Labyrinth Adventures

题意翻译

#### 题目描述 有一个 $n\times n$ 的方格图，坐标编号类似平面直角坐标系，左下角为 $(1, 1)$。 这个方格图被分成了 $n$ 层，左下角 $(1, 1)$ 为第一层，随后每层都向外拓展一圈，如下图就是 $n=5$ 的时候的情况：  层于层之间有墙隔开，但每层都有两个门，分别分布在该层顶部和右侧，门是双向的。 现在给出这些门的坐标，有 $m$ 次询问，每次给定两个坐标 $(x_1, y_1)$ 和 $(x_2,y_2)$，请你回答两点之间的最短路。 #### 输入格式 第一行一个 $n$。 接下来的 $n-1$ 行中，每行有四个整数 $d_{1,x}, d_{1,y}, d_{2,x}, d_{2,y}$，第 $i$ 行表示第 $i$ 层的两个门的坐标。前两个表示顶部门坐标，后两个表示右侧门坐标。 下一行输入 $m$。 接下来 $m$ 行，每行四个整数，$x_1,y_1,x_2,y_2$，含义如题目描述。 #### 输出格式 对每次询问，输出一行一个整数，表示两点之间的最短路长度。**长度的定义是移动的步数。** #### 样例解释 下图是样例二的网格图，红色的是门。 

题目描述

You found a map of a weirdly shaped labyrinth. The map is a grid, consisting of $ n $ rows and $ n $ columns. The rows of the grid are numbered from $ 1 $ to $ n $ from bottom to top. The columns of the grid are numbered from $ 1 $ to $ n $ from left to right. The labyrinth has $ n $ layers. The first layer is the bottom left corner (cell $ (1, 1) $ ). The second layer consists of all cells that are in the grid and adjacent to the first layer by a side or a corner. The third layer consists of all cells that are in the grid and adjacent to the second layer by a side or a corner. And so on. The labyrinth with $ 5 $ layers, for example, is shaped as follows: The layers are separated from one another with walls. However, there are doors in these walls. Each layer (except for layer $ n $ ) has exactly two doors to the next layer. One door is placed on the top wall of the layer and another door is placed on the right wall of the layer. For each layer from $ 1 $ to $ n-1 $ you are given positions of these two doors. The doors can be passed in both directions: either from layer $ i $ to layer $ i+1 $ or from layer $ i+1 $ to layer $ i $ . If you are standing in some cell, you can move to an adjacent by a side cell if a wall doesn't block your move (e.g. you can't move to a cell in another layer if there is no door between the cells). Now you have $ m $ queries of sort: what's the minimum number of moves one has to make to go from cell $ (x_1, y_1) $ to cell $ (x_2, y_2) $ .

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 2 \le n \le 10^5 $ ) — the number of layers in the labyrinth. The $ i $ -th of the next $ n-1 $ lines contains four integers $ d_{1,x}, d_{1,y}, d_{2,x} $ and $ d_{2,y} $ ( $ 1 \le d_{1,x}, d_{1,y}, d_{2,x}, d_{2,y} \le n $ ) — the coordinates of the doors. Both cells are on the $ i $ -th layer. The first cell is adjacent to the top wall of the $ i $ -th layer by a side — that side is where the door is. The second cell is adjacent to the right wall of the $ i $ -th layer by a side — that side is where the door is. The next line contains a single integer $ m $ ( $ 1 \le m \le 2 \cdot 10^5 $ ) — the number of queries. The $ j $ -th of the next $ m $ lines contains four integers $ x_1, y_1, x_2 $ and $ y_2 $ ( $ 1 \le x_1, y_1, x_2, y_2 \le n $ ) — the coordinates of the cells in the $ j $ -th query.

输出格式

For each query, print a single integer — the minimum number of moves one has to make to go from cell $ (x_1, y_1) $ to cell $ (x_2, y_2) $ .

输入输出样例

输入样例 #1

2
1 1 1 1
10
1 1 1 1
1 1 1 2
1 1 2 1
1 1 2 2
1 2 1 2
1 2 2 1
1 2 2 2
2 1 2 1
2 1 2 2
2 2 2 2

输出样例 #1

0
1
1
2
0
2
1
0
1
0

输入样例 #2

4
1 1 1 1
2 1 2 2
3 2 1 3
5
2 4 4 3
4 4 3 3
1 2 3 3
2 2 4 4
1 4 2 3

输出样例 #2

3
4
3
6
2

说明

Here is the map of the labyrinth from the second example. The doors are marked red. 

题意翻译

#### 题目描述 有一个 $n\times n$ 的方格图，坐标编号类似平面直角坐标系，左下角为 $(1, 1)$。 这个方格图被分成了 $n$ 层，左下角 $(1, 1)$ 为第一层，随后每层都向外拓展一圈，如下图就是 $n=5$ 的时候的情况：  层于层之间有墙隔开，但每层都有两个门，分别分布在该层顶部和右侧，门是双向的。 现在给出这些门的坐标，有 $m$ 次询问，每次给定两个坐标 $(x_1, y_1)$ 和 $(x_2,y_2)$，请你回答两点之间的最短路。 #### 输入格式 第一行一个 $n$。 接下来的 $n-1$ 行中，每行有四个整数 $d_{1,x}, d_{1,y}, d_{2,x}, d_{2,y}$，第 $i$ 行表示第 $i$ 层的两个门的坐标。前两个表示顶部门坐标，后两个表示右侧门坐标。 下一行输入 $m$。 接下来 $m$ 行，每行四个整数，$x_1,y_1,x_2,y_2$，含义如题目描述。 #### 输出格式 对每次询问，输出一行一个整数，表示两点之间的最短路长度。**长度的定义是移动的步数。** #### 样例解释 下图是样例二的网格图，红色的是门。