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  • 18、Jugs

    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
     
    解题思路:本题中很重要的一个条件是A和B的容积互质(A and B are relatively prime to one another ),A的整数倍对B取余数,余数可以取到从0到B-1 。这就决定了用A向B倒水可以得到0至Cb之间的任意整数。所以在不要求最优解的情况下直接用A向B不断倒水即可满足要求,即只需执行fill A,pour A B,empty B三项操作。
    代码示例:
     1 #include<iostream>
     2 using namespace std;
     3 
     4 int main(){
     5      int capA, capB, vA, vB, n;
     6      for (; cin >> capA >> capB >> n;){
     7            for (vA = 0, vB = 0; vB != n; cout << "pour A B" << endl){
     8                 if (vA == 0){
     9                      vA = capA;
    10                      cout << "fill A" << endl;
    11                 }
    12                 if (vB == capB){
    13                      vB = 0;
    14                      cout << "empty B" << endl;
    15                 }
    16                 vB += vA;
    17                 vA = 0;
    18                 if (vB > capB){
    19                      vA = vB - capB;
    20                      vB = capB;
    21                 }
    22            }
    23            cout << "success" << endl;
    24      }
    25      return 0;
    26 }
    做题感悟:1、有时间要琢磨一下最优解
    2、学到了互质的两个数A、B,其中A的整数倍对B取余数,余数可以取到从0到B-1
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  • 原文地址:https://www.cnblogs.com/langzi1996/p/7010256.html
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