a simple algorithm, help!

Discussion in 'C Programming' started by Niu Xiao, Dec 26, 2005.

  1. Niu Xiao

    Niu Xiao Guest

    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?
    Niu Xiao, Dec 26, 2005
    #1
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  2. 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.
    Giannis Papadopoulos, Dec 26, 2005
    #2
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  3. 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)
    Richard Heathfield, Dec 26, 2005
    #3
  4. Niu Xiao

    Niu Xiao Guest

    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.
    Niu Xiao, Dec 27, 2005
    #4
  5. Niu Xiao

    Niu Xiao Guest

    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
    Niu Xiao, Dec 27, 2005
    #5
  6. 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...
    Giannis Papadopoulos, Dec 27, 2005
    #6
  7. Niu Xiao <> 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) <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.
    Keith Thompson, Dec 27, 2005
    #7
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