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Topic DescriptionWe all know the Fibonacci sequence, and now you're going to need to enter an integer n, so you output the nth item in the Fibonacci sequence.
n
Method 1:
Cycle.
#-*-Coding:utf-8-*-
class Solution:
def Fibonacci (self, N):
# Write code here
Fibonacci sequence
The Fibonacci sequence refers to a sequence of 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,377,610,987,1597,2584,4181,6765,10946,17711,28657, 46368 .....This sequence starts with the 3rd item and e
In front of the iterator and generator principle, it has been said that the __iter__ method and the role of the __next__ method, here do not repeat the description.In this complement an example of implementing an iterator protocol.Example 1: (The iterator generates an infinite value before the exception is thrown stopiteration)Class C1:def __init__ (Self,start):Self.start = Startdef __iter__ (self):return selfDef next (self):Self.start + = 1Return Self.startO1 = C1 (10)For I in O1:Print IExample
The Fibonacci sequence cannot be expressed as a list production type, but can be derived from a function:1 #_*_coding:utf-8_*_2 #__author__ = "Csy"3 deffib (max):4N,a,b = 0,0,15 whileN Max:6 Print(b)7A, B = B,a +b #初始a = 0, b=1,a=b and b=a+b can be understood as simultaneous execution, i.e. A=1, b=0+1=18n = n +19 return 'OK'Ten OneFIB (9)Output:1123581321st34###############################
Fibonacci SequenceRefers to such a sequence of 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368 ... This sequence starts with the 3rd item and each item is equal to the sum of the first two items.recursive way to implement:DefFN (n): If n==1: Return 1elif n==2:return 1Else:return fn (n1) +fn (n-2)n=I
In this paper, we describe the method for Python to print Fibonacci sequences. Share to everyone for your reference. The implementation method is as follows:
#打印斐波拉契数列 #!/usr/bin/pythondef Feibolaqi (n): if n = = 0 or N = = 1: return n else: return Feibolaqi (n-1) + FE Ibolaqi (n-2) num = Int (raw_input (' please input a int: ') "If num >= 0: print ' Feibolaqi (%d) is%d '% (Num,feibolaqi (nu m)
1. Recursion# Recursive def fibs (n): if N : return 0 elif n = =1 : Return 1 return fibs (n-2) + fibs (n-1)print(fibs (6))2. Cycle # loop def fibs (n): a = [1, 1 for i in range (n-2-2] + a[-1]) return a[n-1 print (fibs (6)) class Solution: def fib (self, N): if or n==2: return n a=1;b=2;c=3 for in Range (3,n+1): c=a+b;a=b;b=c return C3. Combinatorial number formulaSet the frog to jump on the N-step of
Outputs the number of previous Fibonacci sequence numbers.Using functions#!/usr/bin/env python#-*-coding:utf-8-*-# author:hiuhung wan#----Fibonacci sequence (Fibonacci sequence)-----def
The T-SQL implementation of the Fibonacci sequence (Fibonacci sequence); withT as (SELECT 1 asNumCAST(1 as BIGINT) asCurrCAST(NULL as BIGINT) asPRVUNION AllSELECTCurr. Num+ 1 asNumCAST( Case whenPrv is NULL ThenCurrELSECurr+PrvEND as BIGINT) asCurrCAST(Curr as BIGINT) asPRV fromT CurrWHERE CAST( Case whenPrv i
Topic Requirements: Write program output Fibonacci number 20 in the console, 5 lines per output
Java programming: Three ways to implement the Fibonacci sequenceOne way:
public class Demo2 {
//define three variable methods public
static void Main (string[] args) {
int a = 1, b = 1, c = 0;
System.out.println ("The first 20 items of the Fibonacci series are:"
Calculate the sum of the First n items of the Fibonacci fractional sequence (N is a constant, and the Fibonacci fractional sequence is 2/1, 3/2, 5/3, 8/5 ,...).
# Include
Stdio. h
>
# Include
Conio. h
>
Void
Main (){
Int
I, N;
Float
F1
=
1
, F2
=
2
, F, Sum
=
0
;Scanf (
*/: Power_n (intAintN) {if(n==0)return 1;Else if(n==1)returnAElse if(n%2==0)returnPower_n (A*a, n>>1) ;Else returnA*power_n(A, n1) ;} can also be used whileRealization: It can be understood that the N power series is expanded, and the cycle I is using the coefficient of the first Order power series. Long Pow1_n (intAintN) {long d=1, T=a; while(n>0) {if(n%2==1) d= (d*t); n>>=1; T=t*t; }returnD;} Here's2The shift operation greatly accelerates the speed. Then for many times the power oper
Algorithm ListIn this paper, the optimal algorithm is found from the perspective of time efficiency and occupied space memory.
Classic recursive algorithm recursive algorithm (very slow)
Dynamic storage algorithm programming (slow)
Matrix Power algorithm exponentiation (FAST)
Multiple formula algorithm fast doubling (soon)
Multiple formula algorithm + fast multiplication fast doubling with Karatsuba (fastest)
Fibonacci Se
In fact, the Fibonacci sequence of things I have learned in elementary school, but only then did not learn so clearly, now let us take a look at the Fibonacci sequence of some algorithms (beginners can see)Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... [
One: Recursive implementationusing the formula F[n]=f[n-1]+f[n-2], recursion is computed sequentially, and the recursive end condition is f[1]=1,f[2]=1.
Two: Array implementationthe space complexity and time complexity are all 0 (n), and the efficiency is generally faster than that of recursion.
Three:vectorthe time complexity is 0 (n), the time complexity is 0 (1), the vector is not known to be highly efficient, of course the vector has its own attributes will occupy resources.
Four:queueof
is equal to the first two months the sum of the large rabbit logarithm. If the N-month large rabbit logarithm is expressed in un, there isUN = un-1 + un-2, n >2 each month the number of large rabbits in the series is: 1,1,2,3,5,8,13,21,34,55,89,144, /c5> this sequence is called the Fibonacci sequence. Recursive method:Using the formula F[n]=f[n-1]
/** * Title: * There are a pair of rabbits, from the 3rd month after birth, each month has a pair of rabbits, the rabbit long to the third month after the birth of a pair of rabbits each month. * If the rabbit is not dead, ask after month months, how many rabbits total? */public class Fibonacci {//month static Integer month = 3;//NOTE: month > 0public static void Main (string[] args) {Integer pair = f (month); System.out.println ("A: after" + month +
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