Pots
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
1 //2017-02-24 2 #include <iostream> 3 #include <cstdio> 4 #include <cstring> 5 #include <algorithm> 6 7 using namespace std; 8 9 struct node 10 { 11 int a, b, step, pre, op; 12 }q[1000]; 13 14 int pots[3], POT[3], book[105][105]; 15 string option[10] = {"", "FILL(1)", "FILL(2)", "DROP(1)", "DROP(2)", "POUR(1,2)", "POUR(2,1)"}; 16 17 void fill(int i) 18 { 19 pots[i] = POT[i]; 20 } 21 22 void drop(int i) 23 { 24 pots[i] = 0; 25 } 26 27 void pour(int i, int j) 28 { 29 if(pots[i] > POT[j]-pots[j]){ 30 pots[i] -= (POT[j]-pots[j]); 31 pots[j] = POT[j]; 32 }else{ 33 pots[j] += pots[i]; 34 pots[i] = 0; 35 } 36 } 37 38 void init(int a, int b) 39 { 40 pots[1] = a; 41 pots[2] = b; 42 } 43 44 void push(int pos, int a, int b, int step, int pre, int op) 45 { 46 q[pos].a = a; 47 q[pos].b = b; 48 q[pos].step = step; 49 q[pos].pre = pre; 50 q[pos].op = op; 51 } 52 53 void print(int pos) 54 { 55 if(q[pos].pre == -1)return; 56 print(q[pos].pre); 57 cout<<option[q[pos].op]<<endl; 58 } 59 60 int min(int a, int b) 61 { 62 return a < b ? a : b; 63 } 64 65 int main() 66 { 67 int C, a, b, step; 68 while(cin>>POT[1]>>POT[2]>>C) 69 { 70 int head = 0, tail = 1; 71 q[0].a = 0; 72 q[0].b = 0; 73 q[0].step = 0; 74 q[0].pre = -1; 75 memset(book, 0, sizeof(book)); 76 book[0][0] = 1; 77 while(head < tail) 78 { 79 a = q[head].a; 80 b = q[head].b; 81 step = q[head].step; 82 83 if(a==C || b==C){ 84 cout<<step<<endl; 85 print(head); 86 break; 87 } 88 89 init(a, b); 90 fill(1); 91 if(!book[pots[1]][pots[2]]){ 92 book[pots[1]][pots[2]] = 1; 93 push(tail, pots[1], pots[2], step+1, head, 1); 94 tail++; 95 } 96 97 init(a, b); 98 fill(2); 99 if(!book[pots[1]][pots[2]]){ 100 book[pots[1]][pots[2]] = 1; 101 push(tail, pots[1], pots[2], step+1, head, 2); 102 tail++; 103 } 104 105 if(a>0){ 106 init(a, b); 107 drop(1); 108 if(!book[pots[1]][pots[2]]){ 109 book[pots[1]][pots[2]] = 1; 110 push(tail, pots[1], pots[2], step+1, head, 3); 111 tail++; 112 } 113 } 114 115 if(b>0){ 116 init(a, b); 117 drop(2); 118 if(!book[pots[1]][pots[2]]){ 119 book[pots[1]][pots[2]] = 1; 120 push(tail, pots[1], pots[2], step+1, head, 4); 121 tail++; 122 } 123 } 124 125 init(a, b); 126 pour(1, 2); 127 if(!book[pots[1]][pots[2]]){ 128 book[pots[1]][pots[2]] = 1; 129 push(tail, pots[1], pots[2], step+1, head, 5); 130 tail++; 131 } 132 133 init(a, b); 134 pour(2, 1); 135 if(!book[pots[1]][pots[2]]){ 136 book[pots[1]][pots[2]] = 1; 137 push(tail, pots[1], pots[2], step+1, head, 6); 138 tail++; 139 } 140 141 head++; 142 } 143 if(head>=tail)cout<<"impossible"<<endl; 144 } 145 return 0; 146 }