斐波纳契数列

注意事项：

斐波那契数列增长的速度很快，高于几何级。超过40级的数列值很可能突破4GB的取值范围，从而发生溢出。

         其隐式和显式求解的结果是不同的，必须在显式求解的基础上对计算结果进行取整修正。

代码1：用迭代的方法实现斐波那数列。

#include<stdio.h>

main()

{

                  Long fn1,fn2,fn3;

                  int i,n;

                  printf("Please anter month number(less than 40):");

                  scanf("%d",&n);

                  if(n<1) n=1;

                  printf("\n");

                  fn1=fn2=1;

                  printf(" M. 1:%10d",fn1);

                  if(n>1)

                            printf(" M. 2:%10d",fn2);

                  for(i=3;i<=n;i++)

                  {

                            fn3=fn2+fn1;

                            printf(" M.%2d:%10d",i,fn3)   ;

                            if(i%4==0)

                            printf("\n");

                            fn1=fn2;

                            fn2=fn3;

                  }

                  getch();

}

代码2：用使用公式法实现斐波那契数列。

#include<stdio.h>

#include<math.h>

main()

{

                  int n;

                  printf("Please input the number of n:\n");

                  scanf("%d",&n);

                  printf("%d\n",n);

                  printf("f%d=%lf",n,pow((1+pow(5,0.5))/2,n));

                  getch();

}

代码3：验证斐波那契数列性质，前后元素的比例符合黄金分割。

#include<stdio.h>

#define Limit 40

main()

{

                  long f0=0,f1=1,n,temp;

                  printf("%7s%19s%29s\n%7s%19s%29s\n%7s%19s%29s\n",

                            " ","Fibonacci","Fibonacci",

                            " n"," number","quotient",

                            "--","-------","--------");

                  printf("%7d%19d\n%7d%19d\n",0,0,1,1);

                            for(n=2;n<=Limit;n++)

                            {

                                     temp=f1;

                                     f1+=f0;

                                     f0=temp;

                                     printf("%7d%19d%29.16f\n",n,f1,(double)f1/f0);

                            }

                            return 0;

}