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문제

Jian-Jia is a young boy who loves playing games. When he is asked a question, he prefers playing games rather than answering directly. Jian-Jia met his friend Mei-Yu and told her about the flight network in Taiwan. There are n cities in Taiwan (numbered 0, ..., n - 1), some of which are connected by flights. Each flight connects two cities and can be taken in both directions.

Mei-Yu asked Jian-Jia whether it is possible to go between any two cities by plane (either directly or indirectly). Jian-Jia did not want to reveal the answer, but instead suggested to play a game. Mei-Yu can ask him questions of the form "Are cities x and y directly connected with a flight?", and Jian-Jia will answer such questions immediately. Mei-Yu will ask about every pair of cities exactly once, giving r = n(n - 1)/2 questions in total. Mei-Yu wins the game if, after obtaining the answers to the first i questions for some i < r, she can infer whether or not it is possible to travel between every pair of cities by flights (either directly or indirectly). Otherwise, that is, if she needs all r questions, then the winner is Jian-Jia.

In order for the game to be more fun for Jian-Jia, the friends agreed that he may forget about the real Taiwanese flight network, and invent the network as the game progresses, choosing his answers based on Mei-Yu's previous questions. Your task is to help Jian-Jia win the game, by deciding how he should answer the questions.

예제

We explain the game rules with three examples. Each example has n = 4 cities and r = 6 rounds of question and answer.

In the first example (the following table), Jian-Jia loses because after round 4, Mei-Yu knows for certain that one can travel between any two cities by flights, no matter how Jian-Jia answers questions 5 or 6.

round question answer
1 0, 1 yes
2 3, 0 yes
3 1, 2 no
4 0, 2 yes
----- -------- ------
5 3, 1 no
6 2, 3 no

In the next example Mei-Yu can prove after round 3 that no matter how Jian-Jia answers questions 4, 5, or 6, one cannot travel between cities 0 and 1 by flights, so Jian-Jia loses again.

round question answer
1 0, 1 no
2 2, 0 no
3 0, 1 no
----- -------- ------
4 1, 2 yes
5 1, 3 yes
6 2, 3 yes

In the final example Mei-Yu cannot determine whether one can travel between any two cities by flights until allsix questions are answered, so Jian-Jia wins the game. Specifically, because Jian-Jia answered yes to the last question (in the following table), then it is possible to travel between any pair of cities. However, if Jian-Jia had answered no to the last question instead then it would be impossible.

round question answer
1 0, 3 no
2 1, 0 yes
3 0, 2 no
4 3, 1 yes
5 1, 2 no
6 2, 3 yes

구현

Please write a program that helps Jian-Jia win the game. Note that neither Mei-Yu nor Jian-Jia knows the strategy of each other. Mei-Yu can ask about pairs of cities in any order, and Jian-Jia must answer them immediately without knowing the future questions. You need to implement the following two functions.

  • void initialize(int n);
    • We will call your initialize first. The parameter n is the number of cities.
  • int hasEdge(int u, int v);
    • Then we will call hasEdge for r = n(n -1)/2 times. These calls represent Mei-Yu's questions, in the order that she asks them. You must answer whether there is a direct flight between cities u and v. Specifically, the return value should be 1 if there is a direct flight, or 0 otherwise.

서브태스크

번호 배점 조건
1 15

n = 4

2 27

4 ≤ n ≤ 80

3 58

4 ≤ n ≤ 1500

샘플 그레이더

The sample grader reads the input in the following format:

  • line 1: n
  • the following r lines: each line contains two integers u and v that describe a question regarding cities u and v.

제출할 수 있는 언어

C++17, C++14, C++20, C++14 (Clang), C++17 (Clang), C++20 (Clang)

채점 및 기타 정보

  • 예제는 채점하지 않는다.