Erase Leaves

AtCoder

IDabc333_d

Time2000ms

Memory256MB

Difficulty—

You are given a tree with $N$ vertices: vertex $1,$ vertex $2$, $\ldots$, vertex $N$. The $i$\-th edge $(1\leq i\lt N)$ connects vertex $u _ i$ and vertex $v _ i$. Consider repeating the following operation some number of times: * Choose one leaf vertex $v$ and delete it along with all incident edges. Find the minimum number of operations required to delete vertex $1$. What is a tree? A tree is an undirected graph that is connected and has no cycles. For more details, see: [Wikipedia "Tree (graph theory)"](https://en.wikipedia.org/wiki/Tree_(graph_theory)). What is a leaf? A leaf in a tree is a vertex with a degree of at most $1$. ## Constraints * $2\leq N\leq3\times10^5$ * $1\leq u _ i\lt v _ i\leq N\ (1\leq i\lt N)$ * The given graph is a tree. * All input values are integers. ## Input The 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

Output #1

5

The given graph looks like this:
![image](https://img.atcoder.jp/abc333/6089239ee0c331bec4cd4472c032d197.png)
For example, you can choose vertices $9,8,7,6,1$ in this order to delete vertex $1$ in five operations.
![image](https://img.atcoder.jp/abc333/7dba9a660bfabdd403fe6882dac4e8ab.png)
Vertex $1$ cannot be deleted in four or fewer operations, so print $5$.

Input #2

Output #2

1

In the given graph, vertex $1$ is a leaf. Hence, you can choose and delete vertex $1$ in the first operation.

Input #3

Output #3

API Response (JSON)

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  "problem": {
    "name": "Erase Leaves",
    "description": {
      "content": "You are given a tree with $N$ vertices: vertex $1,$ vertex $2$, $\\ldots$, vertex $N$. The $i$\\-th edge $(1\\leq i\\lt N)$ connects vertex $u _ i$ and vertex $v _ i$. Consider repeating the following ope",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc333_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices: vertex $1,$ vertex $2$, $\\ldots$, vertex $N$. The $i$\\-th edge $(1\\leq i\\lt N)$ connects vertex $u _ i$ and vertex $v _ i$.\nConsider repeating the following ope...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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