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Problem 1028
Jugs
Time Limit: 1000ms
Memory Limit: 65536kb Description
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 successwhere "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 |

University of Science and Technology of China

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