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

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Points: 5 (partial)
Time limit: 5.0s
Memory limit: 1G

Problem type

Given positive integers KK, PP, and XX, compute the minimum possible value of f(M) = MX + \dfrac{KP}{M}f(M) = MX + \dfrac{KP}{M} given that MM must be a positive integer.

Constraints

1 \le K, P, X \le 10\,0001 \le K, P, X \le 10\,000

Input Specification

The input consists of a single line containing three space-separated integers KK, PP, and XX.

Output Specification

Print, on a single line, the minimum possible value of ff 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


  • 1
    sankeeth_ganeswaran  commented on May 4, 2019, 8:03 p.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 4, 2019, 8:50 p.m.

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


  • -1
    Woofless77  commented on March 10, 2019, 12:08 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?


    • 2
      Falseman1024  commented on May 3, 2019, 6:40 p.m.

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


  • -2
    xjhlg123555  commented on Oct. 13, 2018, 8:41 p.m.

    How come derivative is not accurate enough?