基于比较的三种排序算法：插入排序、合并排序和快排序

“递归法”之后我们继续探索算法的奥秘。今天慕寒将引领大家走进“基于比较的排序”的世界重点介绍三种方法插入排序、合并排序以及快排序。排序这一看似简单的操作实则蕴含着深奥的学问。在数据处理中它扮演着至关重要的角色能够使数据按照特定规则有序排列从而为我们的分析和决策提供有力支持。011.排序算法综述插入排序通过逆序遍历数组将每个元素插入到正确位置实现有序排列。这种排序方式的基本思想是将一个元素插入到它所属的正确位置。具体来说就是将数组中的某个元素与前面的元素逐一比较找到它的合适位置并插入。这个过程需要逆序遍历数组并与每个元素进行比较和移动直至找到合适的位置。当然在实际操作中还需要考虑一些特殊情况比如数组中只有一个元素时的情况以及新插入元素与前一个元素大小关系等。合并和快排序都是基于分治策略的比较排序算法各有独特的实现方法。接下来我们还将探讨合并排序和快排序这两种方法。这两种排序算法同样基于比较的思想但实现方式各有不同。合并排序通过递归分治的方式将大问题拆解为小问题逐步合并解决而快排序则利用了分区的思想通过一个基准值将数组分为两部分分别进行排序。这些算法各有千秋在实际应用中可以根据需求选择适合的方法。通过今天的介绍希望大家能对“基于比较的排序”有更深入的了解并能灵活运用这些算法解决实际问题。022.插入排序的实现细节2.1 ◆ 插入排序步骤在插入排序中插入排序步骤包括逆序比较及元素插入需要处理数组特殊情形。具体步骤为首先如果self.oriList已排序则直接赋值给self.sortedList。否则我们需要初始化一个空列表sortedList。然后使用for循环遍历self.oriList中的每个元素每次从oriList中取出一个元素并与sortedList中的元素逐一比较。若取出的元素小于sortedList中的所有元素则将其直接添加到sortedList的开头。若取出的元素大于等于sortedList中的部分元素则找到合适的位置插入该元素以确保sortedList仍然保持有序。重复这些步骤直到oriList中的所有元素都被处理完毕。这一步骤涉及逆序遍历和元素插入确保每个元素都能找到其正确的位置。2.2 ◆ 算法复杂度分析在算法复杂度分析中插入排序在最佳情况下的复杂度为O(n)而在最坏情况下的复杂度为O(n²)。在最好情况下比如当输入数组已经有序时我们只需进行一次比较就能确定待插入元素的位置而耗时主要在于插入后的元素位置调整。而在最坏情况下即数组是逆向的每个元素都需要与所有前边的元素进行比较导致复杂度上升到O(n²)。033.合并排序的实现细节3.1 ◆ 分治策略概述合并排序通过“递归法”或“分治法”实现其基本思想是在每一步都将问题拆解为小问题逐层解决后再逐步合并。这种方法能有效提高处理大型数据集时的效率因为它充分利用了递归和分治的思想来优化排序过程。3.2 ◆ 合并排序步骤合并排序的步骤包括分解子数组及有序合并实现数组的有序排列。具体来说分解步骤中我们不断地将原始数组一分为二直到子数组的长度为1。然后在合并步骤中我们将这些已排序的子数组逐步合并以形成最终的有序数组。这种方法确保了从分解到合并的整个过程中数组始终有序。https://ds.163.com/feed/69e0f19a4a435f691273c200/https://ds.163.com/feed/69e0f19a7ca8aa087d004243/https://ds.163.com/feed/69e0f19aca8a0e60d7275fed/https://ds.163.com/feed/69e0f19a2286db49ab03279d/https://ds.163.com/feed/69e0f19ae597710e17194d7b/https://ds.163.com/feed/69e0f1994a420d35118c2e16/https://ds.163.com/feed/69e0f1994a420d35118c2e14/https://ds.163.com/feed/69e0f199d0179a447689bee7/https://ds.163.com/feed/69e0f199d0179a447689bee3/https://ds.163.com/feed/69e0f19979904e31ef571de1/https://ds.163.com/feed/69e0f19842d7e97707f46ed0/https://ds.163.com/feed/69e0f198e597710e17194d77/https://ds.163.com/feed/69e0f1988d4c6a771f19b8e2/https://ds.163.com/feed/69e0f19842d7e97707f46ece/https://ds.163.com/feed/69e0f1981724632a43d94e1f/https://ds.163.com/feed/69e0f198ca8a0e60d7275fe7/https://ds.163.com/feed/69e0f1984a003b446920e454/https://ds.163.com/feed/69e0f198ca8a0e60d7275fe5/https://ds.163.com/feed/69e0f198fdfff55ed37f09de/https://ds.163.com/feed/69e0f197f31000606c0d1f39/https://ds.163.com/feed/69e0f197f89d686a58105972/https://ds.163.com/feed/69e0f197d0179a447689bed9/https://ds.163.com/feed/69e0f1971724632a43d94e1b/https://ds.163.com/feed/69e0f196f31000606c0d1f37/https://ds.163.com/feed/69e0f196fdfff55ed37f09da/https://ds.163.com/feed/69e0f1964a003b446920e44f/https://ds.163.com/feed/69e0f196fdfff55ed37f09d8/https://ds.163.com/feed/69e0f1968d4c6a771f19b8db/https://ds.163.com/feed/69e0f1962be1015603d4666f/https://ds.163.com/feed/69e0f1967ca8aa087d00423a/https://ds.163.com/feed/69e0f1968d4c6a771f19b8d7/https://ds.163.com/feed/69e0f1957ca8aa087d004238/https://ds.163.com/feed/69e0f1952be1015603d4666d/https://ds.163.com/feed/69e0f1958d4c6a771f19b8d3/https://ds.163.com/feed/69e0f0f7f89d686a581057dc/https://ds.163.com/feed/69e0f0f7c43fe47022d5400a/https://ds.163.com/feed/69e0f0f74a420d35118c2c5e/https://ds.163.com/feed/69e0f0f62be1015603d464c0/https://ds.163.com/feed/69e0f0f6f89d686a581057d8/https://ds.163.com/feed/69e0f0f6d0179a447689bd52/https://ds.163.com/feed/69e0f0f6d0179a447689bd50/https://ds.163.com/feed/69e0f0f5ca8a0e60d7275e68/https://ds.163.com/feed/69e0f0f5c43fe47022d54006/https://ds.163.com/feed/69e0f0f41e361d5c4cd2aeb2/https://ds.163.com/feed/69e0f0f4f89d686a581057cd/https://ds.163.com/feed/69e0f0f479904e31ef571c56/https://ds.163.com/feed/69e0f0f486b73875ebd22409/https://ds.163.com/feed/69e0f0f479904e31ef571c54/https://ds.163.com/feed/69e0f0f411391930e91a4726/https://ds.163.com/feed/69e0f0f4fdfff55ed37f0834/https://ds.163.com/feed/69e0f0f4fdfff55ed37f082f/https://ds.163.com/feed/69e0f0f42286db49ab0325f8/https://ds.163.com/feed/69e0f0f379904e31ef571c52/https://ds.163.com/feed/69e0f0f3f89d686a581057c6/https://ds.163.com/feed/69e0f0f37ca8aa087d004099/https://ds.163.com/feed/69e0f0f279904e31ef571c4c/https://ds.163.com/feed/69e0f0f211391930e91a4721/https://ds.163.com/feed/69e0f0f27ca8aa087d004093/https://ds.163.com/feed/69e0f0f24a420d35118c2c49/https://ds.163.com/feed/69e0f0f24a003b446920e284/https://ds.163.com/feed/69e0f0f24a435f691273c02c/https://ds.163.com/feed/69e0f0f1fdfff55ed37f0829/https://ds.163.com/feed/69e0f0f14a435f691273c029/https://ds.163.com/feed/69e0f0f142d7e97707f46d01/https://ds.163.com/feed/69e0f0f1ca8a0e60d7275e58/https://ds.163.com/feed/69e0f0f1f89d686a581057b7/https://ds.163.com/feed/69e0f0f14a003b446920e281/https://ds.163.com/feed/69e0efca89492f4215a5e552/https://ds.163.com/feed/69e0efca8d4c6a771f19b485/https://ds.163.com/feed/69e0efca89492f4215a5e54e/https://ds.163.com/feed/69e0efcaca8a0e60d7275b72/https://ds.163.com/feed/69e0efc9c43fe47022d53d10/https://ds.163.com/feed/69e0efc94a701e2c775a0b6d/https://ds.163.com/feed/69e0efc92be1015603d461ce/https://ds.163.com/feed/69e0efc842d7e97707f46a3a/https://ds.163.com/feed/69e0efc886b73875ebd22106/https://ds.163.com/feed/69e0efc886b73875ebd22104/https://ds.163.com/feed/69e0efc811391930e91a4450/https://ds.163.com/feed/69e0efc72286db49ab032329/https://ds.163.com/feed/69e0efc742d7e97707f46a38/https://ds.163.com/feed/69e0efc779904e31ef571996/https://ds.163.com/feed/69e0efc72be1015603d461c9/https://ds.163.com/feed/69e0efc789492f4215a5e546/https://ds.163.com/feed/69e0efc7c43fe47022d53d02/https://ds.163.com/feed/69e0efc74a701e2c775a0b64/https://ds.163.com/feed/69e0efc72be1015603d461c7/https://ds.163.com/feed/69e0efc6c43fe47022d53cfe/https://ds.163.com/feed/69e0efc642d7e97707f46a34/https://ds.163.com/feed/69e0efc679904e31ef57198c/https://ds.163.com/feed/69e0efc6c43fe47022d53cfa/https://ds.163.com/feed/69e0efc5e597710e171948d3/https://ds.163.com/feed/69e0efc579904e31ef57198a/https://ds.163.com/feed/69e0efc52be1015603d461c0/https://ds.163.com/feed/69e0efc5f89d686a581054ab/https://ds.163.com/feed/69e0efc5f89d686a581054a9/https://ds.163.com/feed/69e0efc52286db49ab032325/https://ds.163.com/feed/69e0efc54a435f691273bd73/https://ds.163.com/feed/69e0efc589492f4215a5e53c/https://ds.163.com/feed/69e0efc54a435f691273bd70/https://ds.163.com/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