DMOPC '15 Contest 3 P4 - Contagion

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Points:12 (partial)
Time limit:2.0s
PyPy 210.0s
PyPy 310.0s
Memory limit:128M
PyPy 2256M
PyPy 3256M

Problem type

cheesecake works part-time at the Centre for Disease Control and Prevention (CDC), where he researches the spread of diseases. An unknown pathogen has just broken out and cheesecake is determined to save the world!

The CDC’s model of the world consists of N countries numbered 1 through N, represented by points on a 2-D coordinate plane. Country i is located at integral coordinates (x_i, y_i).

Through extensive research, cheesecake has determined a vital piece of information: the time in hours it takes for the pathogen to spread from one country to another is equal to the square of the distance between the two countries. For example, if country A is located at (0,0) and country B is located at (2,3), it will take 13 hours for country B to be infected after the initial infection of country A. The source of the breakout, country X (1 \le X \le N), is infected at the 0-th hour.

In order to take preventative measures, cheesecake has been tasked with projecting the rate of infection. Specifically, he has to answer Q queries of the following form:

How many countries will be infected after Q_i hours?

Unfortunately, cheesecake isn't taking data management this semester, so he's at a total loss. Help him save the world!


Subtask 1 [20%]

1 \le N \le 100, 0 \le x_i, y_i \le 100

1 \le Q \le 10, 0 \le Q_i \le 10^5

Subtask 2 [30%]

1 \le N \le 1000, 0 \le x_i, y_i \le 10^4

1 \le Q \le 1000, 0 \le Q_i \le 10^9

Subtask 3 [50%]

1 \le N \le 3000, 0 \le x_i, y_i \le 10^6

1 \le Q \le 10^6, 0 \le Q_i \le 10^{14}

Note: For PyPy 2 and PyPy 3 and Haskell, the time limit is 10s and the memory limit is 256M.

Input Specification

The first line of input will contain N, the number of countries.

The next N lines will contain x_i and y_i, the coordinates of the i-th country, it is guaranteed that no two countries will have the same coordinates.

The next line will contain X, the source of the breakout.

The next line will contain Q, the number of queries.

The next Q lines will each contain a query.

Output Specification

For each query, output the answer on a new line.

Sample Input

2 2
0 3
5 1
4 0

Sample Output


Explanation for Sample Output

After 4 hours, the pathogen has not yet spread from its source, therefore answer is 1. After 7 hours, country 2 is infected. After 8 hours, country 4 is also infected. At 10 hours, the pathogen has spread from country 4 to country 3.


  • 0
     commented on Aug. 20, 2017 edit 3

    EDIT Make sure you use correct types!

  • -1
     commented on June 17, 2017

    Please, for the sanity of DMOJ programmers, allow submissions that don't pass the sample case to run on the other batches. It's a nightmare debugging an RTE with no output.

  • 0
     commented on Jan. 5, 2016

    Why are so many people (including myself) getting runtime error? :'(

    • 0
       commented on Jan. 5, 2016 edited

      It's very expensive memory-wise to maintain a priority queue of up to \dfrac{N\times(N-1)}{2} edges. Even if I raise the memory limit to 1 GB, your solution will TLE. The editorial might help you.

      Edit: I think it depends on which judge your submission was run on. 64-bit judges will give you RTE and 32-bit judges will give you TLE.

    • 0
       commented on Jan. 5, 2016 edit 6

      It's probably because you're initializing a long long array of 9*10^6 elements, although I didn't look at your code in detail enough to be 100\% sure.

      Since a long long takes up 64 bits of memory and you're allocating 9*10^6 of them, that means you're using up 576,000,000 bits, or 72,000,000 bytes, or 72MB. That should technically pass the memory limit, maybe? But you'd be cutting it close with all of your other variables and arrays.

      Be aware that if you wanted mathematical rigor, you should have specifically asked for Bruce or Jason's help. :)

      Anyway, that might be why, or maybe I'm totally off. Cheers!

      • 0
         commented on March 29, 2016

        Bruce or Jason's help lol

  • 2
     commented on Dec. 19, 2015
    Hint for Python

    If you're getting TLE on Python, try using multiplication instead of power.

  • 0
     commented on Dec. 18, 2015
    Only PHP judge available?

    I'm not sure if this is a bug or something, but the code can only be submitted in php

    • 0
       commented on Dec. 18, 2015

      It's fixed now; these issues occur sometimes when we update the judges.