LIS on Tree

AtCoder

IDabc165_f

Time2000ms

Memory256MB

Difficulty—

We have a tree with $N$ vertices, whose $i$\-th edge connects Vertex $u_i$ and Vertex $v_i$. Vertex $i$ has an integer $a_i$ written on it. For every integer $k$ from $1$ through $N$, solve the following problem: * We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex $1$ to Vertex $k$, in the order they appear. Find the length of the longest increasing subsequence of this sequence. Here, the longest increasing subsequence of a sequence $A$ of length $L$ is the subsequence $A_{i_1} , A_{i_2} , ... , A_{i_M}$ with the greatest possible value of $M$ such that $1 \leq i_1 < i_2 < ... < i_M \leq L$ and $A_{i_1} < A_{i_2} < ... < A_{i_M}$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq a_i \leq 10^9$ * $1 \leq u_i , v_i \leq N$ * $u_i \neq v_i$ * The given graph is a tree. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ $u_1$ $v_1$ $u_2$ $v_2$ $:$ $u_{N-1}$ $v_{N-1}$ [samples]

Samples

Input #1

10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10

Output #1

1
2
3
3
4
4
5
2
2
3

For example, the sequence $A$ obtained from the shortest path from Vertex $1$ to Vertex $5$ is $1,2,5,3,4$. Its longest increasing subsequence is $A_1, A_2, A_4, A_5$, with the length of $4$.

API Response (JSON)

{
  "problem": {
    "name": "LIS on Tree",
    "description": {
      "content": "We have a tree with $N$ vertices, whose $i$\\-th edge connects Vertex $u_i$ and Vertex $v_i$. Vertex $i$ has an integer $a_i$ written on it. For every integer $k$ from $1$ through $N$, solve the follow",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc165_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a tree with $N$ vertices, whose $i$\\-th edge connects Vertex $u_i$ and Vertex $v_i$. Vertex $i$ has an integer $a_i$ written on it. For every integer $k$ from $1$ through $N$, solve the follow...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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