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56 lines
1.4 KiB
Forth
56 lines
1.4 KiB
Forth
The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower
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and sometimes pluralized) is a mathematical game or puzzle. It
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consists of three rods and a number of disks of different sizes,
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which can slide onto any rod. The puzzle starts with the disks in
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a neat stack in ascending order of size on one rod, the smallest
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at the top, thus making a conical shape.
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The objective of the puzzle is to move the entire stack to another
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rod, obeying the following simple rules:
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- Only one disk can be moved at a time.
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- Each move consists of taking the upper disk from one of the
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stacks and placing it on top of another stack.
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- No disk may be placed on top of a smaller disk.
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With 3 disks, the puzzle can be solved in 7 moves. The minimal
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number of moves required to solve a Tower of Hanoi puzzle is
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2^n-1, where n is the number of disks.
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Taken from https://en.m.wikipedia.org/wiki/Tower_of_Hanoi
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I am tracking state in a few variables, so I define them first.
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~~~
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'Num var
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'From var
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'To var
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'Via var
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~~~
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Next, a quick word to setup all the variables.
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~~~
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:set-vars !Via !To !From !Num ;
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~~~
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Then, implementing the recursive algorithm from the Wikipedia article:
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~~~
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:hanoi (num,from,to,via-)
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set-vars
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@Num n:-zero?
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[
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@Num @From @To @Via
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@Num n:dec @From @Via @To hanoi
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set-vars
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@To @From '\nMove_a_ring_from_%n_to_%n s:format s:put
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@Num n:dec @Via @To @From hanoi
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] if ;
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~~~
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And a test.
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~~~
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#3 #1 #3 #2 hanoi nl
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~~~
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