fibonacci

问题 I\'m new to Javascript and was reading up on it, when I came to a chapter that described function recursion. It used an example function to find the nth number of the Fibonacci sequence. The code is as follows: function fibonacci(n) { if (n < 2){ return 1; }else{ return fibonacci(n-2) + fibonacci(n-1); } } console.log(fibonacci(7)); //Returns 21 I\'m having trouble grasping exactly what this function is doing. Can someone explain what\'s going on here? I\'m getting stuck on the 5th line,

问题 I have a Fibonacci struct that can be used as an iterator for anything that implements One , Zero , Add and Clone . This works great for all integer types. I want to use this struct for BigInteger types which are implemented with a Vec and are expensive to call clone() on. I would like to use Add on two references to T which then returns a new T (no cloning then). For the life of me I can\'t make one that compiles though... Working: extern crate num; use std::ops::Add; use std::mem; use num:

问题 I\'m working on a Project Euler problem: the one about the sum of the even Fibonacci numbers. My code: def Fibonacci(n): if n == 0: return 0 elif n == 1: return 1 else: return Fibonacci(n-1) + Fibonacci(n-2) list1 = [x for x in range(39)] list2 = [i for i in list1 if Fibonacci(i) % 2 == 0] The problem\'s solution can be easily found by printing sum(list2). However, it is taking a lot of time to come up with the list2 I\'m guessing. Is there any way to make this faster? Or is it okay even this

问题 I was wondering about how can one find the nth term of fibonacci sequence for a very large value of n say, 1000000. Using the grade-school recurrence equation fib(n)=fib(n-1)+fib(n-2) , it takes 2-3 min to find the 50th term! After googling, I came to know about Binet\'s formula but it is not appropriate for values of n>79 as it is said here Is there an algorithm to do so just like we have for finding prime numbers? 回答1: You can use the matrix exponentiation method (linear recurrence method).

问题 Please explain this simple code: public int fibonacci(int n) { if(n == 0) return 0; else if(n == 1) return 1; else return fibonacci(n - 1) + fibonacci(n - 2); } I\'m confused with the last line especially because if n = 5 for example, then fibonacci(4) + fibonacci(3) would be called and so on but I don\'t understand how this algorithm calculates the value at index 5 by this method. Please explain with a lot of detail! 回答1: In fibonacci sequence each item is the sum of the previous two. So,

问题 By what mechanism is this fibonacci-function memoized? fib = (map fib\' [0..] !!) where fib\' 1 = 1 fib\' 2 = 1 fib\' n = fib (n-2) + fib (n-1) And on a related note, why is this version not? fib n = (map fib\' [0..] !! n) where fib\' 1 = 1 fib\' 2 = 1 fib\' n = fib (n-2) + fib (n-1) 回答1: The evaluation mechanism in Haskell is by-need : when a value is needed, it is calculated, and kept ready in case it is asked for again. If we define some list, xs=[0..] and later ask for its 100th element,

问题 Is there any algorithm to compute the nth fibonacci number in sub linear time? 回答1: The n th Fibonacci number is given by f(n) = Floor(phi^n / sqrt(5) + 1/2) where phi = (1 + sqrt(5)) / 2 Assuming that the primitive mathematical operations ( + , - , * and / ) are O(1) you can use this result to compute the n th Fibonacci number in O(log n) time ( O(log n) because of the exponentiation in the formula). In C#: static double inverseSqrt5 = 1 / Math.Sqrt(5); static double phi = (1 + Math.Sqrt(5))

问题 I understand Big-O notation, but I don\'t know how to calculate it for many functions. In particular, I\'ve been trying to figure out the computational complexity of the naive version of the Fibonacci sequence: int Fibonacci(int n) { if (n <= 1) return n; else return Fibonacci(n - 1) + Fibonacci(n - 2); } What is the computational complexity of the Fibonacci sequence and how is it calculated? 回答1: You model the time function to calculate Fib(n) as sum of time to calculate Fib(n-1) plus the

问题 I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1 & 20), I have written for the program to display all Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 displays = First 20 Fibonacci numbers). I thought I had a sure-fire code. I also do not see why this is happening. startNumber = int(raw_input(\"Enter the start number here \")) endNumber = int(raw_input