[SNCPC2019] Unrooted Trie

Luogu

IDLGP9648

Time3000ms

Memory256MB

DifficultyP4

2019O2优化陕西树的遍历省赛/邀请赛

Recall the definition of a trie: - A trie of size $n$ is a rooted tree with $n$ vertices and $(n-1)$ edges, where each edge is marked with a character; - Each vertex in a trie represents a string. Let $s(x)$ be the string vertex $x$ represents; - The root of the trie represents an empty string. Let vertex $u$ be the parent of vertex $v$, and let $c$ be the character marked on the edge connecting vertex $u$ and $v$, we have $s(v)$ = $s(u) + c$. Here $+$ indicates string concatenation, not the normal addition operation. We say a trie is valid, if the string each vertex represents is distinct. Given an unrooted tree with $n$ vertices and $(n-1)$ edges, where each edge is marked with a character, how many different vertices can be selected as the root of the tree so that the tree becomes a valid trie? ## Input There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case: The first line contains an integer $n$ ($1 \le n \le 10^5$), indicating the size of the tree. For the following $(n-1)$ lines, the $i$-th line contains two integers $u_i$, $v_i$ ($1 \le u_i, v_i \le n$) and a character $c_i$ separated by a space, indicating that there is an edge marked with a character $c_i$ connecting vertex $u_i$ and $v_i$. It's guaranteed that $c_i$ will only be lower-case English letters. It's guaranteed that the given graph is a tree, and the sum of $n$ of all test cases will not exceed $10^6$. ## Output For each test case output one line containing one integer, indicating the number of different vertices that can be selected as the root of the tree to make it a valid trie. [samples] ## Note For the first sample test case, we can only select vertex 1 or vertex 2 as the root, otherwise $s(1)$ and $s(2)$ will be the same. For the second sample test case, no matter which vertex we select as the root, $s(1)$ and $s(2)$, or $s(5)$ and $s(6)$ will be the same.

Samples

Input #1

Output #1

2
0

API Response (JSON)

{
  "problem": {
    "name": "[SNCPC2019] Unrooted Trie",
    "description": {
      "content": "Recall the definition of a trie: - A trie of size $n$ is a rooted tree with $n$ vertices and $(n-1)$ edges, where each edge is marked with a character; - Each vertex in a trie represents a string. Le",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": {
      "LuoguStyle": "P4"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9648"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Recall the definition of a trie:\n\n- A trie of size $n$ is a rooted tree with $n$ vertices and $(n-1)$ edges, where each edge is marked with a character;\n- Each vertex in a trie represents a string. Le...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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