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The Use of BFS (Breadth-First Search)

ZOJ 1005 is a classical example for using BFS. The basic idea is: in a tree-like structure, each time when you visit a node, you traverse all its siblings before going to its children. When there is one finite path while the others are infinite, you need to search by BFS. Otherwise you will get stuck in one of the infinite paths. For the convenience, here is the problem:

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 
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 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 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.

My habit of using BFS is keeping an array Queue[]. We start from the head of the queue and the children of each node are appended to the end of the queue. In this way, it is guaranteed that nodes from the same level are visited before their children are.


About Xiang 'Anthony' Chen

Making an Impact in Your Life


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