1.4.2 Mother's Milk(dfs)

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

代码：

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;
int x,y,z;
int cnt=0;
int v[200100];
int ans[30];

void dfs(int a, int b ,int c){

if(v[a*10000+b*1000+c]==1)
{
return;
}
v[a*10000+b*1000+c]=1;
if(a==0){
cnt++;
ans[c]=1;
}
// c--->a,b
if(c!=0){
//c->a
if(a+c>=x&&a!=x) dfs(x,b,c-x+a);
else if(a+c<x) dfs(a+c,b,0);
//c->b
if(b+c>=y&&b!=y) dfs(a,y,c-y+b);
else if(b+c<y) dfs(a,b+c,0);
}
// b--->a,c
if(b!=0){
//b->a
if(b+a>=x&&a!=x) dfs(x,b+a-x,c);
else if(b+a<x) dfs(b+a,0,c);
//b->c
if(b+c>=z&&c!=z) dfs(a,b+c-z,z);
else if(b+c<z) dfs(a,0,b+c);
}
// a--->c,b
if(a!=0){
//a->c
if(a+c>=z&&c!=z) dfs(a+c-z,b,z);
else if(a+c<z) dfs(0,b,a+c);
//a->b
if(b+a>=y&&b!=y) dfs(a+b-y,y,c);
else if(a+b<y) dfs(0,a+b,c);
}
}

int main() {
freopen("milk3.in","r",stdin);
freopen("milk3.out","w",stdout);
cin>>x>>y>>z;
memset(v,0,sizeof(v));
memset(ans,0,sizeof(ans));
cnt=0;
dfs(0,0,z);
int k=0;
for(int i=0;i<=20;i++){
if(ans[i]){
if(k) cout<<" ";
k++;
cout<<i;
}
}
cout<<endl;
return 0;
}