The nth item of the Fibonacci sequence.

The first type: recursive functions

  1  #include <stdio.h>  2  #include <stdlib.h>  3 # Include<assert.h>  4   5 int fabonacci (int n)   6  {  7     if (n<=1&&n>=0)   8      {  9         return n; 10      } 11     return fabonacci (n-1) +Fabonacci (n-2);  12  } 13 int main ()  14 { 15     int n; 16      printf ("please input the value of n\n"); 17  &NBSP;&NBSP;&NBSP;&NBSP;SCANF ("%d", &n);  18     printf ("the result  Of %d is %d\n ", N,fabonacci (n));  19     return 0; 20  }

The second type: array implementations

Create an array of two elements, initialize to 1, find the value of the nth item, and sequentially find the first two items.

Time complexity: O (N)

Space complexity: O (1)

  1  #include <stdio.h>  2 int fib (int n)   3 {   4   int a[2]={1,1};  5   int i=3;  6    if (n<0)   7   {  8        return -1;  9   } 10   if (n==0)  11    { 12       return 0; 13   } 14    if (n<=2)  15   { 16        Return a[n-1]; 17   } 18   for (; i<=n;i++)  19    { 20       int tmp=a[0]; 21        a[0]=a[1]; 22       a[1]=a[0]+tmp; 23    } 24  &nbsP;return a[1]; 25 } 26 int main ()  27 { 28      int n=0; 29     printf ("Please input the value of  n\n "); &NBSP;30&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;SCANF ("%d ", &n); 31      printf ("the num is %d\n", FIB (n));  32     return 0; 33  } results:please input the value of n0the num is 0[[email  Protected] key]$ ./testplease input the value of n5the num is  5[[email protected] key]$ ./testplease input the value of n4the  num is 3[[email protected] key]$ ./testplease input the value  of n-1the num is -1

The third type: queue implementation

Thinking with the second kind

#include <iostream> #include <queue>using namespace std;int fib (int n) {if (n<0) {return-1;} if (n<=2) {return 1;} Queue<int> Q;q.push (1); Q.push (1); for (int i=2;i<n;i++) {int tmp=q.front (); Q.pop (); Q.push (Tmp+q.front ());} Q.pop (); return Q.front ();}    void Test () {int N1 =-1;int n2=2;int n3=5;cout<<fib (N1) <<endl;    Cout<<fib (n2) <<endl; Cout<<fib (n3) <<endl;} int main () {test (); System ("pause"); return 0;}

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The fourth type: Formula implementation

int fib (int n)

{

if (n<0)

{

return-1;

}

Double Gh5=sqrt ((double) 5);

Return (POW ((1+GH5), N)-pow ((1-gh5), N)/(Pow ((double) 2,n) *gh5);

}

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The nth item of the Fibonacci sequence.