USACO1.4.4--Mother's Milk

Mother's Milk

Farmer John has three milking buckets of capacity A, B, and C liters. Each of the numbers A, B, and C is an integer from 1 through 20, inclusive. Initially, buckets A and B are empty while bucket C is full of milk. Sometimes, FJ pours milk from one bucket to another until the second bucket is filled or the first bucket is empty. Once begun, a pour must be completed, of course. Being thrifty, no milk may be tossed out.

Write a program to help FJ determine what amounts of milk he can leave in bucket C when he begins with three buckets as above, pours milk among the buckets for a while, and then notes that bucket A is empty.

PROGRAM NAME: milk3

INPUT FORMAT

A single line with the three integers A, B, and C.

SAMPLE INPUT (file milk3.in)

8 9 10

OUTPUT FORMAT

A single line with a sorted list of all the possible amounts of milk that can be in bucket C when bucket A is empty.

SAMPLE OUTPUT (file milk3.out)

1 2 8 9 10

SAMPLE INPUT (file milk3.in)

2 5 10

SAMPLE OUTPUT (file milk3.out)

5 6 7 8 9 10
解题思路：果断DFS啊，总共六种状态，C->A,C->B,B->A,A->B,A->C,B->C。每次要么被灌的桶装满或者原桶空了。要求按升序输出，由于桶容量最大才20，所以C桶的剩余量用一个20的数组标记一下就可以了。
偶滴代码：

View Code

 1 /*

 2 ID:spcjv51

 3 PROG:milk3

 4 LANG:C

 5 */

 6 #include<stdio.h>

 7 int f[25][25][25];

 8 int path[25];

 9 int a,b,c,total;

10 void init()

11 {

12     scanf("%d%d%d",&a,&b,&c);

13     memset(f,0,sizeof(f));

14     memset(path,0,sizeof(path));

15     total=0;

16 }

17 void search(int x,int y,int z)

18 {

19     if (f[x][y][z]) return;

20     f[x][y][z]=1;

21     if(x==0) path[z]=1;

22     if(x+z<=a) search(x+z,y,0);

23     else       search(a,y,z-a+x);

24     if(y+z<=b) search(x,y+z,0);

25     else       search(x,b,z+y-b);

26     if(x+y<=a) search(x+y,0,z);

27     else       search(a,y+x-a,z);

28     if(x+y<=b) search(0,x+y,z);

29     else       search(x+y-b,b,z);

30     if(x+z<=c) search(0,y,x+z);

31     else       search(x+z-c,y,c);

32     if(y+z<=c) search(x,0,y+z);

33     else       search(x,y+z-c,c);

34 }

35 void output()

36 {

37     int i,flag;

38     flag=0;

39     for(i=0; i<=20; i++)

40         if(path[i]&&flag==0)

41         {

42             printf("%d",i);

43             flag=1;

44         }

45         else if (path[i]&&flag!=0) printf(" %d",i);

46     printf("\n");

47 }

48 int main(void)

49 {

50 

51     freopen("milk3.in","r",stdin);

52     freopen("milk3.out","w",stdout);

53     init();

54     search(0,0,c);

55     output();

56     return 0;

57 }