CCC '20 J2 - Epidemiology

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Points: 3
Time limit: 1.0s
Python 3 3.0s
Memory limit: 512M

Problem type
Canadian Computing Competition: 2020 Stage 1, Junior #2

People who study epidemiology use models to analyze the spread of disease. In this problem, we use a simple model.

When a person has a disease, they infect exactly R other people but only on the very next day. No person is infected more than once. We want to determine when a total of more than P people have had the disease.

(This problem was designed before the current coronavirus outbreak, and we acknowledge the distress currently being experienced by many people worldwide because of this and other diseases. We hope that including this problem at this time highlights the important roles that computer science and mathematics play in solving real-world problems.)

Input Specification

There are three lines of input. Each line contains one positive integer. The first line contains the value of P. The second line contains N, the number of people who have the disease on Day 0. The third line contains the value of R. Assume that P \le 10^7 and N \le P and R \le 10.

Output Specification

Output the number of the first day on which the total number of people who have had the disease is greater than P.

Sample Input 1

750
1
5

Output for Sample Input 1

4

Explanation of Output for Sample Input 1

The 1 person on Day 0 with the disease infects 5 people on Day 1. On Day 2, exactly 25 other people are infected. On Day 3, exactly 125 other people are infected. A total of 1 + 5 + 25 + 125 + 625 = 781 people have had the disease by the end of Day 4 and 781 > 750.

Sample Input 2

10
2
1

Output for Sample Input 2

5

Explanation of Output for Sample Input 2

There are 2 people on Day 0 with the disease. On each other day, exactly 2 other people are infected. By the end of Day 4, a total of exactly 10 people have had the disease and by the end of Day 5, more than 10 people have had the disease.


Comments


  • -3
    fangL  commented on Feb. 24, 2024, 1:21 a.m.

    Heute bin ich dran


  • 1
    christin910  commented on Jan. 15, 2024, 1:39 a.m.

    I use ChatGPT to walk me through the process for CCC problems while practicing, but ChatGPT seems to really struggle to understand this one.


  • 0
    daveys  commented on Jan. 12, 2024, 10:27 a.m.

    Interesting problem and surprisingly more difficult to solve than I expected it to be.


  • 53
    Spitfire720  commented on Feb. 22, 2022, 1:10 a.m.

    Only in Canada will you have contest organizers apologize for a pandemic that they didn't know would happen.


    • 17
      thomas_li  commented on Feb. 22, 2022, 1:38 a.m.

      meanwhile USACO made COWVID-19 themed problems


  • 6
    QooModa  commented on Feb. 21, 2022, 9:42 p.m.

    An important lesson I have learned. Don't forget to delete the code you write to check new values.

    I lost half an hour trying to find out why my answer was correct, and then I noticed I had some print statements to check the values.


  • 6
    Amateur360  commented on Oct. 10, 2020, 1:53 a.m. edited

    It's a very interesting challenge though.


  • 24
    euphoria  commented on April 3, 2020, 7:59 p.m.

    This question was surprisingly difficult compared to the other questions during this years contest