Ex - Ball Collector

AtCoder

IDabc302_h

Time2000ms

Memory256MB

Difficulty—

We have a tree with $N$ vertices. The $i$\-th $(1 \le i \le N-1)$ edge is an undirected edge between vertices $U_i$ and $V_i$. Vertex $i$ $(1 \le i \le N)$ has a ball with $A_i$ written on it and another with $B_i$. For each $v = 2,3,\dots,N$, answer the following question. (Each query is independent.) * Consider traveling from vertex $1$ to vertex $v$ on the shortest path. Every time you visit a vertex (including vertices $1$ and $v$), you pick up one ball placed there. Find the maximum number of distinct integers written on the picked-up balls. ## Constraints * $2 \le N \le 2 \times 10^5$ * $1 \le A_i,B_i \le N$ * 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: $N$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ $U_1$ $V_1$ $U_2$ $V_2$ $\vdots$ $U_{N-1}$ $V_{N-1}$ [samples]

Samples

Input #1

Output #1

2 3 3

For example, when $v=4$, you visit vertices $1,2,3$, and $4$. By choosing balls with $A_1,B_2,B_3,B_4(=1,3,1,2)$ written on them, the number of distinct integers on the balls is $3$, which is the maximum.

Input #2

Output #2

4 3 2 3 4 3 4 2 3

API Response (JSON)

{
  "problem": {
    "name": "Ex - Ball Collector",
    "description": {
      "content": "We have a tree with $N$ vertices. The $i$\\-th $(1 \\le i \\le N-1)$ edge is an undirected edge between vertices $U_i$ and $V_i$. Vertex $i$ $(1 \\le i \\le N)$ has a ball with $A_i$ written on it and anot",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc302_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a tree with $N$ vertices. The $i$\\-th $(1 \\le i \\le N-1)$ edge is an undirected edge between vertices $U_i$ and $V_i$. Vertex $i$ $(1 \\le i \\le N)$ has a ball with $A_i$ written on it and anot...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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