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 }