From 0f865d2727fed06f60c32384b49f316d6cbdf756 Mon Sep 17 00:00:00 2001 From: krahets Date: Mon, 29 Jul 2024 21:16:16 +0800 Subject: [PATCH] Update the definition of "adaptive sorting". --- docs/chapter_sorting/bucket_sort.md | 3 +-- docs/chapter_sorting/quick_sort.md | 2 +- docs/chapter_sorting/sorting_algorithm.md | 6 ++---- .../sorting_algorithms_comparison.png | Bin 59466 -> 59701 bytes docs/chapter_sorting/summary.md | 2 +- .../sorting_algorithms_comparison.png | Bin 62191 -> 59613 bytes .../sorting_algorithms_comparison.png | Bin 64579 -> 62391 bytes 7 files changed, 5 insertions(+), 8 deletions(-) diff --git a/docs/chapter_sorting/bucket_sort.md b/docs/chapter_sorting/bucket_sort.md index 5f361b16c..84b7f08d0 100644 --- a/docs/chapter_sorting/bucket_sort.md +++ b/docs/chapter_sorting/bucket_sort.md @@ -24,8 +24,7 @@ 桶排序适用于处理体量很大的数据。例如,输入数据包含 100 万个元素,由于空间限制,系统内存无法一次性加载所有数据。此时,可以将数据分成 1000 个桶,然后分别对每个桶进行排序,最后将结果合并。 -- **时间复杂度为 $O(n + k)$** :假设元素在各个桶内平均分布,那么每个桶内的元素数量为 $\frac{n}{k}$ 。假设排序单个桶使用 $O(\frac{n}{k} \log\frac{n}{k})$ 时间,则排序所有桶使用 $O(n \log\frac{n}{k})$ 时间。**当桶数量 $k$ 比较大时,时间复杂度则趋向于 $O(n)$** 。合并结果时需要遍历所有桶和元素,花费 $O(n + k)$ 时间。 -- **自适应排序**:在最差情况下,所有数据被分配到一个桶中,且排序该桶使用 $O(n^2)$ 时间。 +- **时间复杂度为 $O(n + k)$** :假设元素在各个桶内平均分布,那么每个桶内的元素数量为 $\frac{n}{k}$ 。假设排序单个桶使用 $O(\frac{n}{k} \log\frac{n}{k})$ 时间,则排序所有桶使用 $O(n \log\frac{n}{k})$ 时间。**当桶数量 $k$ 比较大时,时间复杂度则趋向于 $O(n)$** 。合并结果时需要遍历所有桶和元素,花费 $O(n + k)$ 时间。在最差情况下,所有数据被分配到一个桶中,且排序该桶使用 $O(n^2)$ 时间。 - **空间复杂度为 $O(n + k)$、非原地排序**:需要借助 $k$ 个桶和总共 $n$ 个元素的额外空间。 - 桶排序是否稳定取决于排序桶内元素的算法是否稳定。 diff --git a/docs/chapter_sorting/quick_sort.md b/docs/chapter_sorting/quick_sort.md index 60dccec92..96be54bac 100755 --- a/docs/chapter_sorting/quick_sort.md +++ b/docs/chapter_sorting/quick_sort.md @@ -61,7 +61,7 @@ ## 算法特性 -- **时间复杂度为 $O(n \log n)$、自适应排序**:在平均情况下,哨兵划分的递归层数为 $\log n$ ,每层中的总循环数为 $n$ ,总体使用 $O(n \log n)$ 时间。在最差情况下,每轮哨兵划分操作都将长度为 $n$ 的数组划分为长度为 $0$ 和 $n - 1$ 的两个子数组,此时递归层数达到 $n$ ,每层中的循环数为 $n$ ,总体使用 $O(n^2)$ 时间。 +- **时间复杂度为 $O(n \log n)$、非自适应排序**:在平均情况下,哨兵划分的递归层数为 $\log n$ ,每层中的总循环数为 $n$ ,总体使用 $O(n \log n)$ 时间。在最差情况下,每轮哨兵划分操作都将长度为 $n$ 的数组划分为长度为 $0$ 和 $n - 1$ 的两个子数组,此时递归层数达到 $n$ ,每层中的循环数为 $n$ ,总体使用 $O(n^2)$ 时间。 - **空间复杂度为 $O(n)$、原地排序**:在输入数组完全倒序的情况下,达到最差递归深度 $n$ ,使用 $O(n)$ 栈帧空间。排序操作是在原数组上进行的,未借助额外数组。 - **非稳定排序**:在哨兵划分的最后一步,基准数可能会被交换至相等元素的右侧。 diff --git a/docs/chapter_sorting/sorting_algorithm.md b/docs/chapter_sorting/sorting_algorithm.md index 88ca9f628..ded41fd5a 100644 --- a/docs/chapter_sorting/sorting_algorithm.md +++ b/docs/chapter_sorting/sorting_algorithm.md @@ -35,14 +35,12 @@ ('E', 23) ``` -**自适应性**:自适应排序的时间复杂度会受输入数据的影响,即最佳时间复杂度、最差时间复杂度、平均时间复杂度并不完全相等。 - -自适应性需要根据具体情况来评估。如果最差时间复杂度差于平均时间复杂度,说明排序算法在某些数据下性能可能劣化,因此被视为负面属性;而如果最佳时间复杂度优于平均时间复杂度,则被视为正面属性。 +**自适应性**:自适应排序能够利用输入数据已有的顺序信息来减少计算量,达到更优的时间效率。自适应排序算法的最佳时间复杂度通常优于平均时间复杂度。 **是否基于比较**:基于比较的排序依赖比较运算符($<$、$=$、$>$)来判断元素的相对顺序,从而排序整个数组,理论最优时间复杂度为 $O(n \log n)$ 。而非比较排序不使用比较运算符,时间复杂度可达 $O(n)$ ,但其通用性相对较差。 ## 理想排序算法 -**运行快、原地、稳定、正向自适应、通用性好**。显然,迄今为止尚未发现兼具以上所有特性的排序算法。因此,在选择排序算法时,需要根据具体的数据特点和问题需求来决定。 +**运行快、原地、稳定、自适应、通用性好**。显然,迄今为止尚未发现兼具以上所有特性的排序算法。因此,在选择排序算法时,需要根据具体的数据特点和问题需求来决定。 接下来,我们将共同学习各种排序算法,并基于上述评价维度对各个排序算法的优缺点进行分析。 diff --git a/docs/chapter_sorting/summary.assets/sorting_algorithms_comparison.png b/docs/chapter_sorting/summary.assets/sorting_algorithms_comparison.png index 6a6559d0886745eca4030469a5e25519f3f3f77b..832dfb4dd09bb3d754880350155a537d8c612342 100644 GIT binary patch literal 59701 zcmdSARa_iF*EiTRgS)$h0KtQY1P>Nmf+on|7J|DCkl-5JU4pv@26qo`LvRZkJh0?> z-u=GsVt;$L7u$6)Q`LRy$p4&E-6f%_%CguP6c_*iV9ULeQU?I!r@!C{G|1D>bsmT5 zQ)O3GQA7Ii@p1cf``6CR!qJ_OkWgr7=-Aj;Mn=Y`PoG+QS|ubTViRK}C8fl~#m~;p zL_|a)A|lMpt<5dXqhnL=?(Sq{WiKx;|Ni|eEiElCuW)^ReSCbZp{cRHzOJaKxPG|a z(a~XSVY9HXuz9@M)z#J1He_jInVgyYPEJnkz2@B9+}g&U=+vB_t3Qh?i}UjGtgNis z+S>a1`r_i^dU|@))zzn_ro!UWEG%s`bw3)L7{|uOR#sLH3=C*#YZa9=Y;SKnxOf#6 z73t~g>FDU>d zii(Pkj_#UX>mKR${}S%$>uK}Z=I73Zy@S1;p>bN~_n$w1R(A}2%P4Sia!N@_Nk~gD 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