Score : $525$ points

问题描述

高桥和一件货物在一个坐标平面上。

目前，高桥位于坐标 $(X_A,Y_A)$，而货物位于坐标 $(X_B,Y_B)$。他希望将货物移动到坐标 $(X_C,Y_C)$。

当他在坐标 $(x,y)$ 时，他可以在一个动作中执行以下四种移动之一：

• 移动到 $(x+1,y)$。如果在移动前货物位于 $(x+1,y)$，则将其移动到 $(x+2,y)$。
• 移动到 $(x-1,y)$。如果在移动前货物位于 $(x-1,y)$，则将其移动到 $(x-2,y)$。
• 移动到 $(x,y+1)$。如果在移动前货物位于 $(x,y+1)$，则将其移动到 $(x,y+2)$。
• 移动到 $(x,y-1)$。如果在移动前货物位于 $(x,y-1)$，则将其移动到 $(x,y-2)$。

求解将货物移动到 $(X_C,Y_C)$ 所需的最小动作次数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi and a cargo are on a coordinate plane.

Takahashi is currently at $(X_A,Y_A)$, and the cargo is at $(X_B,Y_B)$. He wants to move the cargo to $(X_C,Y_C)$.

When he is at $(x,y)$, he can make one of the following moves in a single action.

• Move to $(x+1,y)$. If the cargo is at $(x+1,y)$ before the move, move it to $(x+2,y)$.
• Move to $(x-1,y)$. If the cargo is at $(x-1,y)$ before the move, move it to $(x-2,y)$.
• Move to $(x,y+1)$. If the cargo is at $(x,y+1)$ before the move, move it to $(x,y+2)$.
• Move to $(x,y-1)$. If the cargo is at $(x,y-1)$ before the move, move it to $(x,y-2)$.

Find the minimum number of actions required to move the cargo to $(X_C,Y_C)$.

Constraints

• $-10^{17}\leq X_A,Y_A,X_B,Y_B,X_C,Y_C\leq 10^{17}$
• $(X_A,Y_A)\neq (X_B,Y_B)$
• $(X_B,Y_B)\neq (X_C,Y_C)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$X_A$ $Y_A$ $X_B$ $Y_B$ $X_C$ $Y_C$

Output

Print the minimum number of actions required to move the cargo to $(X_C,Y_C)$.

Sample Input 1

1 2 3 3 0 5

Sample Output 1

9

Takahashi can move the cargo to $(0,5)$ in nine actions as follows.

• Move to $(2,2)$.
• Move to $(3,2)$.
• Move to $(3,3)$. The cargo moves to $(3,4)$.
• Move to $(3,4)$. The cargo moves to $(3,5)$.
• Move to $(4,4)$.
• Move to $(4,5)$.
• Move to $(3,5)$. The cargo moves to $(2,5)$.
• Move to $(2,5)$. The cargo moves to $(1,5)$.
• Move to $(1,5)$. The cargo moves to $(0,5)$.

It is impossible to move the cargo to $(0,5)$ in eight or fewer actions, so you should print $9$.

Sample Input 2

0 0 1 0 -1 0

Sample Output 2

6

Sample Input 3

-100000000000000000 -100000000000000000 100000000000000000 100000000000000000 -100000000000000000 -100000000000000000

Sample Output 3

800000000000000003

update @ 2024/3/10 01:45:18