Data Structures Algorithms 简明教程
Fibonacci Series Using Recursion
Fibonacci Series Using Recursion
斐波那契数列通过将两个前一个数字相加来生成后续数字。斐波那契数列从两个数字开始 − F0 & F1 。F0 & F1 的初始值可以分别取 0, 1 或 1, 1。
Fibonacci series generates the subsequent number by adding two previous numbers. Fibonacci series starts from two numbers − F0 & F1. The initial values of F0 & F1 can be taken 0, 1 or 1, 1 respectively.
斐波那契数列满足以下条件：
Fibonacci series satisfies the following conditions −
Fn = Fn-1 + Fn-2因此，一个斐波那契数列看起来可能是这样 −
Hence, a Fibonacci series can look like this −
F8 = 0 1 1 2 3 5 8 13
或者，这样 −
or, this −
F8 = 1 1 2 3 5 8 13 21
为了说明，F8 的斐波那契显示为 −
For illustration purpose, Fibonacci of F8 is displayed as −
Fibonacci Iterative Algorithm
首先，我们尝试起草斐波那契数列的迭代算法。
First we try to draft the iterative algorithm for Fibonacci series.
Procedure Fibonacci(n)
declare f0, f1, fib, loop
set f0 to 0
set f1 to 1
<b>display f0, f1</b>
for loop ← 1 to n
fib ← f0 + f1
f0 ← f1
f1 ← fib
<b>display fib</b>
end for
end procedureFibonacci Recursive Algorithm
让我们学习如何创建斐波那契数列的递归算法。递归的基本准则。
Let us learn how to create a recursive algorithm Fibonacci series. The base criteria of recursion.
START
Procedure Fibonacci(n)
declare f0, f1, fib, loop
set f0 to 0
set f1 to 1
display f0, f1
for loop ← 1 to n
fib ← f0 + f1
f0 ← f1
f1 ← fib
display fib
end for
END