Mock CCC '18 Contest 1 J3/S1 - A Math Problem

Points: 5 (partial)

Time limit: 5.0s

Memory limit: 1G

Problem type

Given positive integers $K$ ~K~, $P$ ~P~, and $X$ ~X~, compute the minimum possible value of $f(M) = MX + \dfrac{KP}{M}$ ~f(M) = MX + \dfrac{KP}{M}~ given that $M$ ~M~ must be a positive integer.

Constraints

$1 \le K, P, X \le 10\,000$ ~1 \le K, P, X \le 10\,000~

Input Specification

The input consists of a single line containing three space-separated integers $K$ ~K~, $P$ ~P~, and $X$ ~X~.

Output Specification

Print, on a single line, the minimum possible value of $f$ ~f~ subject to the above constraint, rounded to exactly three decimal places.

The input data will be set such that the correct answer will not be within $10^{-5}$ ~10^{-5}~ of the aforementioned rounding boundary.

Sample Input 1

31 41 59

Sample Output 1

549.200

Sample Input 2

3 4 5

Sample Output 2

16.000

Comments

2

sankeeth_ganeswaran commented on May 5, 2019, 12:03 a.m. ← edited →

...was my solution intended? I thought for sure that I needed some calculus for this or else I would TLE haha

3

discoverMe commented on May 5, 2019, 12:50 a.m.

nope, the problem is only 5 points, it's not supposed to be that hard!

-2

Woofless77 commented on March 10, 2019, 5:08 a.m.

How come I am getting the answers to be actually 15.492 and 547.682? I tested these answers and they seem to yield lower answers for f(M) which makes the test cases wrong. But I must be missing something... I initially thought maybe they only wanted the first decimal place but when I do that, I get some of the other answers wrong. So could someone tell me what is wrong with these answers?

1

Falseman1024 commented on May 3, 2019, 10:40 p.m.

I am assuming you are directly applying AM-GM, and the inequality holds iff $MX = \frac{KP}{M}$ ~MX = \frac{KP}{M}~ but $M$ ~M~ may have non-integer solutions.

-2

xjhlg123555 commented on Oct. 14, 2018, 12:41 a.m.

How come derivative is not accurate enough?

0

ryanawad commented on March 24, 2022, 9:20 p.m. ← edited →

Try ceiling or flooring certain values

-4

andrewfeng123 commented on Jan. 23, 2019, 9:04 p.m.

gotta use double