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Fibonacci NumberTonny XuVoyageGroup LT @ 2012/03/22
Agenda•What’s Fibonacci number•What’s golden ratio•How to implement an algorithm to calculate••Other pitfalls
If you are an interviewer
And also, you plan to ask thecandidate to write analgorithm to calculate
Glad to see you are here!
What’s Fibonacci Number
What’s Fibonacci Number•an integer sequence
What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of Pisa
What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of(aka Fib...
What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of(aka Fib...
What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of(aka Fib...
What’s Fibonacci Number•in picture
What’s Fibonacci Number•in picture
What’s Fibonacci Number•in picture
What’s Fibonacci Number•in picture
What’s golden ratio
What’s golden ratio           0.618
What’s golden ratio           0.618•
What’s golden ratio                 0.618••relation to Fibonacci Number
What’s golden ratio                 0.618••relation to Fibonacci Number
How to implement the     algorithm?
Naive method
Time?
Bottom up
Time?
Can we do better?
Use φ
Time?But.... precision
Use table
Time?
another formula
another formula
another formula
Time?
Other pitfalls•bounds check!
Other pitfalls•bounds check!   INT32_MAX = 2147483647   fib(47) = 2971215073   UINT32_MAX = 4294967295   fib(48) = 4807526...
Thank you ^_^
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An overview of Fibonacci Number

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fibonacci number @VoyageGroup.com

  1. 1. Fibonacci NumberTonny XuVoyageGroup LT @ 2012/03/22
  2. 2. Agenda•What’s Fibonacci number•What’s golden ratio•How to implement an algorithm to calculate••Other pitfalls
  3. 3. If you are an interviewer
  4. 4. And also, you plan to ask thecandidate to write analgorithm to calculate
  5. 5. Glad to see you are here!
  6. 6. What’s Fibonacci Number
  7. 7. What’s Fibonacci Number•an integer sequence
  8. 8. What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
  9. 9. What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of Pisa
  10. 10. What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of(aka Fibonacci) Pisa
  11. 11. What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of(aka Fibonacci) Pisa•in mathematics
  12. 12. What’s Fibonacci Number•an integer sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...•named after Leonardo of(aka Fibonacci) Pisa•in mathematics with: F1 = F2 = 1
  13. 13. What’s Fibonacci Number•in picture
  14. 14. What’s Fibonacci Number•in picture
  15. 15. What’s Fibonacci Number•in picture
  16. 16. What’s Fibonacci Number•in picture
  17. 17. What’s golden ratio
  18. 18. What’s golden ratio 0.618
  19. 19. What’s golden ratio 0.618•
  20. 20. What’s golden ratio 0.618••relation to Fibonacci Number
  21. 21. What’s golden ratio 0.618••relation to Fibonacci Number
  22. 22. How to implement the algorithm?
  23. 23. Naive method
  24. 24. Time?
  25. 25. Bottom up
  26. 26. Time?
  27. 27. Can we do better?
  28. 28. Use φ
  29. 29. Time?But.... precision
  30. 30. Use table
  31. 31. Time?
  32. 32. another formula
  33. 33. another formula
  34. 34. another formula
  35. 35. Time?
  36. 36. Other pitfalls•bounds check!
  37. 37. Other pitfalls•bounds check! INT32_MAX = 2147483647 fib(47) = 2971215073 UINT32_MAX = 4294967295 fib(48) = 4807526976 INT64_MAX = 9223372036854775807 fib(93) = 12200160415121876738 UINT64_MAX = 18446744073709551615 fib(94) = 19740274219868223167
  38. 38. Thank you ^_^

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