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] ^ N-[(1-√ 5)/2] ^ n }, the power query problem is involved here. We can use the divide and conquer method to solve the problem. complexity O (lgn)

3. In addition, the Fibonacci series can also use the matrix method,Sums of "Shallow" diagonals inPascal's
Triangle

Here we adopt the simplest method of recursive solution. The complexity of recursion is different from that of the top-down space.

 
# Include "stdafx. H "# include <iostream> using namespace STD; int Fibonacci (int n) // The disadvantage is that you need to apply for N integer spaces {int * result = (int *) malloc (sizeof (INT) * n + 1); Result [0] = 0; Result [1] = 1; if (n <2) return result [N]; for (INT I = 2; I <= N; I ++) result [I] = Result [I-1] + result [I-2]; return result [N];} int fibonacci2 (int n) // do not need to apply for space of O (n) {If (n = 0) return 0; If (n = 1) return 1; int first = 0; int second = 1; int result = 0; For (INT I = 2; I <= N; I ++) {result = first + second; first = Second; second = result;} return result;} int main () {cout <fibonacci2 (12); getchar (); Return 0 ;}