Interview Question 9: Fibonacci Series

 

Method 1: It is easy to think of using recursion directly.

C ++ code:

 

#include "stdafx.h"   #include <iostream>   using namespace std;    long long Fibonacci(unsigned int n)  {      if (n == 0)      {          return 0;      }        if (n == 1)      {          return 1;      }        return Fibonacci(n-1) + Fibonacci(n-2);  }    int _tmain(int argc, _TCHAR* argv[])  {      unsigned int n = 10;      cout << Fibonacci(n) << endl;      system("pause");      return 0;  }  #include "stdafx.h"#include <iostream>using namespace std;long long Fibonacci(unsigned int n){    if (n == 0)    {return 0;    }if (n == 1){return 1;}return Fibonacci(n-1) + Fibonacci(n-2);}int _tmain(int argc, _TCHAR* argv[]){unsigned int n = 10;cout << Fibonacci(n) << endl;system("pause");return 0;}

Disadvantage: it is obvious that the efficiency is very low because of repeated computing problems.

 

Method 2: the improved method is to save the intermediate items of the obtained series and directly search for them next time to avoid repeated computation.

C ++ code:

 

#include "stdafx.h"   #include <iostream>   using namespace std;    long long Fibonacci(unsigned int n)  {      if (n == 0)      {          return 0;      }        if (n == 1)      {          return 1;      }        long long one = 0;      long long two = 1;      long long result = 0;        for (unsigned int i=2; i<=n; i++)      {          result = one + two;          one = two;          two = result;      }        return result;  }    int _tmain(int argc, _TCHAR* argv[])  {      unsigned int n = 100;      cout << Fibonacci(n) << endl;      system("pause");      return 0;  }  #include "stdafx.h"#include <iostream>using namespace std;long long Fibonacci(unsigned int n){    if (n == 0)    {return 0;    }if (n == 1){return 1;}long long one = 0;long long two = 1;long long result = 0;for (unsigned int i=2; i<=n; i++){result = one + two;        one = two;two = result;}return result;}int _tmain(int argc, _TCHAR* argv[]){unsigned int n = 100;cout << Fibonacci(n) << endl;system("pause");return 0;}