Lost Tree

题意翻译

**这是一道交互题。** 你有一棵 $n$ 个节点的树，树上每条边长度为 $1$，但你不知道这棵数的结构。 你可以对系统进行不超过 $\lceil \frac{n}{2} \rceil$ 次的询问，每次可以询问一个满足 $1 \le x \le n$ 的节点 $x$。 对于询问的 $x$，系统会给你 $n$ 个数，第 $i$ 个数代表节点 $i$ 与节点 $x$ 的**简单路径**长度。 请你还原出这棵树的结构。 ### 数据范围及相关提醒 $2 \le n \le 2000$。 当你要向系统询问节点 $i$ 时，输出 `? i`，且要换行。 当你知道答案的时候，先输出一行一个 `!` ； 然后紧跟着 $n-1$ 行，每行两个数 $u,v$，代表一条树上的边。 **每一次输出记得清空缓冲区。** 翻译提供 HoshizoraZ

题目描述

This is an interactive problem. Little Dormi was faced with an awkward problem at the carnival: he has to guess the edges of an unweighted tree of $ n $ nodes! The nodes of the tree are numbered from $ 1 $ to $ n $ . The game master only allows him to ask one type of question: - Little Dormi picks a node $ r $ ( $ 1 \le r \le n $ ), and the game master will reply with an array $ d_1, d_2, \ldots, d_n $ , where $ d_i $ is the length of the shortest path from node $ r $ to $ i $ , for all $ 1 \le i \le n $ . Additionally, to make the game unfair challenge Little Dormi the game master will allow at most $ \lceil\frac{n}{2}\rceil $ questions, where $ \lceil x \rceil $ denotes the smallest integer greater than or equal to $ x $ . Faced with the stomach-churning possibility of not being able to guess the tree, Little Dormi needs your help to devise a winning strategy! Note that the game master creates the tree before the game starts, and does not change it during the game.

输入输出格式

输入格式

The first line of input contains the integer $ n $ ( $ 2 \le n \le 2\,000 $ ), the number of nodes in the tree. You will then begin interaction.

输出格式

When your program has found the tree, first output a line consisting of a single "!" followed by $ n-1 $ lines each with two space separated integers $ a $ and $ b $ , denoting an edge connecting nodes $ a $ and $ b $ ( $ 1 \le a, b \le n $ ). Once you are done, terminate your program normally immediately after flushing the output stream. You may output the edges in any order and an edge $ (a,b) $ is considered the same as an edge $ (b,a) $ . Answering is not considered as a query. Interaction After taking input, you may make at most $ \lceil\frac{n}{2}\rceil $ queries. Each query is made in the format "? r", where $ r $ is an integer $ 1 \le r \le n $ that denotes the node you want to pick for that query. You will then receive $ n $ space separated integers $ d_1, d_2, \ldots, d_n $ , where $ d_i $ is the length of the shortest path from node $ r $ to $ i $ , followed by a newline. After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use: - fflush(stdout) or cout.flush() in C++; - System.out.flush() in Java; - flush(output) in Pascal; - stdout.flush() in Python; - see documentation for other languages. If at any point you make an invalid query or try to make more than $ \lceil \frac{n}{2} \rceil $ queries, the interaction will terminate immediately and you will receive a Wrong Answer verdict. Hacks To hack a solution, use the following format. The first line contains the integer $ n $ ( $ 2 \le n \le 2\,000 $ ). The next $ n−1 $ lines contain two integers $ u $ and $ v $ ( $ 1 \le u,v \le n $ ) denoting an edge between $ u $ and $ v $ ( $ u \neq v $ ). These $ n-1 $ edges must form a tree.

输入输出样例

输入样例 #1

4

0 1 2 2

1 0 1 1

输出样例 #1

? 1

? 2

!
4 2
1 2
2 3

输入样例 #2

5

2 2 1 1 0

输出样例 #2

? 5

!
4 5
3 5
2 4
1 3

说明

Here is the tree from the first example. Notice that the edges can be output in any order. Additionally, here are the answers for querying every single node in example $ 1 $ : - $ 1 $ : $ [0,1,2,2] $ - $ 2 $ : $ [1,0,1,1] $ - $ 3 $ : $ [2,1,0,2] $ - $ 4 $ : $ [2,1,2,0] $ Below is the tree from the second example interaction. Lastly, here are the answers for querying every single node in example $ 2 $ : - $ 1 $ : $ [0,4,1,3,2] $ - $ 2 $ : $ [4,0,3,1,2] $ - $ 3 $ : $ [1,3,0,2,1] $ - $ 4 $ : $ [3,1,2,0,1] $ - $ 5 $ : $ [2,2,1,1,0] $