数据结构(三)--栈
数据结构(三)–栈
通常程序开发中内存管理是非常重要的,而内存主要分为占内存和堆内存。那么栈和堆内存有什么区别呢?希望在这篇文章里能带你找到答案!
1. 栈和堆的引入
在一个简单的程序中我们定义和声明几个基本类型的变量、结构体和数组,先来直观看一下栈和堆的不同:
- 静态变量 和 局部变量是以压栈出栈的方式分配内存的,系统会在一个代码段中分配和回收局部变量,实际上每个代码段、函数都是一个或多个嵌套的栈,我们不需要手动管理栈区内存。
- 动态内存是一种堆排序的方式分配内存的,内存分配好后便不会自动回收,需要程序员手动回收。否则就会造成内存泄漏,内存越用越少。
简单了解了一下程序中内存栈与堆的区别,下面就正式开始讲数据结构中的栈。
(注意:数据结构栈、内存栈、函数调用栈三者在含义上略有不同,但是其核心思想和理念是相同的)
2. 栈的定义
栈是一种“先进后出”的一种数据结构,有压栈出栈两种操作方式。如下图:
3. 栈的分类
栈主要分为两类:
- 静态栈
- 动态栈
【静态栈】
静态栈的核心是数组,类似于一个连续内存的数组,我们只能操作其栈顶元素。
【动态栈】
静态栈的核心是数组,类似于一个连续内存的数组,我们只能操作其栈顶节点。
4. 栈的算法
栈的算法主要是压栈和出栈两种操作的算法,下面我就用代码来实现一个简单的栈。
首先要明白以下思路:
- 栈操作的是一个一个节点
- 栈本身也是一种存储的数据结构
- 栈有
初始化
、压栈
、出栈
、判空
、遍历
、清空
等主要方法
4.1 栈的头文件定义
头文件定义如下:
typedef struct Node{ // 节点
int data;
struct Node *pNext;
}*PNODE,NODE;
typedef struct Stack{ // 栈
PNODE pTop;
PNODE pBottom;
}STACK,*PSTACK;
/**栈的初始化*/
void init(PSTACK);
/**压栈*/
void push(PSTACK,int);
/**出栈*/
int pop(PSTACK , int *);
/**遍历打印栈*/
void traverse(PSTACK);
/**是否为空栈*/
int isEmpty(PSTACK);
/**清空栈*/
void clearStack(PSTACK);
有了头文件定义,基本就确定了栈的使用结构和使用方式。下面是在主函数中对这个栈的创建和使用。
int main(void){
STACK stack; // 声明一个栈
init(&stack); // 初始化
// 压栈
push(&stack, 10);
push(&stack, 20);
push(&stack, 30);
push(&stack, 40);
push(&stack, 50);
traverse(&stack); // 遍历打印栈
int val;
int isPopSuccess = pop(&stack,&val);
if (isPopSuccess) {
printf("pop 的值为 %d\n",val);
}
traverse(&stack);
clearStack(&stack); // 清空栈
traverse(&stack);
return 0;
}
4.2 栈的初始化
思路:
拿到栈声明的指针,开辟一块内存空间给栈顶栈底,此时是一个空栈,栈顶栈底指向同一块内存,且栈底栈顶以外不再指向其他节点。
/**栈的初始化*/
void init(PSTACK pS){
pS->pTop = (PNODE)malloc(sizeof(NODE));
if (pS->pTop == NULL) {
printf("内存分配失败退出");
return;
}else
{
pS->pBottom = pS->pTop;
pS->pTop->pNext = NULL;
}
}
4.3 压栈 和 出栈
思路:
压栈是把新的节点放入栈顶,且每次压栈操作只能将新的节点放到栈的顶部。
出栈需判断是否原本为空栈,存在出栈失败的情况,把栈顶指向栈顶元素的下一个元素,并释放原来栈顶元素空间。
/**
压栈
@param pS 执行压栈的栈指针
@param val 被压栈的值
*/
void push(PSTACK pS,int val){
// 创建新节点,放到栈顶
PNODE pNew = (PNODE)malloc(sizeof(NODE));
pNew->data = val;
pNew->pNext = pS->pTop;
pS->pTop = pNew; // 栈顶指针指向新元素
}
/**
出栈
@param pS 执行出栈的栈地址
@param val 出栈值的地址
@return 是否出栈成功
*/
int pop(PSTACK pS , int *val){
if (isEmpty(pS)) {
printf(" 空栈 ,出栈失败");
return 0;
}else
{
PNODE p = pS->pTop;
pS->pTop = p->pNext;
if (val != NULL) {
*val = p->data;
}
free(p); // 释放原来top内存
p = NULL;
return 1;
}
}
/**是否为空栈*/
int isEmpty(PSTACK pS)
{
if (pS->pTop == pS->pBottom) {
return 1;
}else
{
return 0;
}
}
4.4 栈的清空 和 遍历
当一个代码段执行完成之后,实际上就是这个栈所有分配的空间都被回收,栈随之被清空!
思路:
栈清空,实际就是需要循环执行出栈操作。
栈遍历,实际就是栈元素从栈顶一个个遍历到栈底,可以打印栈中元素的值
/**清空栈*/
void clearStack(PSTACK pS){
if (isEmpty(pS)) {
return;
}else{
PNODE p = pS->pTop;
PNODE q = NULL;
while (p!=pS->pBottom) {
q = p->pNext;
free(p); // 释放原栈顶元素空间
p = q;
}
pS->pTop = pS->pBottom;
}
// 偷懒的做法
// while (!isEmpty(pS)) {
// pop(pS, NULL);
// }
}
/**遍历打印栈*/
void traverse(PSTACK pS){
// 只要不是空栈,就一直输出
PNODE p = pS->pTop;
while (p != pS->pBottom) {
printf("%d ",p->data);
p = p->pNext; // 把top的下一个节点付给top,继续遍历
}
printf("\n");
}
5. 栈的应用
栈结构固有的先进后出的特性,使它成为在程序设计中非常有用的工具,这里列举几个典型的例子。
5.1 数制转换
十进制数 N 和其他 d 进制数的转换是计算机实现计算的基本问题,其解决方法有很多种,其中一个简单的方法基于如下原理:N = (N div d) * d + N mod d
(其中div是整除运算,mod 为求余运算)
例如:1348(10进制) == 2504(8进制)运算过程如下:
N | N div 8 | N mod 8 |
---|---|---|
1348 | 168 | 4 |
168 | 21 | 0 |
21 | 2 | 5 |
2 | 0 | 2 |
需求:输入一个任意非负十进制整数,打印输出其对应的八进制整数
思路:由于上述计算过程是从低到高位顺序产生八进制数的各个数位,而打印输出,一般来说应从高位到低位进行,恰好和计算过程相反。因此可利用栈先进后出特性,将计算过程中得到的八进制数各位顺序进栈,再按出栈序列打印输出既为与输入对应的八进制数。
void conversion(void){
// 创建栈
STACK S;
init(&S);
// 用户输入十进制数
scanf("%d",&N);
// 放入栈中
while (N) {
push(&S, N % 8);
N = N / 8;
}
// 打印出来
printf("对应八进制数字为:");
int a;
while (!isEmpty(&S)) {
pop(&S, &a);
printf("%d",a);
}
printf("\n");
}
思考 用数组实现貌似更简单,为什么不用数组?
从算法上分析不难看出,栈的引入简化了程序设计的问题,划分了不同的关注层次,使思考范围缩小了。而使用数组不仅掩盖了问题的本质,还要分散精力去思路数组下标增减等细节问题。
这也是早期面向对象编程的一种思想,要把对应的功能划分关注层次,在逻辑的实现上面更加专注问题的本质。
5.2 括号匹配的检验
编程语言中基本都允许使用 (),[],{}
这几种括号,假设现在让使用两种,一段完整代码中其须成对匹配,检验括号是否匹配的方法可用”期待的紧迫程度”这个概念来描述。
当计算机接受了第一个括号后,它期待着与其匹配的第八个括号出现,然而等来的确实第二个括号,此时第一个括号[
只能暂时靠边,而迫切等待与第二个括号匹配的第七个括号)
出现,类似地,等来的是第三个括号[
,其期待的匹配程度比第二个更加急迫,则第二个括号也只能靠边,让位于第三个括号,显然第二个括号的期待急迫性高于第一个括号,在接受了第四个括号之后,第三个括号的期待得到满足,消解之后,第二个括号的期待匹配变成最紧迫的任务了·····,以此类推。
可见此处理过程与栈的特点相吻合,由此,在算法中设置一个栈,每读入一个括号,若是右括号则使至于栈顶的最紧迫的期待得以消解,若是不合法的情况(左括号),则作为一个新的更紧迫的期待压入栈中,自然使原来所有未消解的期待的紧迫性都降了一级。另外在算法开始和结束的时候,栈都应该是空的。
算法实现:
/**
检测括号(本实例用数字代替括号)
[ ] --> 1 , 2
( ) --> 3 , 4
*/
void checkBracelet(void)
{
// 创建栈
STACK S;
init(&S);
// 用户输入括号
int N;
printf("请输入对应的括号(end结束):\n");
scanf("%d",&N);
if (isEmpty(&S)) {
push(&S, N);
printf("第一个括号输入\n");
traverse(&S); // 打印此时栈内容
}
while (!isEmpty(&S)) {
// 用户输入括号
int N;
printf("请输入对应的括号(0结束):\n");
scanf("%d",&N);
if (N == 0) {
break; // 用户输入0直接退出
}
// 判断当前栈顶是否符合标准,
if (S.pTop->data == N) {
printf("消除一对\n");
pop(&S, NULL);
traverse(&S); // 打印此时栈内容
}else
{
printf("未消除\n");
push(&S, N);
traverse(&S); // 打印此时栈内容
}
}
}
这里的实例我列举了两个,实际上还有很多。比如 行编辑程序、迷宫求解、表达式求值等。这里我就先不做列举了。
6. 小结
通过这里复习数据结构中栈的内容,感觉重新理解了很多计算机实现的底层知识,虽然不知道的更多,但是面对计算机心中又多了一层认知!
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