IOI '13 P4 - Cave

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Points: 20 (partial)
Time limit: 2.0s
Memory limit: 32M

Problem type
Allowed languages
C, C++

While lost on the long walk from the college to the UQ Centre, you have stumbled across the entrance to a secret cave system running deep under the university. The entrance is blocked by a security system consisting of N consecutive doors, each door behind the previous; and N switches, with each switch connected to a different door.

Switches

The doors are numbered 0, 1, \dots, (N - 1) in order, with door 0 being closest to you. The switches are also numbered 0, 1, \dots, (N - 1), though you do not know which switch is connected to which door.

The switches are all located at the entrance to the cave. Each switch can either be in an up or down position. Only one of these positions is correct for each switch. If a switch is in the correct position then the door it is connected to will be open, and if the switch is in the incorrect position then the door it is connected to will be closed. The correct position may be different for different switches, and you do not know which positions are the correct ones.

You would like to understand this security system. To do this, you can set the switches to any combination, and then walk into the cave to see which is the first closed door. Doors are not transparent: once you encounter the first closed door, you cannot see any of the doors behind it.

You have time to try 70\,000 combinations of switches, but no more. Your task is to determine the correct position for each switch, and also which door each switch is connected to.

Implementation

You should submit a file that implements the procedure exploreCave(). This may call the grader function tryCombination() up to 70\,000 times, and must finish by calling the grader procedure answer(). These functions and procedures are described below.

Grader Function: tryCombination()

C/C++ function

int tryCombination(int S[]);

Pascal

procedure tryCombination(var S: array of LongInt) : LongInt;

Description

The grader will provide this function. It allows you to try a combination of switches, and then enter the cave to determine the first closed door. If all doors are open, the function will return -1.

This function runs in \mathcal{O}(N) time; that is, the running time is at worst proportional to N.

This function may be called at most 70\,000 times.

Parameters

  • S: An array of length N, indicating the position of each switch. The element S[i] corresponds to switch i. A value of 0 indicates that the switch is up, and a value of 1 indicates that the switch is down.
  • Returns: The number of the first door that is closed, or -1 if all doors are open.

Grader Procedure: answer()

C/C++

void answer(int S[], int D[])

Pascal

procedure answer(var S, D: array of LongInt)

Description

Call this procedure when you have identified the combination of switches to open all doors, and the door to which each switch is connected.

Parameters

  • S : An array of length N, indicating the correct position of each switch. The format matches that of the function tryCombination() described above.
  • D: An array of length N, indicating the door each switch is connected to. Specifically, element D[i] should contain the door number that switch i is connected to.

  • Returns: This procedure does not return, but will cause the program to exit.

Your Procedure: exploreCave()

C/C++

void exploreCave(int N)

Pascal

procedure exploreCave(N: longint)

Description

Your submission must implement this procedure.

This function should use the grader routine tryCombination() to determine the correct position for each switch and the door each switch is connected to, and must call answer() once it has determined this information.

Parameters

  • N: The number of switches and doors in the cave.

Sample Session

Suppose the doors and switches are arranged as in the picture above:

Function Call Returns Explanation
Function Call Returns Explanation
tryCombination([1, 0, 1, 1]) 1 This corresponds to the picture. Switches 0, 2 and 3 are down, while switch 1 is up. The function returns 1, indicating that door 1 is the first door from the left that is closed. Doors 0, 1 and 2 are all opened, while door 3 is closed.
tryCombination([0, 1, 1, 0]) 3 Doors 0, 1 and 2 are all opened, while door 3 is closed.
tryCombination([1, 1, 1, 0]) -1 Moving switch 0 down causes all doors to be opened, indicated by the return value of -1.
answer([1, 1, 1, 0], [3, 1, 0, 2]) (Program exits) We guess that the correct combination is [1, 1, 1, 0], and that switches 0, 1, 2 and 3 connect to doors 3, 1, 0 and 2 respectively.

Constraints

  • Time limit: 2 seconds
  • Memory limit: 32 MiB
  • 1 \le N \le 5\,000

Subtasks

Subtask Points Additional Input Constraints
1 12 For each i, switch i is connected to door i. Your task is simply to determine the correct combination.
2 13 The correct combination will always be [0, 0, 0, …, 0]. Your task is simply to determine which switch connects to which door.
3 21 N \le 100
4 30 N \le 2\,000
5 24 (None)

Attachment


Comments


  • 0
    yeerk16  commented on Aug. 21, 2019, 3:48 p.m.

    It looks like the attachment (Dropbox) link is broken. It's still OK because the IOI site has it, but a mirror here may be convenient. Thank you!


  • 2
    kobortor  commented on April 16, 2015, 11:42 p.m. edited

    Something like the one for Inaho.

    Edit: NVM I made one myself. Here it is if anyone's interested.

    grader

    cave.h


    • 1
      Xyene  commented on April 16, 2015, 11:46 p.m.

      Since this is an IOI task, you can obtain a grader from the IOI site for the specific year, in this case http://www.ioi2013.org/competition/tasks/.


      • 1
        kobortor  commented on April 16, 2015, 11:49 p.m.

        Ah didn't see your reply in time before editing my post, thanks for the link anyways.


        • 1
          Xyene  commented on April 17, 2015, 1:06 a.m.

          No worries. It so happens that the problem statement also ends with an Attachment link from where we mirror the same data.


          • 1
            kobortor  commented on April 17, 2015, 7:41 a.m.

            I need to read the problem statements more when commenting...