Codeforces 549 H. Degenerate Matrix binary

Codeforces 549 H. Degenerate Matrix binary

 

Returns the binary absolute value and determines whether a matrix exists.

 

H. Degenerate Matrix time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output

The determinant of a matrix 2? ×? 2 is defined as follows:

A matrix is called degenerate if its determinant is equal to zero.

The norm |A| Of a matrixAIs defined as a maximum of absolute values of its elements.

You are given a matrix. Consider any degenerate matrixBSuch that norm |A? -?B| Is minimum possible. Determine |A? -?B|.

Input

The first line contains two integersAAndB(|A| ,? |B|? ≤? 109), the elements of the first row of matrixA.

The second line contains two integersCAndD(|C| ,? |D|? ≤? 109) the elements of the second row of matrixA.

Output

Output a single real number, the minimum possible value of |A? -?B|. Your answer is considered to be correct if its absolute or relative error does not exceed 10? -? 9.

Sample test (s) input

1 23 4

Output

0.2000000000

Input

1 00 1

Output

0.5000000000

Note

In the first sample matrixBIs

In the second sample matrixBIs

import java.util.*;public class Main{double a,b,c,d;double[][] range = new double[4][2];double getMin(double L,double R,double l,double r){   return Math.min(L*l,Math.min(L*r,Math.min(R*l,R*r)));}double getMax(double L,double R,double l,double r){   return Math.max(L*l,Math.max(L*r,Math.max(R*l,R*r)));}boolean check(double e){range[0][0]=a-e; range[0][1]=a+e; // xrange[1][0]=b-e; range[1][1]=b+e; // yrange[2][0]=c-e; range[2][1]=c+e; // zrange[3][0]=d-e; range[3][1]=d+e; // wdouble A=getMin(range[0][0],range[0][1],range[3][0],range[3][1]);double B=getMax(range[0][0],range[0][1],range[3][0],range[3][1]);double C=getMin(range[1][0],range[1][1],range[2][0],range[2][1]);double D=getMax(range[1][0],range[1][1],range[2][0],range[2][1]);if((A>=C&&A<=D)||(B>=C&&B<=D)||(C>=A&&C<=B)||(D>=A&&D<=B)) return true;return false;}double Search(){double low=0.00000,high=100000000000.;int T_T=170;while(T_T-->0){double mid=(low+high)/2.;if(check(mid)==true) high=mid;else low=mid;}return high; }Main(){Scanner in = new Scanner(System.in);a=in.nextDouble(); b=in.nextDouble(); c=in.nextDouble(); d=in.nextDouble();System.out.printf("%.12f\n",Search());}public static void main(String[] args){new Main();}}