Issue in Broken Clock of FEB18 in codechef

I've been trying to get the final y coordinate, so I've accepted the initial y coordinate at 1 second time and found the inverse of it's cosine . I've then multiplies the angle with time and then converted to the y coordinate by using the required trigo function but the issue is in case of -2 coordinate my code gives -1.99.... which is not accurate.

Also require help in the part of converting a huge decimal value to two integral integer values as numerator and denominator, since multiplying by a power of 10 doesn't give accurate results and might need multiplication with a prime number.

c++ codechef feb18 java brokenclock broclk

Asked by: Liman_Rahman on April 7, 2019, 6:34 p.m. Last updated on April 7, 2019, 6:34 p.m.

1 Answer(s)

mathematically your approach is correct but since there is always a loss of precision when working with floating-point numbers(while doing any arithemetic/trigonometric operation) this apporach will never give accurate results.

Instead what you could do is create a structure which will allow you to operate on fractions. This was you can operate on p and q seperatly and it will never result in loss of precision.

struct fraction
{
   int num; //numerator
   int den; //denominator
};
fraction subtraction(fraction fract1,fraction fract2)   //for subtraction of two fractions
{
         fraction result;
         result.num = (fract1.num * fract2.den) - (fract2.num* fract1.den);
         result.den = (fract1.den * fract2.den);
         return result;     
}   
fraction multiplication(fraction fract1,fraction fract2)   //for multiplying two fractions
{
         fraction result;
         result.num = (fract1.num * fract2.num);
         result.den = (fract1.den * fract2.den);
         return result;
}
 
//likewise for other arithmetical operations

aslo you can't directly use trigonometric function to find cos (t*theta) as it will also not give precise results.

so you have to use divide and conquer + subtract and conquer strategy with memonization to get 100 pts.

we already have the value of cos(theta),

now if t is power of 2 then we can easily get value of cos(t*theta) using the identity cos (2*theta)=2*cos^2(theta) -1 in divide and conquer.

If t is not power of two then we can break t in two terms A and B ,where A is power of 2 and can use the identity : cos (A+B)=2cosA*cosB-cos(A-B)

Shubham_Kumar_Gupta last updated on April 7, 2019, 6:34 p.m. 0 Reply Upvote

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Issue in Broken Clock of FEB18 in codechef

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