在 http://en.wikipedia.org/wiki/Closest_pair_of_points_problem 我们可以看到，它提到是至多6个点中最接近上的另一半的点，这可以被重新psented如下的图表$ P $：

In http://en.wikipedia.org/wiki/Closest_pair_of_points_problem we can see that it mentions that is at most 6 points that is closest to the point on the other half, which can be represented as the graph below:

我的问题是点P1和P2点，以红点的距离将超过的sqrt（2）* D，为什么它是解决方案的一部分？为什么它不是至多4个点是最接近至P而非至多6个点？谢谢你。

My question is for point P1 and Point P2, the distance to the red point will exceed sqrt(2)*d, why it is part of the solution? Why it is not at most 4 points that is closest to P rather than at most 6 points? Thanks.

推荐答案

P1 和 P2 的不是解决方案的一部分，但他们必须进行检查的方式到该溶液中，因为该算法检查所有分的盒子，并 P1 的和的 P2 的是，在框中

P1 and P2 are not part of the solution, but they have to be examined on the way to the solution, because the algorithm examines all points in the box, and P1 and P2 are in the box.

请注意，没有这样的点作为问：的可以存在的，因为通过设定点之间的最小距离在右侧的图的一半是ð的

Note that no such point as your Q can exist, because by hypothesis the minimum distance between points in the right-hand half of the diagram is d.

编辑补充：您似乎认为，维基百科的文章作出这样的要求：

Edited to add: you seem to think that the Wikipedia article is making a claim like this:

在可能有多达6点右侧是 P 的距离的ð的范围内，该行的。 There may be up to 6 points on the right side of the line that are within a distance d of P.

这种说法是错误的。但文章并没有提出这样的要求。相反，它使两个独立的权利要求，这两者都为真：

This claim would be false. But the article does not make such a claim. Instead, it makes two separate claims, both of which are true:

所有右侧的行是一个距离的ð的范围内的点的 P 的是箱内。 可以有多达6个点中的框。 All the points on the right side of the line that are within a distance d of P are inside the box. There may be up to 6 points in the box.