斐波那契系列(Fibonacci Series)
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2023-12-01
Fibonacci系列通过添加两个先前的数字来生成后续数字。 Fibonacci系列从两个数字开始--F 0和F 1 。 F 0和F 1的初始值可分别取0,1或1,1。
斐波那契系列满足以下条件 -
F<sub>n</sub> = F<sub>n-1</sub> + F<sub>n-2</sub>
所以Fibonacci系列看起来像这样 -
F 8 = 0 1 1 2 3 5 8 13
或者,这个 -
F 8 = 1 1 2 3 5 8 13 21
算法 (Algorithm)
这个程序的算法很简单 -
START
Step 1 → Take integer variable A, B, C
Step 2 → Set A = 0, B = 0
Step 3 → DISPLAY A, B
Step 4 → C = A + B
Step 5 → DISPLAY C
Step 6 → Set A = B, B = C
Step 7 → REPEAT from 4 - 6, for n times
STOP
伪代码 (Pseudocode)
procedure fibonacci : fib_num
IF fib_num less than 1
DISPLAY 0
IF fib_num equals to 1
DISPLAY 1
IF fib_num equals to 2
DISPLAY 1, 1
IF fib_num greater than 2
Pre = 1,
Post = 1,
DISPLAY Pre, Post
FOR 0 to fib_num-2
Fib = Pre + Post
DISPLAY Fib
Pre = Post
Post = Fib
END FOR
END IF
end procedure
实现 (Implementation)
该算法的实现如下 -
#include <stdio.h>
int main() {
int a, b, c, i, n;
n = 4;
a = b = 1;
printf("%d %d ",a,b);
for(i = 1; i <= n-2; i++) {
c = a + b;
printf("%d ", c);
a = b;
b = c;
}
return 0;
}
输出 (Output)
该方案的产出应该是 -
1 1 2 3