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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68
｜
第
4
章
可以看到最开始的时候，非递归实现因消除了堆排序中的递归而使性能得到显著提升，
但是这种性能差别随着
n
的不断增加有所减少。
4.5 基于分区的排序算法
分治策略解决问题的方法是将问题分解成两个大小约为原问题一半的独立子问题。将这
种策略应用到排序算法中的过程如下：找出集合
A
中的
中位数
，将其与数组
A
中间位置
的数交换。接着，将左半部分比
A
[
mid
]
大的元素与右半部分小于等于
A
[
mid
]
的元素进
行交换。这样，原数组就被切分成两个完全分开的子数组，这样就可以通过递归地对它
们进行排序来完成对原始集合
A
的排序。
这种方法的实现极具挑战性，因为要在不排序的前提下找出集合的中位数并不那么显而
易见。事实表明，可以使用
A
中的任意元素将
A
切分成两个子数组，如果每次都能“聪明地”
挑选元素，就能使得子数组或多或少地具有相同的大小，从而获得更高效的算法实现。
假定存在函数
p
=
partition
(
A
,
left
,
right
,
pivotIndex
) ,
它使用集合
A
中的一个特殊中枢值
pivot
来对
A
进行修改，并返回
A
中的位置
p
，满足：
•
A
[
p
] =
pivot
。
•
A
[
left
,
p
)
范围内的所有元素都小于等于中枢值
pivot
。
•
A
[
p
+ 1,
right
]
范围内的所有元素都大于中枢值
pivot
。
如果足够幸运，当
分区
完成后，两个子数组的大小会约等于原始集合的一半。例
4-5
给
出了分区的
C
语言实现。
例
4-5
：将
ar[left,right]
针对给定中枢值元素进行分区的
C
语言实现
/**
*
在线性时间内，将数组 ...
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