fibonacci shell

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Programmer interview questions featured 100 questions (16)-O (logn) for the Fibonacci series

Http://zhedahht.blog.163.com/blog/static/25411174200722991933440/ Question: Define the series of Fibonacci: /0 n = 0F (n) = 1 n = 1\ F (n-1) + f (n-2) n = 2 Enter N and use the fastest method to obtain the nth item of the series. Analysis: when we talk about recursive functions in many C language textbooks, we will use Fibonacci as an example. Therefore, many programmers are very familiar with the recursive

51nod 1355 Fibonacci Least common multiple

DescriptionThe Fibonacci sequence is defined as follows:\[f[n]=\begin{cases}1, \text {if $n $ is equal to $0$ or $1$} \f (n-1) + f (n-2), \text{otherwise}\end{cases}\]Give \ (n\) a positive integer \ (a_1, A_2,\cdots, a_n\) , seek the least common multiple of the corresponding Fibonacci number, because the number is large, output \ (\bmod{1000000007}\) The results can be.\ (2\le N \le 50000,1 \le a_i\le 1

Fibonacci data column (this series can solve the problem of rabbit baby)

13 21 34 10 21 34 55 We can see that the total number of rabbits in the next month starting from the first month is:89,144,233... If the preceding data column is deleted, the obtained data column is regarded as a Fibonacci data column.Each number in a data column is the sum of the first two numbers, and the first two numbers in a data column are 1.If F0 = 1, F1 = 1, F2 = 2, F3 = 3, F4 = 5, F5 =

Join the Fibonacci series

From learning algorithms, it is inevitable to recursively implement an interesting question-the Fibonacci series. Born in, the Italian mathematician leonona Fibonacci introduced such a series through rabbit reproduction ...... This series starts from the third item, and each item is equal to the sum of the first two items. It leads to the formula: (1/√ 5) * {[(1 + √ 5)/2] ^ n-[(1-√ 5)/2] ^ n }. If you use t

HDU 1588 Gauss Fibonacci (matrix Rapid power + binary proportional sequence summation), hdufibonacci

HDU 1588 Gauss Fibonacci (matrix Rapid power + binary proportional sequence summation), hdufibonacciHDU 1588 Gauss Fibonacci (matrix Rapid power + binary proportional sequence summation) ACM Topic address: HDU 1588 Gauss Fibonacci Question:G (I) = k * I + B; I is a variable.Given k, B, n, M, question (f (g (0) + f (g (1) +... + f (g (n) % M value. Analysis:If we

[Job interview] Fibonacci series (C)

Classic is classic, no matter how many years, classic will never change. The language and framework will be outdated one day, but the classic will always exist. This is to study these classicAlgorithmOf eternity. When a. netProgramWhen I applied for a job in Java, C ++, and Android, I found that framework language features were all abandoned. In this way, the sponge is crowded and my water is coming out in four years. There are not many remaining vertices. Those who can run through each posi

HDU-1588 Gauss Fibonacci (Matrix High-Speed Power + binary algorithm proportional sequence and)

DescriptionWithout expecting, angel replied quickly. she says: "I 'v heard that you' r a very clever boy. so if you wanna me be your GF, you shoshould solve the problem called GF ~. " How good an opportunity that gardon can not give up! The "problem gf" told by Angel is actually "Gauss Fibonacci ". As we know, Gauss is the famous mathematician who worked out the sum from 1 to 100 very quickly, and Fibonacci

HDU 1588 Gauss Fibonacci (matrix Rapid power)

Gauss Fibonacci Time Limit: 1000/1000 MS (Java/others) memory limit: 32768/32768 K (Java/Others)Total submission (s): 2090 accepted submission (s): 903 Problem descriptionwithout expecting, angel replied quickly. she says: "I 'v heard that you' r a very clever boy. so if you wanna me be your GF, you shoshould solve the problem called GF ~. " How good an opportunity that gardon can not give up! The "problem gf" told by Angel is actually "Gauss

[Poj] 3070 Fibonacci (matrix multiplication)

Http://poj.org/problem? Id = 3070 Calculate the matrix based on this question and use the quick power. Bare question #include Description In the Fibonacci integer sequence, f0 = 0, F1 = 1, and Fn = FN −1 + FN −2 for n ≥ 2. for example, the first ten terms of the Fibonacci sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ,... An alternative formula for the Fibonacci

13. Fibonacci Numbers

Fibonacci numberTime limit: 1 sSpace limit: 128000 KBTitle Level: Golden GoldExercisesView Run ResultsTitle Description DescriptionLittle X is a clever boy who remembers the first 1000 numbers in the Fibonacci series F (N). But because of academic pressure, he could not remember the position of each number in the series.He now knows a number in the Fibonacci sequ

51NOD 1070 Bash Game V4 (Fibonacci game)

Transmission DoorThere are a bunch of stones in total N. A B Two people take turns, a take first. Take at least 1 of the amount, up to twice times the opponent's last fetch (a 1th time request cannot be taken all). The man who got the last 1 stones won. Suppose a B is very clever, there is no mistake in the process of taking the stone. Give N and ask who can win the game at the end.For example n = 3. A can only take 1 or 2, so B can get the last 1 stones.InputLine 1th: A number t that represents

Fast Fibonacci sequence (matrix multiplication + fast power)

Fibonacci sequenceGive you a n;f (n) =f (n-1) +f (n-2)Request out F (f (n)), because the result is large pleaseTo the answer mod 10^9+7;1Using matrix multiplication and fast power to find Fibonacci sequence is a classical application.Matrix Formula C I j=c i k *c K J;Construct 2*2 matrix according to recursive structure;Primitive matrix1 00 1Matrix 21 11 0The original matrix is multiplied by the Matrix 2 to

Lintcode 366 Fibonacci

/* 1st method would lead to time limit *//* The time complexity is exponential sicne t (n) = t (n-1) + t (n-2) */Class Solution { /** * @param n:an integer * @return an integer f (n) */public int Fibonacci (int n) { //Write your code here if (n = = 1 | | n = = 2) { return (n-1); } int sum = (n-1) + (n-2); Return Fibonacci (n-1) +

UVa #11582 Colossal Fibonacci numbers!

huge Fibonacci numbers. The i' th Fibonacci number f (i) is recursively defined in the following: F (0) = 0 and f (1) = 1 f (i+2) = f (i+1) + f (i) for every i≥0 Your task is to compute some values of this sequence.Input begins with an integer T ≤10,000, the number of test cases. Each test case consists of three integers a,b,n where 0≤ b a andb would no T both be zero) and 1≤ n ≤1000.For e

Number of Fibonacci

DescribeThe infinite sequence 1,1,2,3,5,8,13,21,34,55 is called the Fibonacci sequence, which can be recursively defined asF (n) =1 ..... (N=1 or n=2)F (n) =f (n-1) +f (n-2) ..... (N>2)You are now asked to find the nth Fibonacci number. (1th, the second one is 1) Input The first line is an integer m (mEach test data has only one row, and only a single number of shapes N (n

Solving Fibonacci Sequence by recursive method

1, Fibonacci sequence refers to: 1,1,2,3,5,8,13,21,34......fibonacci law is, starting from the 3rd number, each number is its front two number of the and. So how to solve any nth number of Fibonacci by programming???The recursive method is a channel to solve the problem.The so-called recursion, refers to the function can call itself, such a call can be direct or

poj3070--Matrix Fast Power--fibonacci

DescriptionIn the Fibonacci integer sequence, f0 = 0, f1 = 1, and fn = fn −1 + fn −2 F or n ≥2. For example, the first ten terms of the Fibonacci sequence is:0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...An alternative formula for the Fibonacci sequence is.Given an integer n, your goal was to compute the last 4 digits of Fn.InputThe input test file would contain multiple t

Hdoj 1588 Gauss Fibonacci "Matrix fast Power"

Gauss FibonacciTime limit:1000/1000 MS (java/others) Memory limit:32768/32768 K (java/others)Total submission (s): 2584 Accepted Submission (s): 1078Problem DescriptionWithout expecting, Angel replied quickly. She says: "I ' V heard that you ' r a very clever boy. So if you wanna me is your GF, you should solve the problem called gf~. ”How good a opportunity that Gardon can not give up! The "problem GF" told by Angel is actually "Gauss Fibonacci".As w

Find the nth number in the Fibonacci sequence

Title Description DescriptionTo find the nth number in Fibonacci sequence by recursive method input/output format input/outputInput Format:A row, a positive integer noutput Format:A line, a number, that represents the nth number in the Fibonacci sequence. input and Output sample sample Input/outputsample Test point # #Input Sample:15Sample output:610idea: After discussion, the recursive formula of

The Fibonacci sequence of recursion

Mathematically, the number of charges is defined in a recursive way: (n≧2) In words, the Fibonacci sequence begins with 0 and 1, and then the Fibonacci sequence is added from the previous two numbers.This is also from Wikipedia on the expression, comparative professional points. The simple one is to write the previous few:0,1,1,2,3,5,8,13,21,34,55,89,144,233 ......This is also an exponentia

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