microsoft Agent Scripting Helper:http://www.bellcraft.com/mash/

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