fibonacci sequence python

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Fibonacci Sequence--matrix multiplication optimization

; j + +) for(intk=1; k2; k++) d[i][j]+= ((a[i][k]%p) * (a[k][j]%p))%p; for(intI=1; i2; i++) for(intj=1; j2; j + +) {a[i][j]=d[i][j];d [i][j]=0;} X=x/2; } for(intI=1; i2; i++) for(intj=1; j2; j + +) for(intk=1; k2; k++) d[i][j]+= (A[i][k]*c[k][j])%p;//to multiply the c[][] and a[][];return(d[1][1]+d[2][1])%P;//fn=f1*d[1][1]+f0*d[2][1], which is obtained after matrix multiplication is simplified;}intMain () {scanf ("%d",t); for(intI=1; i) { for(intI=1

Returns the nth Number of the Fibonacci sequence.

The Fibonacci sequence is defined as follows in recursion: F0 = 0, F1 = 1 Fn = f (n-1) + f (n-2) (N> = 2, N *) 1. The simplest method for solving the Fibonacci series is recursive. The best time complexity is O (n ). 2. the Fibonacci series also has its own production formula:F (n) = (√ 5/5) * {[(1 + √ 5)/2] ^

Using PHP iterators to implement a Fibonacci sequence _php tutorial

The Fibonacci sequence is usually done recursively, and of course there are other methods. This is now learning to sell, using a PHP iterator to implement a Fibonacci sequence, with little difficulty, just rewrite the next () method in the class. Comments have been written into the code and are quite well understood.

Recursive method for Fibonacci sequence C + +

//the recursive method is implemented as follows:#include"stdafx.h"#includeusing namespacestd;voidFintnum) { int*p =New int[Num],i; p[0] =0; p[1] =1; for(i =2; i ) {P[i]= P[i-1] + p[i-2]; } coutEndl; cout"The output Fibonacci sequence is as follows:"Endl; for(i =0; i ) {cout" "; }}intMain () {intnum; cout"Please enter the number of Fibonacci

"Data Structure" recursive algorithm-Fibonacci sequence

The Fibonacci sequence, the one who learned math, is 1 1 2 3 5 8 13 21 34 ...That is, each item is the same as the first two items.The algorithm itself is very simple, the key is to understand the idea of recursion.Print out the Fibonacci sequence of num lengths, and paste the code directly:============================

The language realization of Fibonacci sequence

Enter a positive n to find the nth number of the Fibonacci sequence. Fibonacci Sequence Features: The first number and the second number are one, starting with the third number, followed by the number of the preceding two numbers. The input integer n is required to be no more than 50.C Language implementation:#include

Java Implementation Fibonacci sequence

Package Algorithm.cxg.Fibonacci; Import Java.util.Scanner; /** * Implementation of the Fibonacci pull function * Fibonacci sequence: * Starting with 0 and 1, the Faiponasi coefficients are added to the previous two numbers, and the form is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, .... * In math

The go language implements the Fibonacci sequence

This is a creation in Article, where the information may have evolved or changed. The Fibonacci sequence, also known as the Golden Section, refers to a sequence of numbers: 1, 1, 2, 3, 5, 8, 13, 、...... In mathematics, the Fibonacci sequence is defined as a recursive method:

Algorithm subsection (i)--Fibonacci sequence (Java implementation)

See the company's written test questions to write the Fibonacci sequence, I wrote a bit of a sneakWhat is a Fibonacci sequence: The Fibonacci sequence refers to a sequence of 0, 1, 1, 2

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

HDU 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 include the Fibonacci matrix, we will find that this is

HDU 5451 Generalized Fibonacci sequence

This topic can be translated first:Make f (1) = 5+2√6F (2) = f (1) * (5+2√6)...F (n) = f (n-1) * (5+2√6)F (n) = f (n-1) * (10-(5-2√6)) = 10*f (n-1)-(5-2√6) f (n-1) = 10*f (n-1)-10/(5+2√6) f (n-1) = 10*f (n-1)-10/(5+2√6) * (5+2√6) F (n -2)= 10*f (n-1)-F (n-2)Then it can be written in the form of matrix multiplication.(f (n), F (n-1)) = (f (n-1), F (n-2)) (10, 1-1, 0)But the 2^x+1 here is still very large, and here we use the generalized Fibonacci

The method of the Fibonacci sequence is written in two ways: The program ape Thinking and the program designer's thinking.

Use Java to implement the Fibonacci sequence (Fibonacci) public class Test {public int f (int n)//n represents the first number. The program returns its corresponding value {return n>2?f (n-1) +f (n-2): 1;//seems so graceful a program}//the programmer's mind: The above code will be refactored. Make them easier to read. Recommended!!! public int Fibo (final int po

Solving Fibonacci sequence problems using recursion and recursion ~ ~ ~

/*** Use recursion to process Fibonacci sequences* @param sum* @param i* @return*/public static int findvalue (int n) {if (n==1){return 1;}if (n==2){return 2;}int sum=1;int pre=1;for (int i=3;i{int temp=sum;Sum+=pre;Pre=temp;}return sum;}/*** The Fibonacci sequence is handled in a recursive manner* @param i* @return*/public static int findValue2 (int i) {int sum=

Php_i love u (2) php food and clothing parents: Java and PHP efficiency battle one: Fibonacci sequence

Php_i love u (1) php Food and clothing parents: Java and PHP efficiency battle one: Fibonacci sequence Fibonacci EXPLANATION See: http://zh.wikipedia.org/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B0%E5%88%97 (should be 1, Wiki's formula is wrong!?! ) (n?2) This time write the Java code First: Class FB {static int f1b (int x) {if ((0==x) | | |

The memory search and dynamic programming solution of Fibonacci sequence C + + implementation and related case analysis (leetcode70-stair climbing) __c++

the memory search and dynamic programming solution of Fibonacci sequence C + + implementation and related case analysis (leetcode70-stair climbing) Recursive analytic formula for Fibonacci series: F (N) =f (n-1) +f (n-2) the solution of ordinary no optimization #include using a Memory search method for Top-down optimization #include Solution of bottom-up

Fibonacci Sequence hdu1250

Hat ' s Fibonaccicrawling in process ... crawling failed Time limit:1000MS Memory Limit:32768KB 64bit IO Format:%i64d %i64u Description A Fibonacci sequence is calculated by adding the previous and the sequence, with the first and both members Being both 1.F (1) = 1, f (2) = 1, f (3) = 1,f (4) = 1, f (n>4) = f (n-1) + f (n-2) + f (n-3) + f (n-4)Your task is to ta

Fibonacci Sequence (Formula)

counting method of the original number of the first part of the number of methodsHow do you find the first few when a number is very large?If given a specific number, of course, you can gradually take out each bit. Such asA is a bit, A/10 hundred, A/10/10 thousands.But what happens when you ask for the first few x^y? If the x, Y are very large, it is obviously difficult to solve: perhaps with large number multiplication, brute force solution, the result is both memory, and time consuming.Also,

HDU 4893 wow! Such sequence! (Line Segment tree function: Single Point update, Interval Update adjacent smaller Fibonacci numbers)

Reprint please indicate the source: http://blog.csdn.net/u012860063? Viewmode = Contents Question link: http://acm.hdu.edu.cn/showproblem.php? PID = 1, 4893 ---------------------------------------------------------------------------------------------------------------------------------------------------------- Welcome to tianci Hut: http://user.qzone.qq.com/593830943/main --------------------------------------------------------------------------------------------------------------------------

Optimization of the Fibonacci sequence Java algorithm with HashMap

Fibonacci is the first item of 0, the second item is 1, and each subsequent item is a sequence of two items in front.Source: Fibonacci.javapublic class Fibonacci{private static int times=0, public static void Main (String args[]) { int nums = Fibonacci (+); SYSTEM.OUT.PRINTLN ("Result:" +nums); System.out.println

"Algorithmic" Fibonacci sequence

"Algorithmic" Fibonacci sequence //////Recursive mode/////////PublicStaticint Fn (IntN) {if (Default (n))Return1;Return Fn (N-1) + Fn (N-2); }//////Cycle mode/////////PublicStaticint Fnfor (IntN) {if (Default (n))Return1;int first =1;int second =1;for (int i =3; I ) {second = first + (first =second); }ReturnSecond }//////Default processing////// private static bool Default (int n) { if (n 0) { thro

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