POJ 3414 Pots (BFS pouring water)

POJ 3414 Pots (BFS pouring water)

You have two capacities: a and B. Each time you fill a cup with water, you can pour it out, or pour it into another cup. Ask if you can use these two capacities to produce c-capacity water.

Similar to the last cola problem, this operation is more. The water contained in each of the two cups is used as the status. Each time a queue is sent, the water may arrive in all possible states until there is a cup. the volume of water is c, and the print path is directly recursive.

 

#include 

# Include # Include Using namespace std; const int N = 105; int a, B, c, t, le, ri, v [N] [N]; int x [N * N], p [N * N], op [N * N], d [N * N]; pair Q [N * N]; void check (int I, int j, int o, int k) {if (v [I] [j]) return; v [I] [j] = 1, p [ri] = le; op [ri] = o, x [ri] = k, d [ri] = d [le] + 1; q [ri ++] = make_pair (I, j);} int bfs () {int ca, cb = le = ri = 0; q [ri ++] = make_pair (0, 0); memset (v, 0, sizeof (v )), v [0] [0] = 1; while (le <ri) {ca = q [le]. first, cb = q [le]. second; if (ca = c | cb = c) return le; check (a, cb, 1, 1); // FILL (1); check (ca, b, 1, 2); // FILL (2); check (0, cb, 2, 1); // DROP (1); check (ca, 0, 2, 2); // DROP (2); if (ca> B-cb) check (ca-B + cb, B, 3, 1); else check (0, ca + cb, 3, 1); // POUR (1, 2); if (cb> a-ca) check (a, cb-a + ca, 3, 2 ); else check (ca + cb, 0, 3, 2); // POUR (); + + le;} return 0;} void print (int k) {if (p [k]> 0) print (p [k]); if (op [k] = 1) printf ("FILL (% d) \ n ", x [k]); if (op [k] = 2) printf ("DROP (% d) \ n", X [k]); if (op [k] = 3) printf ("POUR (% d, % d) \ n", x [k], 3-x [k]);} int main () {int ans; while (~ Scanf ("% d", & a, & B, & c) {if (ans = bfs () printf ("% d \ n ", d [ans]), print (ans); else puts ("impossible");} return 0 ;}

 

Pots

 

Description

You are given two pots, having the volumeAAndBLiters respectively. The following operations can be saved med:

FILL (I) fill the pot I(1 ≤ I≤ 2) from the tap; DROP (I) empty the pot ITo the drain; POUR (I, j) pour from pot ITo pot J; After this operation either the pot JIs full (and there may be some water left in the pot I), Or the pot IIs 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 exactlyCLiters of water in one of the pots.

Input

On the first and only line are the numbersA,B, AndC. These are all integers in the range from 1 to 100 andC≤ Max (A,B).

Output

The first line of the output must contain the length of the sequence of operationsK. The followingKLines 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

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