Tree Diameter I

# Tree Diameter ## Problem Statement You are given a tree consisting of $n$ nodes. The nodes are numbered from $1$ to $n$. The diameter of a tree is defined as the maximum distance (number of edges) between any two nodes in the tree. Your task is to determine and print the diameter of the given tree. ## Input Format The first line contains a single integer $n$ ($1 \le n \le 2 \times 10^5$), representing the number of nodes in the tree. The nodes are numbered from $1$ to $n$. Each of the next $n-1$ lines contains two integers $u$ and $v$ ($1 \le u, v \le n$, $u \ne v$), indicating that there is an edge between node $u$ and node $v$. ## Output Format Print a single integer, the diameter of the tree. ## Sample Test Cases ### Sample Input 1 ``` 5 1 2 1 3 3 4 3 5 ``` ### Sample Output 1 ``` 3 ``` ## Constraints - $1 \le n \le 2 \times 10^5$ - $1 \le u, v \le n$ - The given graph is guaranteed to be a tree. - Time limit: 1 second - Memory limit: 256 MB ## Explanation For Sample Input 1, the tree has 5 nodes and 4 edges. The longest path in this tree has a length of 3 edges. One such path is between node 2 and node 5, specifically $2 \to 1 \to 3 \to 5$. Another path of length 3 is $4 \to 3 \to 1 \to 2$. Thus, the diameter of the tree is 3.