Kangaroo problem, np complete :)

[Agamemnus]

This was originally a 10th grade maths extra credit problem. I made a computer program to solve it and display the kangaroo steps recently.

Can you solve it and/or make a program that shows each step?

Here it is, the Kangaroo Problem (I rewrote it from memory)

Code:

'The point of this program is to solve
'the Kangaroo Problem, defined as follows:

'There are N kangaroos crossing a bridge from both sides.
'(so 2N kangaroos total)
'
'They need to get to their respective other sides.
'The only problem is that the bridge is so narrow
'that they can only move forward and not sideways.
'
'At first the kangaroos line up like this: >>>_<<< (n = 3)
'They need to line up like this:           <<<_>>>
'
'Kangaroos can HOP and JUMP.
'A kangaroo HOP moves the Kangaroo forward one space: >_ to _>
'A kangaroo JUMP moves the Kangaroo forward two spaces: ><_ to >_>
'
'How to HOP and JUMP the kangaroos to the other side?
'(two kangaroos can't occupy one space!)
'HINT Try to solve the problems with small N's first!

[xhantt]

I can't understand JUMP.

[SCM]

Agamemnus,
The solution is fairly straight foreward. Your comment about starting with simple cases is a good general strategy, and worked well for me here. The code took me longer to write than I would like to admit. It would be nice to see some others try this problem, so I am PMing my solution and code to you. Feel free to post them.

Xhantt,
The kangaroos can only move straight forward one space(hop) or two spaces (jump). This all you need to worry about. By moving them one or two spaces, you will either solve the problem or create a road block.

[na_th_an]

I think this is solved using backtracking and cutting recursive branches which are detected to be inviable, just like the priest, the wolf and the goose problem. Maybe I try a simple approach later.

[SCM]

It's not the way a programmer is likely to think, but some times a pencil and a piece of paper is a good start.

[Phydaux]

It's not the way a programmer is likely to think, but some times a pencil and a piece of paper is a good start.

Thats the way I always start a serious project, or when I try to figure out a problem... pencil and paper gives so much freedom.

I have a desk full of notlets, mostly parts of envelopes and scraps of messed up print jobs with little equations and drawings on them

Just the way I work.

[Agamemnus]

arrr

[Lanzaa]

so hop is

__>___ to ___>__

and jump is

__>___ to ____>_
or
__><__ to ___<>_

Btw how long is the bridge?

im just coming out of algebra one AKA 8th grade math

[SCM]

Lanzaa asked

Code:

Btw how long is the bridge?

In Agamemnus' description of the problem he wrote

Code:

'At first the kangaroos line up like this: >>>_<<< (n = 3)
'They need to line up like this:           <<<_>>>

Think of the bridge as being 2*n+1 spaces long. Since there are 2*n kangaroos, there is always one free space to move into by either a

Code:

>>_<<      (n=2)
    hop    >_><<

or a

Code:

>_><<      
    jump   ><>_<

[Agamemnus]

arr arr