#### 题意

• the distance from a point to itself is zero,
• the distance between two distinct points is non-negative,
• the distance from A to B is the same as the distance from B to A, and
• the distance from A to B (directly) is less than or equal to the distance from A to B via any third point C, i.e., $d(A, B) ≤ d(A, C) + d(C, B)$.

#### 解法

1. 自己和自己的距离是否为0
2. $i$到$j$的距离是否等于$j$到$i$的距离
3. 原始的点的距离是否被改变