Transit Tree Path

AtCoder

IDabc070_d

Time2000ms

Memory256MB

Difficulty—

You are given a tree with $N$ vertices. Here, a _tree_ is a kind of graph, and more specifically, a connected undirected graph with $N-1$ edges, where $N$ is the number of its vertices. The $i$\-th edge $(1≤i≤N-1)$ connects Vertices $a_i$ and $b_i$, and has a length of $c_i$. You are also given $Q$ queries and an integer $K$. In the $j$\-th query $(1≤j≤Q)$: * find the length of the shortest path from Vertex $x_j$ and Vertex $y_j$ via Vertex $K$. ## Constraints * $3≤N≤10^5$ * $1≤a_i,b_i≤N (1≤i≤N-1)$ * $1≤c_i≤10^9 (1≤i≤N-1)$ * The given graph is a tree. * $1≤Q≤10^5$ * $1≤K≤N$ * $1≤x_j,y_j≤N (1≤j≤Q)$ * $x_j≠y_j (1≤j≤Q)$ * $x_j≠K,y_j≠K (1≤j≤Q)$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ $c_1$ $:$ $a_{N-1}$ $b_{N-1}$ $c_{N-1}$ $Q$ $K$ $x_1$ $y_1$ $:$ $x_{Q}$ $y_{Q}$ [samples]

Samples

Input #1

Output #1

3
2
4

The shortest paths for the three queries are as follows:

*   Query $1$: Vertex $2$ → Vertex $1$ → Vertex $2$ → Vertex $4$ : Length $1+1+1=3$
*   Query $2$: Vertex $2$ → Vertex $1$ → Vertex $3$ : Length $1+1=2$
*   Query $3$: Vertex $4$ → Vertex $2$ → Vertex $1$ → Vertex $3$ → Vertex $5$ : Length $1+1+1+1=4$

Input #2

Output #2

5
14
22

The path for each query must pass Vertex $K=2$.

Input #3

10
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
7 8 1000000000
8 9 1000000000
9 10 1000000000
1 1
9 10

Output #3

17000000000

API Response (JSON)

{
  "problem": {
    "name": "Transit Tree Path",
    "description": {
      "content": "You are given a tree with $N$ vertices.   Here, a _tree_ is a kind of graph, and more specifically, a connected undirected graph with $N-1$ edges, where $N$ is the number of its vertices.   The $i$\\-t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc070_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices.  \nHere, a _tree_ is a kind of graph, and more specifically, a connected undirected graph with $N-1$ edges, where $N$ is the number of its vertices.  \nThe $i$\\-t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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