To prove safety offer8-Fibonacci series

A description of the subject

We all know that Fibonacci number, and now asked to enter an integer n, you output the n-th Fibonacci number Fibonacci sequence of item (from 0, the first 0 is 0). n <= 39

 

Two Solution 1

1 analysis

Fibonacci sequence mathematical language description may be represented as f (n) = f (n-1) + f (n-2), (n> 1); f (n) = n, (n = 0, 1); apparent You can use a recursive thinking to solve this problem, recursive recursive formula and have a termination condition.

Complexity: time complexity of O (n ^ 2), the spatial complexity is O (1).

2 code implementation

 1 class Solution {
 2 public:
 3     int Fibonacci(int n) {
 4         if (n <= 0)
 5             return 0;
 6         if (n == 1)
 7             return 1;
 8         
 9         return Fibonacci(n - 1) + Fibonacci(n - 2);
10     }
11 };

 

Two Solution 2

1 analysis

Instead of using the iterative recursion, f (n) = f (n-1) + f (n-2), to calculate f (n) is calculated on the first f (n-1), f (n-2), the other way round sufficient to know f (1), f (2), then eventually know f (n).

Complexity: time complexity of O (n), the spatial complexity is O (1).

2 code implementation

. 1  class Solution {
 2  public :
 . 3      int the Fibonacci ( int n-) {
 . 4          IF (n-<= 0 )
 . 5              return  0 ;
 . 6          IF (n-== . 1 )
 . 7              return  . 1 ;
 . 8          
. 9          int lastValue = . 1 ;    // F ( n-1) value of 
10          int lastLastValue = 0 ;    // F (n-2-) values 
. 11          int RET;    // return value 
12         for ( int i = 2 ; i <= n; ++ i)
 13          {
 14              ret = load value + goods load value;
15              goods load value = load value;
16              load value = ret;
17          }
 18          
19          return ret;
20      }
 21 };

 

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