Analysis of python recursive functions and Hanoi Tower problems, analysis of python recursive Hanoi

Analysis of python recursive functions and Hanoi Tower problems, analysis of python recursive Hanoi

Recursive functions:

The function calls its own function.

Take the n factorial as an example:

F (n) = n! = 1x2x3x4 x .. x (n-1) x (n) = n x (n-1 )!

def factorial(n):   if n==1:     return 1   return n * f(n-1)

// The call process is as follows:

>>f(5)>>5 * f(4)>>5 * 4 * f(3)>>5 * 4 * 3 * f(2)>>5 * 4 * 3 * 2 * f(1)>>5 * 4 * 3 * 2 * 1>>120

From the above example, we can intuitively see That recursive functions are constantly calling their own functions until n = 1 (function exit ).

About Hanoi:

Rules:

1. Three columns, A, B, C

2. The plates on pillar A are arranged from small to large. The top is the smallest and the bottom is the largest.

3. Move the plate on A to C. It is always maintained during the moving process. The biggest part is below and the smallest part is above.

Assume that there is A plate on column A, which can be directly moved from column A to column C:

A --> C

Assume that there are two plates on column A, and you need to use column B to move them to column C:

A --> B

A --> C

B --> C

Move the top disk (2-1) of A to B, move the remaining disk in A to C, and finally move the disk in B to C.

Assume that there are three plates on column A. Use B to move the two disks on column A, move the largest disk on column A to column C, and finally move the disk on column B to column C.

A --> C

A --> B

C --> B // move the first two plates of A to B.

A --> C // move the largest plate on A to C

B -->

B --> C

A --> C // move the plate on B to C in the next three steps

The principle is to move the (n-1) block Disk On A to B, then the remaining and largest block in A to C, and finally the (n-1) block disk on B to C.

def Hanoi(n , a, b, c):  if n==1:    print (" Hanoi Tower move", a, "-->", c)    return  Hanoi(n-1, a, c, b)  Hanoi(1, a, b, c)  Hanoi(n-1, b, a, c)print (" When there is 1 ring on A")Hanoi(1, 'A', 'B', 'C')print (" When there are 2 rings on A")Hanoi(2, 'A', 'B', 'C')print (" When there are 3 rings on A")Hanoi(3, 'A', 'B', 'C')print(" When there are 4 rings on A")Hanoi(4, 'A', 'B', 'C')

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