顺序栈的基本概念

顺序栈是基于数组实现的栈结构，通过数组的连续存储空间和指针（栈顶指针）动态管理数据。栈遵循后进先出（LIFO）原则，仅允许在栈顶进行插入（入栈）和删除（出栈）操作。

顺序栈的存储结构

顺序栈通常包含以下组成部分：

存储数组：用于存放栈元素的连续空间，如 int data[MAXSIZE]。
栈顶指针：记录当前栈顶位置的变量，通常为整型（如 int top），初始化为 -1 表示空栈。

#define MAXSIZE 100
typedef struct {
    int data[MAXSIZE];
    int top; // 栈顶指针
} SeqStack;

初始化顺序栈

初始化操作将栈顶指针设为 -1，表示栈为空：

void InitStack(SeqStack *S) {
    S->top = -1;
}

判断栈空与栈满

栈空：栈顶指针 top == -1。
栈满：栈顶指针 top == MAXSIZE - 1。

int IsEmpty(SeqStack *S) {
    return S->top == -1;
}

int IsFull(SeqStack *S) {
    return S->top == MAXSIZE - 1;
}

入栈操作（Push）

入栈前需检查栈是否已满。若未满，栈顶指针先增1，再将元素存入栈顶位置：

int Push(SeqStack *S, int value) {
    if (IsFull(S)) {
        return 0; // 栈满，入栈失败
    }
    S->data[++S->top] = value;
    return 1;
}

出栈操作（Pop）

出栈前需检查栈是否为空。若不为空，返回栈顶元素，栈顶指针减1：

int Pop(SeqStack *S, int *value) {
    if (IsEmpty(S)) {
        return 0; // 栈空，出栈失败
    }
    *value = S->data[S->top--];
    return 1;
}

获取栈顶元素（Peek）

获取栈顶元素但不修改栈顶指针：

int Peek(SeqStack *S, int *value) {
    if (IsEmpty(S)) {
        return 0; // 栈空，操作失败
    }
    *value = S->data[S->top];
    return 1;
}

顺序栈的优缺点

优点：
- 实现简单，存取速度快（时间复杂度为 $O(1)$）。
- 无需额外存储指针，空间利用率高。
缺点：
- 容量固定，易发生栈溢出。
- 扩容需重新分配数组，效率较低。

应用场景

顺序栈适用于：

表达式求值（如后缀表达式）。
函数调用栈的模拟。
括号匹配等需要回溯的场景。

以上内容涵盖了顺序栈的核心操作及实现细节，代码示例采用C语言，逻辑可直接应用于实际开发。

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顺序栈：原理、实现与应用详解