http://blog.csdn.net/pipisorry/article/details/37660419
斐波那契数列
因数学家列昂纳多·斐波那契以兔子生殖为样例而引入，故又称为“兔子数列”。
fibonacci 数列定义：
n = 1,2 时，fib(n) = 1
n > 2 时，fib(n) = fib(n-2) + fib(n-1)
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,……….
菲波那契数列编程实现
/* 菲波那契数列递归实现 */
int fibonacci(int index){
if( index == 1 || index == 2 )
return 1;
return fibonacci(index - 2) + fibonacci(index - 1);
}
/* 菲波那契数列非递归实现1 */
int fibonacci1(int index){ //1 0 1 1 2 3 5 ... (加入了1 0项)
int sum = 0;
int pre_pre_sum, pre_sum = 1;
while(index--){
pre_pre_sum = pre_sum; //第n-2项的值
pre_sum = sum; //第n-1项的值
sum = pre_sum + pre_pre_sum; //第n项的值
}
return sum;
}
/* 菲波那契数列非递归实现2 */
int fibonacci2(int index){ //-1 1 0 1 1 2 3 5 ... (加入了1 0项)
int pre_pre_sum = -1, pre_sum = 1;
while(index--){
pre_sum = pre_sum + pre_pre_sum; //第n-1项的值
pre_pre_sum = pre_sum - pre_pre_sum;//第n-2项的值
}
return pre_sum + pre_pre_sum; //第n项的值
}
菲波那契数列的还有一种数学展示Made to Order
Divide the number 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 into 1 and express the result as a decimal expansion, and you’ll find the Fibonacci sequence presented in tidy 24-digit strings:
[http://www.futilitycloset.com/2015/06/28/made-to-order-4/]
from:http://blog.csdn.net/pipisorry/article/details/37660419