[ICPC 2022 Xi'an R] Tree

Luogu

IDLGP9369

Time2000ms

Memory512MB

DifficultyP4

2022O2优化ICPC西安

You are given a tree $T$ with $n$ nodes. The tree is rooted at $1$. Define $\mathrm{subtree}(u)$ as the set of nodes in the subtree of $u$. Call a subset of nodes $S$ good if and only if $S$ satisfies at least one of the following contidions: - For all $u, v\in S$ where $u\neq v$, either $u\in \mathrm{subtree}(v)$ or $v\in \mathrm{subtree}(u)$. - For all $u, v\in S$ where $u\neq v$, both $u\notin \mathrm{subtree}(v)$ and $v\notin \mathrm{subtree}(u)$. You need to partition all nodes of $T$ into several good subsets. Calculate the minimum number of subsets. ## Input The first line contains a single integer $Q$ ($1\leq Q\leq 10 ^ 5$), denoting the number of test cases. For each test case, the first line contains an integer $n$ ($1\leq n\leq 10 ^ 6$). The next line contains $n - 1$ integers $p_2, p_3, \ldots, p_n$ ($1\leq p_i < i$), indicating that there is an edge between $p_i$ and $i$ for each $i=2,3,\ldots,n$. It is guaranteed that the sum of $n$ over all test cases is no more than $10 ^ 6$. ## Output For each test case, output a single integer representing the answer. [samples] ## Note **Source**: The 2022 ICPC Asia Xi'an Regional Contest Problem L. **Author**: Alex_Wei.

Samples

Input #1

2
7
1 1 2 2 2 3
5
1 2 3 4

Output #1

3
1

API Response (JSON)

{
  "problem": {
    "name": "[ICPC 2022 Xi'an R] Tree",
    "description": {
      "content": "You are given a tree $T$ with $n$ nodes. The tree is rooted at $1$. Define $\\mathrm{subtree}(u)$ as the set of nodes in the subtree of $u$. Call a subset of nodes $S$ good if and only if $S$ satisfie",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 524288
    },
    "difficulty": {
      "LuoguStyle": "P4"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9369"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a tree $T$ with $n$ nodes. The tree is rooted at $1$. Define $\\mathrm{subtree}(u)$ as the set of nodes in the subtree of $u$.\n\nCall a subset of nodes $S$ good if and only if $S$ satisfie...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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