First, a solution using addition is written in the header file whichfibonaccinumber.h . There is no verification that the input number is less than 0.#ifndef whichfibonaccinumber_h_#define whichfibonaccinumber_h_typedef unsigned long long uint64;//abbreviated unsigned long long , because it is 64 bits, writing UInt64 (meaning: Unsigned int 64 bit)//max = = 18446744073709551615, try to ensure that no overflow. Another: the "General formula" solution needs to open square. UInt64 whichfibonaccinumb
Luogp1962 Fibonacci series, P1962 Fibonacci SeriesBackground
As we all know, the Fibonacci series is a series that meets the following characteristics:
• F (1) = 1
• F (2) = 1
• F (n) = f (n-1) + f (n-2) (n ≥ 2 and n is an integer)Description
Find the value of f (n) mod 1000000007.Input/Output Format
Input Format:
· Row 1st: an integer n
Output Format:
Row 3:
First: Using a For loopThe use of the For loop, does not involve functions, but this method for my small white is a good understanding of the function of a more abstract ...1 >>> fibs = [0,1]2 for in range (8):3 Fibs.append (Fibs[-2] + fibs[-1])45 >>> fibs6 [0, 1, 1, 2 , 3, 5, 8, 13, 21, 34]Or, enter a dynamic length:1fibs = [0,1]2num = input ('howmany Fibonacci numbers does you want? ' )3 for in range (Num-2):4 fibs.append (Fibs[-2] + Fi
Topic Transfer: UVA-10229Idea: The simple matrix quickly powers the Fibonacci sequence, then notice that the intermediate result can explode int, because 2^19 has more than 500,000AC Code:#include Uva-10229-modular Fibonacci (Matrix fast Power + Fibonacci)
The sum of the First n digits of Fibonacci and the n digits of Fibonacci
Public class Fei_bo_na_qi {Public static void main (String [] args) {// main method, program entryInt I = 10; // declare an int type variable I, and assign a value of 10Int a = 0; // declare an int data type variableFor (int j = I; j> = 1; -- j) {// for Loop: j = I = 10, j> = 1A + = m1 (j); // call the m1 method and assign the value of
Question Link
Give N and M, and find F (n) % m. f (x) is the Fibonacci sequence.
Idea: Because N is big, it is very likely that it will use the formula to calculate it, so we can use the Matrix to quickly solve the power. | (1, 1), (1, 0) | * | f (n-1), F (n-2) | = | f (N), F (n-1) |, so f (N) equivalent to | F (1), F (0) | multiplied by N-1 | (1, 1), (1, 0) |.
Code:
#include
Uva10299-modular Fibonacci
Logu P1306 Fibonacci common count, p1306 FibonacciDescription
You should be familiar with the series of Fibonacci:, 13 ~~~ But now there is a very simple question: what is the maximum number of public appointments between the n and m items?Input/Output Format
Input Format:
Two positive integers n and m. (N, m
Note: The data is large.
Output Format:
The maximum number of common Fn and Fm.
Since reading b
Js Fibonacci series implementation, js Fibonacci Series1. Recursion
Function fib (n) {if (n = 1 | n = 2) {return 1;} return fbnq (n-1) + fbnq (n-2 );} fbnq (10); // 55
The time complexity is O (2 ^ n), and the space complexity is O (n)
2. Non-recursion
Function fb (n) {var res = [1, 1]; if (n = 1 | n = 2) {return 1 ;}for (var I = 2; I
The time complexity is O (n), and the space complexity is O (
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 (
"
% D
"
,
N );
For
(I
=
0
; I
N; I
++
){Sum
+ =
F2
/
The meaning is to use matrix multiplication to find the last four digits of the nth of the Fibonacci series. If the last four digits are all 0, the output is 0. Otherwise
Remove the leading 0 from the last four digits of the output... ... Yes... ... Output FN % 10000.
The question is so clear .. I am still trying to find the last four digits of % and/and determine whether all the values are 0 and whether the output values are 0.
Remove the leading 0.
Calculate the nth entry of a Fibonacci series. The upper limit of n is 10000.
Solution: Because the upper limit of this question is 10000, indentation is required for high precision.
# Include
Question:
Fibonacci series, F [0] = 0, F [1] = 1, F [N] = f [N-2] + F [n-1], n> 1
Given N (0
Solution:
N is too large, so we cannot use the cyclic recursive Calculation of O (n ).
Conclusion: For matrices | 1 1 |, and matrices | FnFn-1 |, after the two are multiplied to obtain a new matrix | Fn + 1FN|, FN indicates the nth Number of fiber ACCI
| 1 0 || Fn-1 Fn-2 || FnFn-1
Therefore, we can use the rapid power modulo + matrix multiplication of O (l
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
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
elif n == 1: return 1 else: return fib1(n - 1) + fib1(n - 2) known = {0: 0, 1: 1} def fib2(n): if n in known: return known[n] res = fib2(n - 1) + fib2(n - 2) known[n] = res return resif __name__ == '__main__': n = 40 print(datetime.datetime.now()) print('fib1(%d)=%d' % (n, fib1(n))) print(datetime.datetime.now()) print('fib2(%d)=%d' % (n, fib2(n))) print(datetime.datetime.now())
Postscript:
It wasn't long before I learned Python, so I was not familiar with its various feat
A simple Fibonacci sequence, with the following code:# Filename: fibonaci.py# author by: stephendef fib(n): #定义一个函数叫 fib() if n [Python learning] Fibonacci sequence Fibonacci Sequence
10229-modular Fibonacci
Time limit:3.000 seconds
Http://uva.onlinejudge.org/index.php?option=com_onlinejudgeItemid=8category=115page=show_ problemproblem=1170
The Fibonacci numbers (0, 1, 1, 2, 3, 5, 8, ...) are defined by the recurrence:
F0 = 0 F1 = 1 Fi = Fi-1 + Fi-2 for i>1
Write a program which calculates Mn = Fn mod 2m for given pair of N and M. 0
Input and Output
Input consists of several lines
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