N
Niu Xiao
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
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