Ex - Sum of Min of Length

AtCoder
IDabc298_h
Time3000ms
Memory256MB
Difficulty
You are given a tree with $N$ vertices. The vertices are numbered $1$ to $N$, and the $i$\-th edge connects vertex $A_i$ and vertex $B_i$. Let $d(x,y)$ denote the distance between vertex $x$ and $y$ in this tree. Here, the distance between vertex $x$ and $y$ is the number of edges on the shortest path from vertex $x$ to $y$. Answer $Q$ queries in order. The $i$\-th query is as follows. * You are given integers $L_i$ and $R_i$. Find $\displaystyle\sum_{j = 1}^{N} \min(d(j, L_i), d(j, R_i))$. ## Constraints * $1 \leq N, Q \leq 2 \times 10^5$ * $1 \leq A_i, B_i, L_i, R_i \leq N$ * 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: $N$ $A_1$ $B_1$ $\vdots$ $A_{N-1}$ $B_{N-1}$ $Q$ $L_1$ $R_1$ $\vdots$ $L_Q$ $R_Q$ [samples]
Samples
Input #1
5
3 4
4 5
2 5
1 5
3
4 1
1 2
5 3
Output #1
4
6
3

Let us explain the first query.  
Since $d(1, 4) = 2$ and $d(1, 1) = 0$, we have $\min(d(1, 4), d(1, 1)) = 0$.  
Since $d(2, 4) = 2$ and $d(2, 1) = 2$, we have $\min(d(2, 4), d(2, 1)) = 2$.  
Since $d(3, 4) = 1$ and $d(3, 1) = 3$, we have $\min(d(3, 4), d(3, 1)) = 1$.  
Since $d(4, 4) = 0$ and $d(4, 1) = 2$, we have $\min(d(4, 4), d(4, 1)) = 0$.  
Since $d(5, 4) = 1$ and $d(5, 1) = 1$, we have $\min(d(5, 4), d(5, 1)) = 1$.  
$0 + 2 + 1 + 0 + 1 = 4$, so you should print $4$.
Input #2
8
4 2
4 1
5 6
6 1
7 6
8 1
3 7
7
8 4
4 4
7 2
4 4
5 3
4 4
6 1
Output #2
14
16
10
16
14
16
8
API Response (JSON)
{
  "problem": {
    "name": "Ex - Sum of Min of Length",
    "description": {
      "content": "You are given a tree with $N$ vertices. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects vertex $A_i$ and vertex $B_i$. Let $d(x,y)$ denote the distance between vertex $x$ and $y$ i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc298_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects vertex $A_i$ and vertex $B_i$.\nLet $d(x,y)$ denote the distance between vertex $x$ and $y$ i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}
Full JSON Raw Segments