1166 The Clocks

 

The Clocks

Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 3980   Accepted: 1434

Description

 

Input
Your program is to read from standard input. Nine numbers give the start positions of the dials. 0=12 o'clock, 1=3 o'clock, 2=6 o'clock, 3=9 o'clock.

Output
Your program is to write to standard output. Output a shortest sorted sequence of moves (numbers), which returns all the dials to 12 o'clock. You are convinced that the answer is unique.

Sample Input

 

Sample Output

 

Source
IOI 1994

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Source Code

# include <iostream.h>int move[9][9]={   //A,B,C,D,E,F,G,H,I{1,1,0,1,1,0,0,0,0},//move1{1,1,1,0,0,0,0,0,0},//move2{0,1,1,0,1,1,0,0,0},//move3{1,0,0,1,0,0,1,0,0},//move4{0,1,0,1,1,1,0,1,0},//move5{0,0,1,0,0,1,0,0,1},//move6{0,0,0,1,1,0,1,1,0},//move7{0,0,0,0,0,0,1,1,1},//move8{0,0,0,0,1,1,0,1,1} //move9};int clock[9];//originalint temp[9];//for tryint m[9];//record the times of each movevoid LoadClock();void Move();bool Check();void Output();void main(){LoadClock();for (m[0]=0;m[0]<=3;m[0]++)for (m[1]=0;m[1]<=3;m[1]++)for (m[2]=0;m[2]<=3;m[2]++)for (m[3]=0;m[3]<=3;m[3]++)for (m[4]=0;m[4]<=3;m[4]++)for (m[5]=0;m[5]<=3;m[5]++)for (m[6]=0;m[6]<=3;m[6]++)for (m[7]=0;m[7]<=3;m[7]++)for (m[8]=0;m[8]<=3;m[8]++){Move();if (Check()==true){Output();break;}}}void LoadClock(){int i;for (i=0;i<9;i++)cin>>clock[i];}void Move(){int i,j;for (i=0;i<9;i++){temp[i]=clock[i];for (j=0;j<9;j++) if(move[j][i])temp[i] += m[j];temp[i] %= 4;}}bool Check(){int i;for (i=0;i<9;i++)if (temp[i]!=0)return false;return true;}void Output(){int i,j;for (i=0;i<9;i++){if (m[i]>0)for (j=0;j<m[i];j++)cout<<i+1<<' ';}cout<<endl;}

4 5 8 9

3 3 02 2 22 1 2

|-------|    |-------|    |-------|
|       |    |       |    |   |   |
|---O   |    |---O   |    |   O   |
|       |    |       |    |       |
|-------|    |-------|    |-------|
    A            B            C    

|-------|    |-------|    |-------|
|       |    |       |    |       |
|   O   |    |   O   |    |   O   |
|   |   |    |   |   |    |   |   |
|-------|    |-------|    |-------|
    D            E            F    

|-------|    |-------|    |-------|
|       |    |       |    |       |
|   O   |    |   O---|    |   O   |
|   |   |    |       |    |   |   |
|-------|    |-------|    |-------|
    G            H            I    
(Figure 1)

There are nine clocks in a 3*3 array (figure 1). The goal is to return all the dials to 12 o'clock with as few moves as possible. There are nine different allowed ways to turn the dials on the clocks. Each such way is called a move. Select for each move a number 1 to 9. That number will turn the dials 90' (degrees) clockwise on those clocks which are affected according to figure 2 below.

Move   Affected clocks
 
 1         ABDE
 2         ABC
 3         BCEF
 4         ADG
 5         BDEFH
 6         CFI
 7         DEGH
 8         GHI
 9         EFHI    
   (Figure 2)