MAXLN - THE MAX LINES

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In this problem you will be given a half-circle. The half-circle’s radius is r. You can take any point A on the half-circle and draw 2 lines from the point to the two sides of the diameter(AB and AC). Let the sum of square of one line’s length and the other line’s length is s

Like in the figure s = AB2 + AC. And BC = 2r.

Now given r you have to find the maximum value of s. That is you have to find point A such that AB2 + AC is maximum.

Input

First line of the test case will be the number of test case T (1 ≤ T ≤ 1000). Then T lines follows. On each line you will find a integer number r (1 ≤ r ≤ 1000000); each representing the radius of the half-circle.

Output

For each input line, print a line containing "Case I: ", where I is the test case number and the maximum value of s. Print 2 digit after decimal (Errors should be less then .01).

Example

Sample Input:
1
1

Sample Output:
Case 1: 4.25

hide comments
ISHPREET: 2016-02-26 03:52:07

Shortest code ever use int only :)

pt97: 2016-01-10 17:45:56

use int and double respectively will cause AC in first

amanjain5221: 2016-01-08 20:19:58

i used int for radius and long double for ans and i used correctly the precision ....... not worked
used double for radius ...... got AC
reason???????

Setter reply: 32bit integer may overflow for the calculation of this problem.

Last edit: 2016-06-03 13:17:53
sarthak_8: 2015-12-28 18:37:27

For the people doing it in C++ just using float or double won't help because it gives the output in scientific notation. Set the precision manually and then give it a try. Got 3 WA because of the double's output format. Otherwise the question is easy. Finally AC :)

pvsmpraveen: 2015-12-26 15:59:18

Once you derived the equation using basic calculus and geometry,
you can understand that this question can be done without float or double :P
dont use float or double might give u WA

archit saxena: 2015-12-22 18:29:34

long long int for radius
double for storing the final answer
:p

sadiq18: 2015-11-13 04:38:12

take radius in double not long int

vishals: 2015-10-19 10:25:55

basic trigonometry and quadratic eqn. .. very easy problem
Happy Coding :)

sampawan: 2015-08-25 13:15:32

easy one :)

sy_117: 2015-08-11 21:20:52

take radius in double ........a 12 lines code in C. Accepted in first go..


Added by:Muhammad Ridowan
Date:2011-03-28
Time limit:1s-1.679s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Own Problem(used for CSE,University of Dhaka, Newbies Contest)