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a simple algorithm, help!

P: n/a
In the movie "Die Hard 3", Bruce Willis and Samuel L. Jackson were
confronted with the following puzzle. They were given a 3-gallon jug and
a 5-gallon jug and were asked to fill the 5-gallon jug with exactly 4
gallons. This problem generalizes that puzzle.

You have two jugs, A and B, and an infinite supply of water. There are
three types of actions that you can use: (1) you can fill a jug, (2) you
can empty a jug, and (3) you can pour from one jug to the other. Pouring
from one jug to the other stops when the first jug is empty or the
second jug is full, whichever comes first. For example, if A has 5
gallons and B has 6 gallons and a capacity of 8, then pouring from A to
B leaves B full and 3 gallons in A.

A problem is given by a triple (Ca,Cb,N), where Ca and Cb are the
capacities of the jugs A and B, respectively, and N is the goal. A
solution is a sequence of steps that leaves exactly N gallons in jug B.
The possible steps are

fill A
fill B
empty A
empty B
pour A B
pour B A
success

where "pour A B" means "pour the contents of jug A into jug B", and
"success" means that the goal has been accomplished.

You may assume that the input you are given does have a solution.

Input

Input to your program consists of a series of input lines each defining
one puzzle. Input for each puzzle is a single line of three positive
integers: Ca, Cb, and N. Ca and Cb are the capacities of jugs A and B,
and N is the goal. You can assume 0 < Ca <= Cb and N <= Cb <=1000 and
that A and B are relatively prime to one another.

Output

Output from your program will consist of a series of instructions from
the list of the potential output lines which will result in either of
the jugs containing exactly N gallons of water. The last line of output
for each puzzle should be the line "success". Output lines start in
column 1 and there should be no empty lines nor any trailing spaces.

Sample Input

3 5 4
5 7 3
Sample Output

fill B
pour B A
empty A
pour B A
fill B
pour B A
success
fill A
pour A B
fill A
pour A B
empty B
pour A B
success

--------------------------------------------

Someone said it can be solved by BFS, but I don't know what's the
relationship between this problem and BFS. Please tell me how to solved
it with BFS, or any better algorithm?
Dec 26 '05 #1
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6 Replies


P: n/a
Niu Xiao wrote:
In the movie "Die Hard 3", Bruce Willis and Samuel L. Jackson were
confronted with the following puzzle. They were given a 3-gallon jug and
a 5-gallon jug and were asked to fill the 5-gallon jug with exactly 4
gallons. This problem generalizes that puzzle.

...


Have you written any relevant C code on your problem, and if yes, then
where did you find problems?

1. Post C code
2. Ask for help on the code
3. Do not ask us to choose for you a solution - it is your homework.
Dec 26 '05 #2

P: n/a
Niu Xiao said:
In the movie "Die Hard 3", Bruce Willis and Samuel L. Jackson were
confronted with the following puzzle. They were given a 3-gallon jug and
a 5-gallon jug and were asked to fill the 5-gallon jug with exactly 4
gallons.


A can hold 5 gallons, and B can hold 3 gallons. C is the source. D is the
sink.

C -> 5 gallons -> A.
A -> 3 gallons -> B.
B -> 3 gallons -> D.
A -> 2 gallons -> B.
C -> 5 gallons -> A.
A -> 1 gallon -> B.

A now holds 4 gallons.

This is trivially solvable using a simple recursive approach.

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/1999
http://www.cpax.org.uk
email: rjh at above domain (but drop the www, obviously)
Dec 26 '05 #3

P: n/a
Richard Heathfield wrote:
Niu Xiao said:

In the movie "Die Hard 3", Bruce Willis and Samuel L. Jackson were
confronted with the following puzzle. They were given a 3-gallon jug and
a 5-gallon jug and were asked to fill the 5-gallon jug with exactly 4
gallons.

A can hold 5 gallons, and B can hold 3 gallons. C is the source. D is the
sink.

C -> 5 gallons -> A.
A -> 3 gallons -> B.
B -> 3 gallons -> D.
A -> 2 gallons -> B.
C -> 5 gallons -> A.
A -> 1 gallon -> B.

A now holds 4 gallons.

This is trivially solvable using a simple recursive approach.

Now I know that the BFS solution is actually brute-force..and I think
there exists much better algorithm.
Dec 27 '05 #4

P: n/a
Giannis Papadopoulos wrote:
Niu Xiao wrote:
In the movie "Die Hard 3", Bruce Willis and Samuel L. Jackson were
confronted with the following puzzle. They were given a 3-gallon jug
and a 5-gallon jug and were asked to fill the 5-gallon jug with
exactly 4 gallons. This problem generalizes that puzzle.

...

Have you written any relevant C code on your problem, and if yes, then
where did you find problems?

1. Post C code
2. Ask for help on the code
3. Do not ask us to choose for you a solution - it is your homework.


1. I have no idea how to solve this problem
2. Same as 1
3. I'm a professional and I have no homework
Dec 27 '05 #5

P: n/a
Niu Xiao wrote:
Giannis Papadopoulos wrote:
Niu Xiao wrote:
In the movie "Die Hard 3", Bruce Willis and Samuel L. Jackson were
confronted with the following puzzle. They were given a 3-gallon jug
and a 5-gallon jug and were asked to fill the 5-gallon jug with
exactly 4 gallons. This problem generalizes that puzzle.

...


Have you written any relevant C code on your problem, and if yes, then
where did you find problems?

1. Post C code
2. Ask for help on the code
3. Do not ask us to choose for you a solution - it is your homework.

1. I have no idea how to solve this problem
2. Same as 1
3. I'm a professional and I have no homework


1. Don't you know C, data structures and algorithms? Then you have
everything you need... Come on, make a decent try.
2. Try 1, and then there is help on the way..
3. Worse, you ask us the solution and then you will get the salary...
Not fair...
Dec 27 '05 #6

P: n/a
Niu Xiao <gn******@gmail.com> writes:
Giannis Papadopoulos wrote:
Niu Xiao wrote:
In the movie "Die Hard 3", Bruce Willis and Samuel L. Jackson were
confronted with the following puzzle. They were given a 3-gallon
jug and a 5-gallon jug and were asked to fill the 5-gallon jug with
exactly 4 gallons. This problem generalizes that puzzle.

...

Have you written any relevant C code on your problem, and if yes,
then where did you find problems?
1. Post C code
2. Ask for help on the code
3. Do not ask us to choose for you a solution - it is your homework.


1. I have no idea how to solve this problem
2. Same as 1
3. I'm a professional and I have no homework


If you have no idea how to solve the problem, then your question isn't
about C. Try comp.programming.

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
Dec 27 '05 #7

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