Example of Hanoi tower and Fibonacci sequence based on recursive algorithm in Python

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example of this article describes Python's Hano tower and Fibonacci sequence based on the recursive algorithm. Share with you for your reference, as follows:

Here we use 2 examples to learn the use of recursion in python.

1. Find the number in the Fibonacci sequence with subscript n (subscript counts from 0)

The form of the Fibonacci sequence is this: 0,1,1,2,3,5,8,13 ...

① Using while loop, python2 code is as follows:

def fib(n):
  a,b=0,1
  count=0
  while count<n:
    a,b=b,a+b
    count=count+1
  print a

The results are as follows:

>>> fib(0)
0
>>> fib(1)
1
>>> fib(2)
1
>>> fib(3)
2
>>> fib(4)
3
>>> fib(5)
5

② Use recursion (recursion must have boundary conditions), python2 code is as follows:

def fib(n):
  if n==0 or n==1:#递归的边界条件
    return n
  else:
    return fib(n-1)+fib(n-2)

The results are as follows:

>>> fib(0)
0
>>> fib(1)
1
>>> fib(2)
1
>>> fib(3)
2
>>> fib(4)
3
>>> fib(5)
5

Recursion is one of the algorithms that can best express computational thinking. Let's take f (4) as an example to look at the execution process of recursion: the
same program, using recursion Although the program is concise, the execution efficiency of recursion is lower than that of the loop, and the system resources The consumption is greater than the cycle. Because recursion is called layer by layer, and returns layer by layer after the end, the execution efficiency of recursion is not high. Why use recursion? Because of some problems, we can't find a very obvious loop scheme, but it is easy to find an obvious recursive scheme. For example, the famous Hanoi Tower problem.

2. Hanota

The following picture is a simplified version of the Hanoi Tower game, with only 4 plates: The
Hanoi Tower game rules are as follows:
Python2 code is as follows:

def hanoi(a,b,c,n):
  if n==1:#递归结束条件
    print a,'->',c
  else:
    hanoi(a,c,b,n-1)
    print a,'->',c
    hanoi(b,a,c,n-1)

operation result:

>>> hanoi('A','B','C',1)
A -> C
>>> hanoi('A','B','C',2)
A -> B
A -> C
B -> C
>>> hanoi('A','B','C',3)
A -> C
A -> B
C -> B
A -> C
B -> A
B -> C
A -> C

Thank you very much for reading
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