August 2017
Intermediate to advanced
360 pages
8h 35m
Chinese
Content preview from 算法技术手册（原书第2 版）
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268
｜
第
10
章
后的查询计算却会因此受益匪浅，因为查询搜索的复杂度变为了
O
(log
n
)
。但是，如果
搜索的量很小，那么使用
O
(
n
)
的穷举法会更好。
10.2 范围查询
与搜索某个特定的目标点不同，范围查询可能要求查询
P
中的所有点是否位于二维平面
上的某个指定矩形区域内。可以用穷举解法来检查每个点是否位于指定的矩形区域内，
因此它的性能是
O
(
n
)
。
最近邻查询中使用的数据结构同样能够支持上述这些查询。这些查询也被称为“正交范
围查询”，因为矩形查询区域对应于平面的
x
轴和
y
轴。要想获得比
O
(
n
)
更好的性能，
我们需要找到这样一种方法——既能够尽量排除不是解的点以减少查询空间，同时也需
要能够高效地将点加入查询结果中，所以我们会考虑使用
k
-
d
树。在
k
-
d
树中，查询会
以递归遍历的形式执行，其性能可达
O
(
n
0.5
+
r
)
，其中
r
是查询结果中点的数量。
10.3 交集查询
有些情况下，待查找的元素远比单个
n
维数据点要复杂得多。这里不妨假设待查找的元
素是一个二维平面的矩形集合
R
，其中每个矩形
r
i
由元组（
x
low
，
y
low
，
x
high
，
y
high
）定义。
在给定集合
R
的情况下，要求寻找包含给定点（
x
，
y
）的所有矩形，或者（更广泛地）
找到与目标矩形（
x
1
，
y
1
，
x
2
，
y
2
）相交的所有矩形。
在没有目标矩形的情况下，我们也许会对二维元素集合的交集感兴趣。这个问题也被称
为
碰撞检测
问题。接下来，我们将介绍一种解决方案，来找到以点集
P
中每个点为中心
的正方形区域的交集。
10.4 空间树
空间树可以合理地表述数据以高效地支持搜索、插入和删除 ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.