MAXLN - THE MAX LINES
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
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ayusofayush:
2018-02-23 14:18:51
simple differentiation and use setprecision() ....only maths |
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Divyam Shah:
2018-02-09 17:24:19
@Nani the value of roots is not imaginary, for AC=0.5 we get "AC^2 - AC = -0.25". |
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vkash:
2018-01-03 10:55:20
4 lines of code...easy 1 :) |
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nani:
2017-12-27 19:37:56
There seems to be some loophole in the question, pythagorean theorem AB^2 + AC^2 = BC^2. For sample input AB^2 + AC^2 = 4, but how will AB^2 + AC = 4.25 this tends to be AC^2 - AC = -0.25 which in return leads to imaginary values of AC. Please clarify me if I am missing anything? |
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Anand Kumar:
2017-06-25 10:57:14
took time.. but finally got it...
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shalini6:
2017-06-08 14:06:41
Use s = AB^2 + AC and pythagoras theorem AB^2 + AC^2 = (2r)^2(traingle in a semi circle is right angled)
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rohit9934:
2017-05-08 12:16:19
Pre-Requisites: High school differentiation. |
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soodan:
2017-04-08 12:31:08
Few points to take care of :
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sushanth_r:
2017-03-29 16:27:25
1 WA because of the output format. My fault, I know. |
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vladimira:
2017-02-21 22:25:52
For python-ers. There are some extra spaces or something else with input is wrong. So try to read input not by lines but by words. For example sys.stdin.read().split(). In advance if you will use this trick further, it is bad way if input is large, so bufferize. |
| 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) |
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