CLTNIS_tester.java

// CLTNIS
// Tester: avijit_agarwal

import java.io.*;
import java.text.DecimalFormat;
class CLTNIS
{
    public static void main(String[] args)throws IOException
    {
        FastReader in=new FastReader(System.in);
        StringBuilder sb=new StringBuilder();
        DecimalFormat df=new DecimalFormat("#.#######");
        int MAXN=50;
        double bounds[]=new double[MAXN];
        double ball[]=new double[MAXN];
        double vel[]=new double[MAXN];
        double chef[]=new double[MAXN];
        int i,t,n,f;
        double cos_alpha,cos_beta,sin_alpha,t_exit,ans;
        t=in.nextInt();
        while(t-->0)
        {
            n=in.nextInt();
            f=0;
            double BE=0,BC=0,CE=0,velocity=0;
            
            for(i=0;i<n;i++)
                bounds[i]=in.nextInt();
            for(i=0;i<n;i++)
                ball[i]=in.nextInt();
            for(i=0;i<n;i++)
                vel[i]=in.nextInt();
            for(i=0;i<n;i++)
                chef[i]=in.nextInt();
            
            t_exit=bounds[0]/vel[0];
            
            for(i=1;i<n;i++)
            {
                if(vel[i]>0)
                    t_exit=Math.min(t_exit,(bounds[i]-ball[i])/vel[i]);
                else if(vel[i]<0)
                    t_exit=Math.min(t_exit,-1*(ball[i]/vel[i]));
            }
            for(i=0;i<n;i++)
            {
                BE+=Math.pow(vel[i]*t_exit,2);
                BC+=Math.pow(chef[i]-ball[i],2);
                CE+=Math.pow(ball[i]-chef[i]+vel[i]*t_exit,2);
                velocity+=Math.pow(vel[i],2);
                if(chef[i]!=ball[i])
                    f=1;
            }
            
            velocity=Math.pow(velocity,0.5);
            cos_alpha=(BE+BC-CE)/(2*Math.pow(BE*BC,0.5));
            cos_beta=(BC+CE-BE)/(2*Math.pow(BC,0.5)+Math.pow(CE,0.5));
            
            if(f==0)
                ans=0;
            else if(cos_alpha<=0 || cos_beta>=0)
                ans=Math.pow(CE,0.5)/t_exit;
            else
            {
               cos_alpha=Math.min(1,cos_alpha);
               sin_alpha=Math.sin(Math.acos(cos_alpha));
               ans=velocity*sin_alpha;
            }
            sb.append(df.format(ans)).append("\n");
        }
        System.out.print(sb);
    }
}
class FastReader {
    
    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;
    
    FastReader(InputStream is) {
        in = is;
    }
    
    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }
    
    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan());
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    String nextLine() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan());
        StringBuilder sb = new StringBuilder();
        for (; c !=10 && c!=13; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    char nextChar() throws IOException{
        int c;
        for (c = scan(); c <= 32; c = scan());
        return (char)c;
    }
    
    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan());
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
    
    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan());
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}