USACO Section 3.2 Spinning Wheels (spin)

Spinning Wheels
1998 ACM NE Regionals

Each of five opaque spinning wheels has one or more wedges cut out of its edges. These wedges must be aligned quickly and correctly. Each wheel also has an alignment mark (at 0 degrees) so that the wheels can all be started in a known position. Wheels rotate in the `plus degrees' direction, so that shortly after they start, they pass through 1 degree, 2 degrees, etc. (though probably not at the same time).

This is an integer problem. Wheels are never actually at 1.5 degrees or 23.51234123 degrees. For example, the wheels are considered to move instantaneously from 20 to 25 degrees during a single second or even from 30 to 40 degrees if the wheel is spinning quickly.

All angles in this problem are presumed to be integers in the range 0 <= angle <= 359. The angle of 0 degrees follows the angle of 359 degrees. Each wheel rotates at a certain integer number of degrees per second, 1 <= speed <= 180.

Wedges for each wheel are specified by an integer start angle and integer angle size (or `extent'), both specified in degrees. Wedges in the test data will be separated by at least one degree. The 'extent' also includes the original "degree" of the wedge, so '0 180' means degrees 0..180 inclusive -- one more than most would imagine.

At the start, which is time 0, all the wheels' alignment marks line up. Your program must determine the earliest time (integer seconds) at or after the start that some wedge on each wheel will align with the wedges on the other wheel so that a light beam can pass through openings on all five wedges. The wedges can align at any part of the rotation.

PROGRAM NAME: spin

INPUT FORMAT

Each of five input lines describes a wheel.

The first integer on an input line is the wheel's rotation speed. The next integer is the number of wedges, 1 <= W <= 5. The next W pairs of integers tell each wedge's start angle and extent.

SAMPLE INPUT (file spin.in)

30 1 0 120
50 1 150 90
60 1 60 90
70 1 180 180
90 1 180 60

OUTPUT FORMAT

A single line with a single integer that is the first time the wedges align so a light beam can pass through them. Print `none' (lower case, no quotes) if the wedges will never align properly.

SAMPLE OUTPUT (file spin.out)

9
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Executing...
   Test 1: TEST OK [0.000 secs, 3228 KB]
   Test 2: TEST OK [0.000 secs, 3228 KB]
   Test 3: TEST OK [0.000 secs, 3228 KB]
   Test 4: TEST OK [0.000 secs, 3228 KB]
   Test 5: TEST OK [0.000 secs, 3228 KB]
   Test 6: TEST OK [0.000 secs, 3228 KB]
   Test 7: TEST OK [0.000 secs, 3228 KB]
   Test 8: TEST OK [0.022 secs, 3228 KB]

All tests OK.

  1 /*
  2 ID:wuhuaju2
  3 PROG:spin
  4 LANG:C++
  5 */
  6 #include <cstdio>
  7 #include <iostream>
  8 #include <cstdlib>
  9 #include <algorithm>
 10 #include <cstring>
 11 #include <string>
 12 using namespace std;
 13 
 14 bool f[370];
 15 int a[10][10],st[10][10],en[10][10],zh[10],tot[10];
 16 int x,y,ans,n,x1,x2,y1,y2;
 17 bool flag;
 18 
 19 void close()
 20 {
 21     fclose(stdin);
 22     fclose(stdout);
 23     exit(0);
 24 }
 25 
 26 bool chuli(int x1,int y1,int x2,int y2)
 27 {
 28     if (x1>=x2 && x1<=y2) return true;
 29     if (y1<=y2 && y1>=x2) return true;
 30     if (x1<=x2 && y1>=y2) return true;
 31     if (x1>=x2 && y2>=y1) return true;
 32     return false;
 33 }
 34 
 35 bool ju()
 36 {
 37     for (int i=1;i<=5;i++)
 38     {
 39         for (int j=i+1;j<=5;j++)
 40         {
 41             x1=a[i][1];y1=a[i][2];
 42             x2=a[j][1];y2=a[j][2];
 43             if (x1>y1)
 44             {
 45                 if (x2>y2)
 46                 {
 47                     if (chuli(x1,359,x2,359))
 48                         continue;
 49                     if (chuli(0,y1,0,y2))
 50                         continue;
 51                     return false;
 52                 }
 53                 if (chuli(x1,359,x2,y2))
 54                     continue;
 55                 if (chuli(0,y1,x2,y2))
 56                     continue;
 57             }
 58             else
 59             {
 60                 if (x2>y2)
 61                 {
 62                     if (chuli(x1,y1,x2,359))
 63                         continue;
 64                     if (chuli(x1,y1,0,y2))
 65                         continue;
 66                     return false;
 67                 }
 68                 if (chuli(x1,y1,x2,y2))
 69                     continue;
 70             }
 71             return false;
 72         }
 73     }
 74     /*
 75     for (int i=1;i<=5;i++)
 76         cout<<a[i][1]<<" "<<a[i][2]<<" ";
 77     cout<<endl;
 78     */
 79     return true;
 80 }
 81 
 82 bool judge()
 83 {
 84     for (int q=1;q<=tot[1];q++)
 85     {
 86         for (int w=1;w<=tot[2];w++)
 87         {
 88             for (int e=1;e<=tot[3];e++)
 89             {
 90                 for (int r=1;r<=tot[4];r++)
 91                 {
 92                     for (int t=1;t<=tot[5];t++)
 93                     {
 94                         a[1][1]=st[1][q];a[1][2]=en[1][q];
 95                         a[2][1]=st[2][w];a[2][2]=en[2][w];
 96                         a[3][1]=st[3][e];a[3][2]=en[3][e];
 97                         a[4][1]=st[4][r];a[4][2]=en[4][r];
 98                         a[5][1]=st[5][t];a[5][2]=en[5][t];
 99                         /*
100                         for (int i=1;i<=5;i++)
101                         {
102                             for (int j=i+1;j<=5;j++)
103                             {
104                                 if (a[i][2]<a[i][1]) // 240 30
105                                 {
106                                     if (min(a[j][1],a[j][2])<=a[i][1])
107                                         continue;
108                                     if (a[j][1])
109                                 }
110                                 */
111                         if (ju())
112                             return true;
113                     }
114                 }
115             }
116         }
117     }
118             return false;
119 }
120 
121 
122 void work()
123 {
124     ans=0;
125     while (ans<=360)  //change!!
126     {
127         if (judge())
128         {
129             printf("%d\n",ans);
130             close();
131         }
132         for (int i=1;i<=5;i++)
133         {
134             for (int j=1;j<=tot[i];j++)
135             {
136                 st[i][j]=(st[i][j]+zh[i]) % 360;
137                 en[i][j]=(en[i][j]+zh[i]) % 360;
138             }
139         }
140         ans++;
141     }
142     cout<<"none"<<endl;
143 }
144 
145 void init ()
146 {
147 freopen("spin.in","r",stdin);
148 freopen("spin.out","w",stdout);
149    for (int i=1;i<=5;i++)
150     {
151         scanf("%d %d",&zh[i],&tot[i]);
152         for (int j=1;j<=tot[i];j++)
153         {
154             scanf("%d %d",&st[i][j],&en[i][j]);
155             en[i][j]=(en[i][j]+st[i][j]) % 360;
156         }
157     }
158         
159 }
160 
161 int main ()
162 {
163     init();
164     work();
165     close();
166     return 0;
167 }

posted on 2013-02-13 00:13 cssystem 阅读(418) 评论(0) 收藏举报