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Problem Description
Mr. West bought a new car! So he is travelling around the city.
One day he comes to a vertical corner. The street he is currently in has a width x, the street he wants to turn to has a width y. The car has a length l and a width d. Can Mr. West go across the corner?  |
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Input
Every line has four real numbers, x, y, l and w.
Proceed to the end of file. |
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Output
If he can go across the corner, print "yes". Print "no" otherwise.
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Sample Input
10 6 13.5 4 10 6 14.5 4 |
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Sample Output
yes no |
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Idea To begin with, if d is smaller than x or y, then it's sure that the car couldn't pass the conner. Besides, we can considerate the l, which can be composed by a. l = [(x / sin(a) + y / cos(a)) * cos(a) - d / sin(a)] / cos(a) simplify the equality, we can get l = x / sin(a) + y / cos(a) - d / sin (a) / cos(a) then I can get l' and l'', but I can't find the any regulation about those. what's a pity! so I just use trichotomy to get similarity of l. I know it's luck. |
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Code 1 #include <stdio.h> 2 #include <math.h> 3 double x, y, l, d; 4 double f(double a) 5 { 6 return x / sin(a) + y / cos(a) - d / sin(a) / cos(a); 7 } 8 void main() 9 { 10 double low, high, mid1, mid2; 11 int i; 12 while (scanf("%lf %lf %lf %lf", &x, &y, &l, &d) != EOF) 13 { 14 //there are two situation 15 if (d >= x || d >= y) 16 { 17 puts("no"); 18 } 19 else 20 { 21 high = acos(-1.0) / 2; 22 low = 0; 23 while (fabs(high - low) >= 1e-7) 24 { 25 mid1 = (high + low) / 2; 26 mid2 = (mid1 + high) / 2; 27 //printf("%f, %f, %f, %f\n", 28 // mid1, mid2, f(mid1), f(mid2)); 29 if (f(mid1) < f(mid2)) 30 high = mid2; 31 else 32 low = mid1; 33 } 34 //printf("high = %f, low = %f\n", high, low); 35 if (l < f(low)) 36 puts("yes"); 37 else 38 puts("no"); 39 } 40 } 41 } |
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Key Points Pay more attention to the algorithm. |