## 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 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 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 . The second line contains , the number of people who have the disease on Day . The third line contains the value of . Assume that and and .

#### Output Specification

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

#### Sample Input 1

750
1
5

#### Output for Sample Input 1

4

#### Explanation of Output for Sample Input 1

The person on Day with the disease infects people on Day . On Day , exactly people are infected. On Day , exactly people are infected. A total of people have had the disease by the end of Day are .

#### Sample Input 2

10
2
1

#### Output for Sample Input 2

5

#### Explanation of Output for Sample Input 2

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

• commented on Aug. 10, 2021, 4:12 p.m.

Very chellenging and fun

• commented on July 30, 2021, 8:45 a.m.

If you try to solve this using the pow() function in python, you will likely get TLE errors. Instead, try to find another way to keep track of current infections and new infections without have to calculate from day 0 to current day for every iteration of the loop.

Hope this helps someone else.

• commented on March 31, 2021, 11:32 a.m.

always use while tho

• commented on Jan. 22, 2021, 10:39 p.m.

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• commented on July 19, 2021, 3:24 p.m.

If R is 1 then the code kinda gets messed up i think.

• commented on Jan. 26, 2021, 9:31 p.m.

Switching to PyPy 3 fixed that problem for me, so it might be worth a try in your case

• commented on Jan. 22, 2021, 11:30 p.m.

Firstly, the number of lines is a poor indication of runtime. Consider the following program:

while True:
pass


it's only 2 lines, but will clearly take longer than the 4-line long program:

print("That's")
print("a")
print("argument")


Your issue is that Python is quite slow, and might time out if you need to loop for many days. Can you find a way to compute the answer for small values of and without looping?

• commented on Oct. 25, 2020, 10:09 a.m.

While loop is recommended for this question

• commented on Oct. 25, 2020, 1:20 p.m.

Writing an AC solution is recommended for this question

• commented on Oct. 9, 2020, 9:53 p.m. edited

It's a very interesting challenge though.

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

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

• commented on April 3, 2020, 5:42 p.m.

Not really.

• commented on March 28, 2020, 2:09 p.m.

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• commented on Nov. 24, 2020, 12:36 p.m. edited

Well, it can be seen as a geometric sequence, where the first term is N, common ratio is R, and the sum of geometric sequence is P. So the second case is the situation which the common ratio is 1, then the total number of people who are infected is N times day = 2 times (5 + 1) = 12. My code has passed and I used the formulas of geometric sequence

• commented on March 28, 2020, 8:16 p.m.

When someone is infected, they infect R other people ONLY on the very next day, not every day after they are infected.

• commented on March 29, 2020, 12:22 p.m.

Kinda doesn't make any sense when you think about it intuitively, but I guess it's what it is.

Like people don't stop infecting others when they've already infected someone, how would they know?