PROGRAMMING:The tower of Hanoi problem
In India, there is such an old legend: in the holy temple in Benares (in northern India), the center of the world, there are three gem needles on a brass plate. When Brahma, the main god of Hinduism, created the world, he put 64 pieces of gold on one of the needles from bottom to top. This is the so-called tower of Hanoi. No matter day or night, there is always a monk moving these gold pieces to another needle according to the following rules. The rule is to move only one piece at a time, and the small piece must be on top of the big piece. When all the gold pieces are moved from the needle that Brahma put on to the third needle, the world will be destroyed in a thunderbolt, and the Vatican pagoda, temple and all living beings will die together.
Using mathematical methods, it can be calculated that if the legend is true, monks need 264-1 steps to complete this task. If they could move the plate once a second, it would take 584.9 billion years. The universe is only 13.7 billion years old.
This is the legend about the tower of Hanoi, which leads to the problem of the tower of Hanoi. This problem seems to be a bit complicated. In fact, it can be analyzed with the idea of recursion
Moving n plates from a column to C column can be divided into the following three steps
(1) Move n-1 plates on a column to B column with the help of C column;
(2) Move the last plate on column a to column C;
(3) Then the N-1 plate on the B column is moved to the C column with the help of the a column.
The first step can be divided into the following three steps:
(1) Move n-2 plates on a column to C column with the help of B column;
(2) Move the n-1st plate on column a to column B;
(3) Then move the N-2 plates on the C column to the B column with the help of the a column.
This decomposition can continue recursively until it becomes moving a plate and the recursion ends. In fact, the above three steps include two operations:
(1) Moving plates from one post to another is a recursive process;
(2) Move a plate from one post to another.
Write two functions to achieve the above two operations.
The function Hanoi (int n, char one, char two, char three) moves n plates on the "one" column to the "three" column with the help of the "two" column;
The function move (char x, char y) moves a plate from the X column to the Y column and outputs a prompt for moving the plate.
Program input the number of gold plate n, and output the process of moving n gold plates from column a (with the help of column B) to column C.
###Input example:
```in
three
```
```out
A-->C
A-->B
C-->B
A-->C
B-->A
B-->C
A-->C
```
answer：If there is no answer, please comment
Using mathematical methods, it can be calculated that if the legend is true, monks need 264-1 steps to complete this task. If they could move the plate once a second, it would take 584.9 billion years. The universe is only 13.7 billion years old.
This is the legend about the tower of Hanoi, which leads to the problem of the tower of Hanoi. This problem seems to be a bit complicated. In fact, it can be analyzed with the idea of recursion
Moving n plates from a column to C column can be divided into the following three steps
(1) Move n-1 plates on a column to B column with the help of C column;
(2) Move the last plate on column a to column C;
(3) Then the N-1 plate on the B column is moved to the C column with the help of the a column.
The first step can be divided into the following three steps:
(1) Move n-2 plates on a column to C column with the help of B column;
(2) Move the n-1st plate on column a to column B;
(3) Then move the N-2 plates on the C column to the B column with the help of the a column.
This decomposition can continue recursively until it becomes moving a plate and the recursion ends. In fact, the above three steps include two operations:
(1) Moving plates from one post to another is a recursive process;
(2) Move a plate from one post to another.
Write two functions to achieve the above two operations.
The function Hanoi (int n, char one, char two, char three) moves n plates on the "one" column to the "three" column with the help of the "two" column;
The function move (char x, char y) moves a plate from the X column to the Y column and outputs a prompt for moving the plate.
Program input the number of gold plate n, and output the process of moving n gold plates from column a (with the help of column B) to column C.
###Input example:
```in
three
```
```out
A-->C
A-->B
C-->B
A-->C
B-->A
B-->C
A-->C
```
answer：If there is no answer, please comment