# poj 3414 pots (bfs+路径记录)

Posted by 111qqz on Monday, July 27, 2015

## TOC

Pots

Description

You are given two pots, having the volume of A and B liters respectively. The following operations can be performed:

1. FILL(i) fill the pot i (1 ≤ **i **≤ 2) from the tap;
2. DROP(i) empty the pot i to the drain;
3. POUR(i,j) pour from pot i to pot j; after this operation either the pot j is full (and there may be some water left in the pot i), or the pot i is empty (and all its contents have been moved to the pot j).

Write a program to find the shortest possible sequence of these operations that will yield exactly C liters of water in one of the pots.

Input

On the first and only line are the numbers A, B, and C. These are all integers in the range from 1 to 100 and C≤max(A,B).

Output

The first line of the output must contain the length of the sequence of operations K. The following K lines must each describe one operation. If there are several sequences of minimal length, output any one of them. If the desired result can't be achieved, the first and only line of the file must contain the word ‘impossible'.

Sample Input

``````3 5 4
``````

Sample Output

``````6
FILL(2)
POUR(2,1)
DROP(1)
POUR(2,1)
FILL(2)
POUR(2,1)
``````

``````/*************************************************************************
> File Name: code/2015summer/searching/H.cpp
> Author: 111qqz
> Email: rkz2013@126.com
> Created Time: 2015年07月27日 星期一 09时11分28秒
************************************************************************/

#include<iostream>
#include<iomanip>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<string>
#include<map>
#include<set>
#include<queue>
#include<vector>
#include<stack>
#define y0 abc111qqz
#define y1 hust111qqz
#define yn hez111qqz
#define j1 cute111qqz
#define tm crazy111qqz
#define lr dying111qqz
using namespace std;
#define REP(i, n) for (int i=0;i<int(n);++i)
typedef long long LL;
typedef unsigned long long ULL;
const int N=1E2+5;
int A,B,C;
int d[N][N];
bool flag;
struct node
{
int d,opt,par,prea,preb;
}q[N][N];

void print(int x,int y)
{
//    cout<<"x:"<<x<<"y:"<<y<<endl;
if (q[x][y].prea!=-1&&q[x][y].preb!=-1)
{
// 	  cout<<"who is 111qqz"<<endl;
print(q[x][y].prea,q[x][y].preb);
if (q[x][y].opt==1){
printf("FILL(%d)\n",q[x][y].par);
}
if (q[x][y].opt==2)
{
printf("DROP(%d)\n",q[x][y].par);
}
if (q[x][y].opt==3)
{
printf("POUR(%d,%d)\n",q[x][y].par,3-q[x][y].par);
}
}

}
void bfs()
{
memset(q,-1,sizeof(q));
queue<int>a;
queue<int>b;
a.push(0);
b.push(0);
q[0][0].d=0;
while (!a.empty()&&!b.empty())
{
int av = a.front();a.pop();
int bv = b.front();b.pop();
// 	  cout<<"av:"<<av<<"bv:"<<bv<<endl;
if (av==C||bv==C)
{
flag = true;
//cout<<"yeah~~~~~~~~~~~~~~~"<<endl;
cout<<q[av][bv].d<<endl;
// 		cout<<"prea:"<<q[av][bv].prea<<"preb:"<<q[av][bv].preb<<endl;
print(av,bv);
return;
}
if (av<A&&q[A][bv].d==-1)
{
q[A][bv].d=q[av][bv].d+1;
q[A][bv].opt=1;
q[A][bv].par=1;
q[A][bv].prea=av;
q[A][bv].preb=bv;
a.push(A);
b.push(bv);
}
if (av>0&&q[0][bv].d==-1)
{
q[0][bv].d=q[av][bv].d+1;
q[0][bv].opt=2;
q[0][bv].par=1;
q[0][bv].prea=av;
q[0][bv].preb=bv;
a.push(0);
b.push(bv);

}
if (bv<B&&q[av][B].d==-1)
{
q[av][B].d=q[av][bv].d+1;
q[av][B].opt=1;
q[av][B].par=2;
q[av][B].prea = av;
q[av][B].preb = bv;
a.push(av);
b.push(B);

}
if (bv>0&&q[av][0].d==-1)
{
q[av][0].d=q[av][bv].d+1;
q[av][0].opt=2;
q[av][0].par=2;
q[av][0].prea=av;
q[av][0].preb=bv;
a.push(av);
b.push(0);
}

if (av+bv<=B&&q[0][av+bv].d==-1)
{
q[0][av+bv].d=q[av][bv].d+1;
q[0][av+bv].opt=3;
q[0][av+bv].par=1;
q[0][av+bv].prea=av;
q[0][av+bv].preb=bv;
a.push(0);
b.push(av+bv);
}
if (av+bv>B&&q[av-(B-bv)][B].d==-1)   //把1往2里倒入的两种情况
{

int tmp = av-(B-bv);
q[tmp][B].d=q[av][bv].d+1;
q[tmp][B].opt=3;
q[tmp][B].par=1;
q[tmp][B].prea=av;
q[tmp][B].preb=bv;
a.push(tmp);
b.push(B);
}

if (bv+av<=A&&q[av+bv][0].d==-1)
{
q[av+bv][0].d=q[av][bv].d+1;
q[av+bv][0].opt=3;
q[av+bv][0].par=2;
q[av+bv][0].prea=av;
q[av+bv][0].preb=bv;
a.push(av+bv);
b.push(0);
}
if (bv+av>A&&q[A][bv-(A-av)].d==-1)
{
int tmp = bv-(A-av);
q[A][tmp].d=q[av][bv].d+1;
q[A][tmp].opt=3;
q[A][tmp].par=2;
q[A][tmp].prea=av;
q[A][tmp].preb=bv;
a.push(A);
b.push(tmp);
}
}
}
int main()
{

flag = false;
cin>>A>>B>>C;
bfs();
if (!flag)
{
cout<<"impossible"<<endl;
}

return 0;
}
``````

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