POJ 3414, Pots

Time Limit: 1000MS  Memory Limit: 65536K
Total Submissions: 2779  Accepted: 1167  Special Judge

Description

You are given two pots, having the volume of A and B liters respectively. The following operations can be performed:
FILL(i)        fill the pot i (1 ≤ i ≤ 2) from the tap;
DROP(i)      empty the pot i to the drain;
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)

Source
Northeastern Europe 2002, Western Subregion

---

// POJ3414.cpp : Defines the entry point for the console application.
//

#include <iostream>
#include <queue>
#include <stack>
#include <string>
using namespace std;

int main(int argc, char* argv[])
{
    int A,B,C;
    cin >> A >> B >> C;

    int status[101][101][4];
    memset(status, -1, sizeof(status));

    queue<pair<char,char>> q;
    q.push(make_pair(0,0));
    status[0][0][0] = 0;
    int x,y;
    bool find = false;
    while (!q.empty())
    {
        pair<char,char> cur = q.front();
        q.pop();

        if (cur.first == C || cur.second == C)
        {
            x = cur.first;
            y = cur.second;
            find = true;
            break;
        }

        //fill pot 1
        if (status[A][cur.second][0]==-1)
        {
            q.push(make_pair(A,cur.second));
            status[A][cur.second][0] = status[cur.first][cur.second][0] + 1;
            status[A][cur.second][1] = cur.first;
            status[A][cur.second][2] = cur.second;
            status[A][cur.second][3] = 1;
        }
        //drop pot 1
        if (status[0][cur.second][0]==-1)
        {
            q.push(make_pair(0,cur.second));
            status[0][cur.second][0] = status[cur.first][cur.second][0] + 1;
            status[0][cur.second][1] = cur.first;
            status[0][cur.second][2] = cur.second;
            status[0][cur.second][3] = 2;
        }
        //Pour pot 1 --> pot 2
        int total = cur.first + cur.second;
        int a, b;
        if (total <= B)
        {
            a = 0;
            b = total;
        }
        else
        {
            a = total - B;
            b = B;
        }
        if (status[a][b][0]==-1)
        {
            q.push(make_pair(a, b));
            status[a][b][0] = status[cur.first][cur.second][0] + 1;
            status[a][b][1] = cur.first;
            status[a][b][2] = cur.second;
            status[a][b][3] = 3;
        }

        //fill pot 2
        if (status[cur.first][B][0]==-1)
        {
            q.push(make_pair(cur.first,B));
            status[cur.first][B][0] = status[cur.first][cur.second][0] + 1;
            status[cur.first][B][1] = cur.first;
            status[cur.first][B][2] = cur.second;
            status[cur.first][B][3] = 4;
        }
        //drop pot 2
        if (status[cur.first][0][0]==-1)
        {
            q.push(make_pair(cur.first,0));
            status[cur.first][0][0] = status[cur.first][cur.second][0] + 1;
            status[cur.first][0][1] = cur.first;
            status[cur.first][0][2] = cur.second;
            status[cur.first][0][3] = 5;
        }
        //Pour pot 2 --> pot 1
        total = cur.first + cur.second;
        if (total <= A)
        {
            a = total;
            b = 0;
        }
        else
        {
            a = A;
            b = total - A;
        }
        if (status[a][b][0]==-1)
        {
            q.push(make_pair(a, b));
            status[a][b][0] = status[cur.first][cur.second][0] + 1;
            status[a][b][1] = cur.first;
            status[a][b][2] = cur.second;
            status[a][b][3] = 6;
        }
    };

    if (find == true)
    {
        int cnt = status[x][y][0];
        stack<string> st;
        for (int i = 0; i < cnt; ++i)
        {
            switch(status[x][y][3])
            {
                case 1: st.push("FILL(1)\n");break;
                case 2: st.push("DROP(1)\n");break;
                case 3: st.push("POUR(1,2)\n");break;
                case 4: st.push("FILL(2)\n");break;
                case 5: st.push("DROP(2)\n");break;
                case 6: st.push("POUR(2,1)\n");break;
            }
            int x1 = status[x][y][1];
            int y1 = status[x][y][2];
            x = x1;
            y = y1;
        }

        cout << cnt << endl;
        while(!st.empty())
        {
            cout << st.top();
            st.pop();
        }
    }
    else
        cout << "impossible\n";
    return 0;
}