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Kim Yang
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# 栈
![image-20200624150012426](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010108.jpg)
## 栈的定义
![image-20200624150149844](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010114.jpg)
![image-20200624150313680](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010121.jpg)
![image-20200624150459308](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010127.jpg)
## 栈的基本操作
![image-20200624150704360](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010132.jpg)
### 出栈顺序
![image-20200624150927909](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010138.jpg)
## 总结
![image-20200624151001874](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010144.jpg)

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# 顺序栈
![image-20200624151201362](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010154.jpg)
## 顺序栈的定义
![image-20200624151329974](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010159.jpg)
## 基本操作
### 初始化操作
![image-20200624151413408](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010206.jpg)
### 进栈操作
![image-20200624151826628](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010237.jpg)
### 出栈操作
![image-20200624152110685](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010246.jpg)
### 读取栈顶元素
![image-20200624152208184](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010251.jpg)
## 另一种基本操作的实现方式:
![image-20200624152341443](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010257.jpg)
![image-20200624152540477](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010304.jpg)
## 共享栈
![image-20200624152655905](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010311.jpg)
## 总结
![image-20200624152849214](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010316.jpg)

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# 链栈
![image-20200624153019827](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010327.jpg)
## 复习单链表
![image-20200624153122502](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010335.jpg)
![image-20200624153252888](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010340.jpg)
## 链栈的定义
![image-20200624153433781](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010345.jpg)
## 总结
![image-20200624153535956](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010350.jpg)

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# 队列
![image-20200624153725089](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010403.jpg)
## 队列的定义
![image-20200624153857510](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010411.jpg)
![image-20200624154000138](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010429.jpg)
![image-20200624154121849](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010439.jpg)
## 队列的基本操作
![image-20200624154224115](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010446.jpg)
## 总结
![image-20200624154248823](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010452.jpg)

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# 顺序队列
![image-20200624154351327](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010502.jpg)
## 顺序队列的定义
![image-20200624154511213](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010511.jpg)
### 顺序队列的初始化
![image-20200624154606843](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010516.jpg)
### 入队操作
![image-20200624155112673](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010521.jpg)
![image-20200624155125271](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010527.jpg)
### 循环队列
![image-20200624155155915](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010537.jpg)
![image-20200624155216098](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010542.jpg)
### 出队
![image-20200624155258305](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010547.jpg)
### 判空/判满
方案一:牺牲一个存储空间
![image-20200624155343663](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010552.jpg)
方案二利用size变量记录队列长度
![image-20200624155414159](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010559.jpg)
方案三利用tag记录最后一次操作
![image-20200624155619066](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010605.jpg)
## 其它实现方式
![image-20200624155808035](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010616.jpg)
![image-20200624155827353](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010620.jpg)
![image-20200624155906039](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010625.jpg)
## 总结
![image-20200624160059508](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010648.jpg)

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# 链队列
![image-20200624160150945](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010936.jpg)
## 链队列的定义
![image-20200624160334221](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010945.jpg)
## 链队列的基本操作
### 链队列的初始化
![image-20200624160434942](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010950.jpg)
### 入队
带头节点
![image-20200624160602691](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810010955.jpg)
不带头节点
![image-20200624160710140](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011000.jpg)
### 出队
带有头节点
![image-20200624160905141](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011005.jpg)
不带头节点
![image-20200624160952329](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011010.jpg)
### 判满
![image-20200624161057518](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011016.jpg)
## 总结
![image-20200624161134905](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011021.jpg)

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# 双端队列
![image-20200624161331529](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011030.jpg)
## 双端队列的定义
![image-20200624161416772](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011037.jpg)
## 考点:判断输出序列的合法性
### 对于栈的输出序列的合法性
![image-20200624161642449](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011052.jpg)
绿色为合法,红色为非法
### 对于输入受限的双端队列的输出序列的合法性
![image-20200624162025565](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011057.jpg)
绿色为合法,红色为非法,带下划线是在栈中不合法,但在输入受限的双端队列中合法的。
### 对于输出受限的双端队列
![image-20200624162509184](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011102.jpg)
绿色为合法,红色为非法,带下划线是在栈中不合法,但在输出受限的双端队列中合法
这种输出受限的双端队列,看序号较大的元素输出的位置,这意味着,在它输出之前,比它小的元素的相对位置是确定的,接下来就是考虑有什么插入的方法能实现这种相对位置关系!
## 总结
## ![image-20200624162951819](https://tva1.sinaimg.cn/large/007S8ZIlly1gg3gmivt6mj30xv09ddla.jpg)

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# 栈的应用
## 括号匹配问题
![image-20200624163218954](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011113.jpg)
### 实际过程
![image-20200624163415891](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011118.jpg)
####正好匹配
![image-20200624163523560](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011122.jpg)
####左右不匹配
![image-20200624163548297](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011127.jpg)
#### 右括号单身
![image-20200624163638571](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011130.jpg)
#### 左括号单身
![image-20200624163721992](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011135.jpg)
#### 整个流程
![image-20200624163928215](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011139.jpg)
### 算法实现
![image-20200624164327998](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011144.jpg)
### 总结
![image-20200624164420239](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011149.jpg)
## 表达式求值
![image-20200624164751528](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011154.jpg)
### 算数表达式是什么?
由三个部分组成(操作数,运算符,界限符)
![image-20200624165021200](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011203.jpg)
### 前/后缀表达式的诞生
![image-20200624165107095](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011211.jpg)
### 中/后/前缀表达式的区别
![image-20200624165500339](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011216.jpg)
#### 中转后的过程:
![image-20200624165755963](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011221.jpg)
**上图中,后缀表达式的算术符的先后次序对应中缀表达式的生效的先后次序**,但是这是一定的吗?
![image-20200624170300224](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011225.jpg)
左优先原则,可保证运算顺序唯一性,以确定机算算法输出结果的唯一性!!
![image-20200624190745666](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011717.jpg)
#### 机算算法实现
![image-20200624191112704](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011725.jpg)
![image-20200624191355054](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011729.jpg)
### 中转前的过程
![image-20200624191538706](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011737.jpg)
中转后和中转前的区别:
![image-20200624191614443](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011742.jpg)
#### 中转前的机算过程:
![image-20200624191810971](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011746.jpg)
### 总结
![image-20200624191919379](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011751.jpg)
"左优先"/“右优先”原则和左/右操作数不是专业说法,仅供理解!
## 表达式求值——具体代码实现
![image-20200624192258712](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011755.jpg)
### 中转后机算
手算过程:
![image-20200624192506786](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011759.jpg)
机算过程:
![image-20200624193355396](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011804.jpg)
### 中缀表达式的计算
![image-20200624193844266](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011809.jpg)
![image-20200624194515343](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011813.jpg)
CPU只能执行单个的加减乘除运算上边这么搞的意义就是为了将高级程序语言编译成简单的机器码让CPU去执行
### 总结
![image-20200624194707110](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011820.jpg)
## 栈在递归中的应用
递归的过程就是函数调用的过程
![image-20200624195132597](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011839.jpg)
![image-20200624195412187](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011847.jpg)
### 适合用“递归”算法解决的问题
![image-20200624195452395](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011853.jpg)
求阶乘:
![image-20200624195709306](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011857.jpg)
**使用递归时,需要注意调用栈溢出!**
![image-20200624200031925](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011902.jpg)
**可以自定义栈将递归算法改造成非递归算法!**
求斐波那契数列
![image-20200624200155981](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011906.jpg)
### 总结
![image-20200624200214150](https://tva1.sinaimg.cn/large/007S8ZIlly1gg3mrhq6wnj30mq0adtbj.jpg)

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# 队列的应用
## 树的层次遍历
提示:不知道树这种数据结构的同学,可以考虑先跳过本文内容,等了解树之后,再来康康~
![image-20200624200711109](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011917.jpg)
详细实现内容在树的章节实现!
## 图的广度优先遍历
遍历是指找出所有元素节点
![image-20200624200822823](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011940.jpg)
## 队列在操作系统中的应用
**CPU资源分配问题**
![image-20200624200936738](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011944.jpg)
**打印数据缓冲区**
![image-20200624201203709](https://cdn.jsdelivr.net/gh/KimYangOfCat/MyPicStorage/2021-CSPostgraduate-408/20200810011949.jpg)