Vertex Deletion

AtCoder

IDabc223_g

Time2000ms

Memory256MB

Difficulty—

Given is a tree with $N$ vertices. The vertices are numbered $1,2,\ldots,N$, and the $i$\-th edge $(1 \leq i \leq N-1)$ connects Vertex $u_i$ and Vertex $v_i$. Find the number of integers $i$ $(1 \leq i \leq N)$ that satisfy the following condition. * The size of the maximum matching of the graph obtained by deleting Vertex $i$ and all incident edges from the tree is equal to the size of the maximum matching of the original tree. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq u_i < v_i \leq N$ * The given graph is a tree. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_{N-1}$ $v_{N-1}$ [samples]

Samples

Input #1

3
1 2
2 3

Output #1

2

The size of the maximum matching of the original tree is $1$.
The size of the maximum matching of the graph obtained by deleting Vertex $1$ and all incident edges from the tree is $1$.
The size of the maximum matching of the graph obtained by deleting Vertex $2$ and all incident edges from the tree is $0$.
The size of the maximum matching of the graph obtained by deleting Vertex $3$ and all incident edges from the tree is $1$.
Thus, two integers $i=1,3$ satisfy the condition, so we should print $2$.

Input #2

2
1 2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Vertex Deletion",
    "description": {
      "content": "Given is a tree with $N$ vertices. The vertices are numbered $1,2,\\ldots,N$, and the $i$\\-th edge $(1 \\leq i \\leq N-1)$ connects Vertex $u_i$ and Vertex $v_i$. Find the number of integers $i$ $(1 \\leq",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc223_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a tree with $N$ vertices. The vertices are numbered $1,2,\\ldots,N$, and the $i$\\-th edge $(1 \\leq i \\leq N-1)$ connects Vertex $u_i$ and Vertex $v_i$.\nFind the number of integers $i$ $(1 \\leq...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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