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考研笔记-计算机之数据结构:基础概览

  • 2026-05-08 13:33:33
考研笔记-计算机之数据结构:基础概览
——如阅读体验不佳,可转为横屏阅读;如微信无法横屏,可尝试文末方法。
基本概念

逻辑:数据数据对象数据元素数据项。

物理:结点∋ 数据域。

数据结构(逻辑):集合、线性结构(表)、层次结构(树)、网状结构(图);

存储结构(物理):顺序存储结构(数组)、链式存储结构(链表)(数组和链表均是使用指针实现的)。

数据结构≔ 数据(数据元素的有限集)+结构(数据关系的有限集)。

数据类型≔ 值的集合一组操作。

数据类型 =原子类型 +结构类型(原子类型也可看作特殊的结构类型)。

原子类型≔ 原子结构一组操作。

结构类型≔ 数据结构一组操作。

抽象数据类型≔ 数据类型的数学抽象。

抽象数据类型 =原子类型(固有数据类型)结构类型(固定聚合类型可变聚合类型)多形数据类型。

抽象数据类型≔ 数据结构(数据对象关系集)基本操作。

ADT 抽象数据类型名{

数据对象;

数据关系:有序对<,>

基本操作;

}ADT抽象数据类型名

递归函数

递归函数:一个直接调用自己或通过一系列的调用语句间接调用自己的函数,称为递归函数

和第二数学归纳法类似,递归定义由基本项归纳项两部分组成。

基本项:递归定义的基本项描述了一个或几个递归过程的终结状态。所谓终结状态是指不需要继续递归而可直接求解的状态。

归纳项:递归定义的归纳项描述了如何实现从当前状态到终结状态的转化。

递归设计的实质:当一个复杂的问题可以分解成若干子问题来处理时,其中某些子问题与原问题有相同的特征属性,则可利用和原问题相同的分析处理方法;反之,这些子问题解决了,原问题也就迎刃而解了。递归定义的归纳项就是描述这种原问题和子问题之间的转化关系。

设计递归函数时应注意的问题:由于递归函数的设计用的是归纳思维的方法,则在设计递归函数时应注意:①首先应书写函数的首部和规格说明,严格定义函数的功能和接口(递归调用的界面),对求解函数中所得的和原问题性质相同的子问题,只要接口一致,便可进行递归调用;②对函数中的每一个递归调用都看成只是一个简单的操作,只要接口一致,必能实现规格说明中定义的功能,切忌想得太远太深。正如用第二数学归纳法证明命题时,由归纳假设进行归纳证明时决不能怀疑归纳假设是否正确。

递归函数的定义中必有两个函数的退出(递归返回)点:①最内(底)层递归调用的返回点,即满足基本项成立条件;②中间层(除最内层)递归调用的返回点,即实现归纳项转换关系。

递归算法和非递归算法的转化

在实现同样功能的前提下,任何递归算法都可借助栈转为非递归算法,但不是所有的非递归算法都可转为递归算法。

基本结构

结构

定义

表示

实现

线性结构—表

(一对一的关系)

线性表

顺序存储

顺序表(SqList

链式存储

静态链表(SLinkList

线性链表LLinkList

循环链表CLinkList

双向链表DLinkList

顺序存储

顺序栈SqStack

链式存储

链栈(LinkStack

队列

顺序存储

循环队列(SqQueue

链式存储

链队列(LinkQueue

层次结构—树

(一对多的关系)

二叉树

顺序存储

完全二叉树(SqBiTree

链式存储

二叉链表TwLinkBiTree

三叉链表(ThLinkBiTree

线索链表ThrLinkBiTree

顺序存储

双亲表示法(PTree

链式存储

孩子表示法CTree

孩子兄弟表示法(CSTree

转化(孩子兄弟表示)为对应的二叉树

森林

转化(孩子兄弟表示)为对应的二叉树

网状结构—图

(多对多的关系)

顶点结点

顺序存储

一维数组

/边结点

链式存储

邻接矩阵(有/无向图)(AMGraph

邻接表(有/无向图)(ALGraph

十字链表(有向图)(OLGraph

邻接多重表(无向图)(AMLGraph

集合结构—查找表

(同属于一个集合的关系)

静态查找表

顺序表

有序表

索引顺序表

动态查找表

二叉排序树

平衡二叉树

B-

B+

哈希表

——可选择【右上角···】→【在浏览器中打开】进行横屏阅读。

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  1. CONNECT:[ UseTime:0.000654s ] mysql:host=127.0.0.1;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000772s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.004231s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000329s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000652s ]
  6. SELECT * FROM `set` [ RunTime:0.000248s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000704s ]
  8. SELECT * FROM `article` WHERE `id` = 489703 LIMIT 1 [ RunTime:0.001756s ]
  9. UPDATE `article` SET `lasttime` = 1778228649 WHERE `id` = 489703 [ RunTime:0.004424s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.000265s ]
  11. SELECT * FROM `article` WHERE `id` < 489703 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000464s ]
  12. SELECT * FROM `article` WHERE `id` > 489703 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.002786s ]
  13. SELECT * FROM `article` WHERE `id` < 489703 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.003189s ]
  14. SELECT * FROM `article` WHERE `id` < 489703 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000951s ]
  15. SELECT * FROM `article` WHERE `id` < 489703 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.002195s ]
0.095652s