Ex - Optimal Path Decomposition

AtCoder

IDabc293_h

Time2000ms

Memory256MB

Difficulty—

You are given a tree with $N$ vertices numbered $1$ through $N$. The $i$\-th edge connects vertex $A_i$ and vertex $B_i$. Find the minimum integer $K$ such that you can paint each vertex in a color so that the following two conditions are satisfied. You may use any number of colors. * For each color, the set of vertices painted in the color is connected and forms a simple path. * For all simple paths on the tree, there are at most $K$ distinct colors of the vertices in the path. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq A_i, B_i \leq N$ * The given graph is a tree. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $\vdots$ $A_{N-1}$ $B_{N-1}$ [samples]

Samples

Input #1

Output #1

3

If $K=3$, the conditions can be satisfied by painting vertices $1,2,3,4$, and $5$ in color $1$, vertex $6$ in color $2$, and vertex $7$ in color $3$. If $K \leq 2$, there is no way to paint the vertices to satisfy the conditions, so the answer is $3$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

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  "problem": {
    "name": "Ex - Optimal Path Decomposition",
    "description": {
      "content": "You are given a tree with $N$ vertices numbered $1$ through $N$. The $i$\\-th edge connects vertex $A_i$ and vertex $B_i$. Find the minimum integer $K$ such that you can paint each vertex in a color so",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
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    "sync_url": null,
    "sign": "abc293_h"
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    {
      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices numbered $1$ through $N$. The $i$\\-th edge connects vertex $A_i$ and vertex $B_i$.\nFind the minimum integer $K$ such that you can paint each vertex in a color so...",
      "is_translate": false,
      "language": "English"
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}

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