A. Circumference of a Tree

Codeforces

IDCF10269A

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Hopefully you know how to find the diameter of a tree. That's the first part of tree basics, after all! But this problem is completely different: now, you need to find the *circumference* of a tree! As you probably know, pi is equal to the ratio between something's circumferance and its diameter. Also, as you may not know, math is a lie and *pi is really equal to 3*. Rumor has it, this is where the number tree(3) comes from. Assuming pi equals 3, what is the circumference of the given tree? The first line will contain a single integer $n$, the number of nodes in the tree. $n -1$ lines follow, each containing two different integers, describing the edges of the tree. Additional constraint on input: these edges will form a tree. $1 <= n <= 3 * 10^5$ Output a single integer: the circumference of the tree. ## Input The first line will contain a single integer $n$, the number of nodes in the tree. $n -1$ lines follow, each containing two different integers, describing the edges of the tree. Additional constraint on input: these edges will form a tree.$1 <= n <= 3 * 10^5$ ## Output Output a single integer: the circumference of the tree. [samples]

**Definitions** Let $ T = (V, E) $ be a tree with $ n $ nodes and $ n-1 $ edges. Let $ d(u, v) $ denote the shortest path distance (number of edges) between nodes $ u $ and $ v $ in $ T $. Let $ \text{diam}(T) = \max_{u,v \in V} d(u, v) $ be the diameter of the tree. **Constraints** 1. $ 1 \le n \le 3 \times 10^5 $ 2. The graph is a tree (connected, acyclic, undirected). **Objective** Given $ \pi = 3 $, compute the circumference of the tree: $$ \text{circumference} = \pi \cdot \text{diam}(T) = 3 \cdot \text{diam}(T) $$ Output this value as an integer.

API Response (JSON)

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