Tree Queries

AtCoder

IDarc142_c

Time2000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices, numbered $1, \ldots, N$. For each pair of integers $u,v\, (1 \leq u,v \leq N)$, the distance $d_{u,v}$ between Vertices $u, v$ is defined as the following. * The number of edges contained in the shortest path connecting Vertices $u$ and $v$. You are allowed to ask between $0$ and $2N$ questions (inclusive) in the following form. * Ask the distance $d_{u,v}$ between Vertices $u,v$ for integers $u,v$ of your choice such that $1\leq u,v \leq N$ and $u+v>3$. Find the distance $d_{1,2}$ between Vertices $1,2$. ## Constraints * $3 \leq N \leq 100$ * $N$ is an integer. * The tree is determined before the start of the interaction between your program and the judge. ## Input And Output **This is an interactive task**, in which your program and the judge interact via input and output. First, your program is given a positive integer $N$ from Standard Input: $N$ Then, you get to ask questions. A question should be printed in the following format (with a newline at the end): ? $u$ $v$ If the question is valid, the response $d_{u,v}$ is given from Standard Input: $d_{u,v}$ If the question is judged invalid because, for example, it is malformed or you have asked too many questions, you get `-1` instead of the response: \-1 At this point, your submission is already judged incorrect. The judge's program then terminates; yours should too, desirably. When you find the answer $d_{1,2}$, print it to Standard Output in the following format (with a newline at the end): ! $d_{1,2}$ ## Notices * **Flush Standard Output after each output. Otherwise, you might get the TLE verdict.** * After printing the answer (or receiving `-1`), immediately terminate the program normally. Otherwise, the verdict would be indeterminate. * The verdict for the case of a malformed output would be indeterminate. * Specifically, note that too many newlines would also be seen as a malformed output. [samples]

API Response (JSON)

{
  "problem": {
    "name": "Tree Queries",
    "description": {
      "content": "There is a tree with $N$ vertices, numbered $1, \\ldots, N$.   For each pair of integers $u,v\\, (1 \\leq u,v \\leq N)$, the distance $d_{u,v}$ between Vertices $u, v$ is defined as the following. *   Th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc142_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tree with $N$ vertices, numbered $1, \\ldots, N$.  \nFor each pair of integers $u,v\\, (1 \\leq u,v \\leq N)$, the distance $d_{u,v}$ between Vertices $u, v$ is defined as the following.\n\n*   Th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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