fibonacci number @VoyageGroup.com
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The document discusses Fibonacci numbers, which are an integer sequence where each number is the sum of the two preceding ones, starting from 0 and 1. It describes how the sequence is named after Leonardo of Pisa, also known as Fibonacci. It also discusses how the golden ratio of approximately 0.618 is related to Fibonacci numbers. The document then explores different algorithms to calculate Fibonacci numbers and their time complexities, such as a naive recursive method, bottom-up dynamic programming, and using a formula involving the golden ratio. It notes some potential issues like bounds checking for integer overflow.
fibonacci number @VoyageGroup.com
- 1. Fibonacci Number Tonny Xu VoyageGroup LT @ 2012/03/22
- 2. Agenda •What’s Fibonacci number •What’s golden ratio •How to implement an algorithm to calculate • •Other pitfalls
- 3. If you are an interviewer
- 4. And also, you plan to ask the candidate to write an algorithm to calculate
- 5. Glad to see you are here!
- 7. What’s Fibonacci Number •an integer sequence
- 8. What’s Fibonacci Number •an integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
- 9. What’s Fibonacci Number •an integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... •named after Leonardo of Pisa
- 10. What’s Fibonacci Number •an integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... •named after Leonardo of(aka Fibonacci) Pisa
- 11. What’s Fibonacci Number •an integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... •named after Leonardo of(aka Fibonacci) Pisa •in mathematics
- 12. What’s Fibonacci Number •an integer sequence 0, 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. What’s Fibonacci Number •in picture
- 14. What’s Fibonacci Number •in picture
- 15. What’s Fibonacci Number •in picture
- 16. What’s Fibonacci Number •in picture
- 18. What’s golden ratio 0.618
- 19. What’s golden ratio 0.618 •
- 20. What’s golden ratio 0.618 • •relation to Fibonacci Number
- 21. What’s golden ratio 0.618 • •relation to Fibonacci Number
- 22. How to implement the algorithm?
- 23. Naive method
- 24. Time?
- 25. Bottom up
- 26. Time?
- 27. Can we do better?
- 28. Use φ
- 30. Use table
- 31. Time?
- 32. another formula
- 33. another formula
- 34. another formula
- 35. Time?
- 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. Thank you ^_^