栈与队列的模拟实现解析

栈的模拟实现

栈是一种后进先出（LIFO）的数据结构，核心操作包括压栈（push）、弹栈（pop）和查看栈顶元素（peek）。可以通过数组或链表实现。

数组实现栈
定义一个固定大小的数组存储元素，同时维护一个栈顶指针（通常为整型变量）。压栈时将元素放入数组并移动指针，弹栈时返回栈顶元素并移动指针。

#define MAX_SIZE 100

typedef struct {
    int data[MAX_SIZE];
    int top;
} Stack;

void push(Stack *s, int value) {
    if (s->top < MAX_SIZE) {
        s->data[s->top++] = value;
    }
}

int pop(Stack *s) {
    if (s->top > 0) {
        return s->data[--s->top];
    }
    return -1; // 栈空标志
}

链表实现栈
使用单链表，每次压栈在链表头部插入节点，弹栈时删除头节点。无需预设容量限制。

typedef struct Node {
    int data;
    struct Node *next;
} Node;

typedef struct {
    Node *top;
} Stack;

void push(Stack *s, int value) {
    Node *newNode = (Node *)malloc(sizeof(Node));
    newNode->data = value;
    newNode->next = s->top;
    s->top = newNode;
}

int pop(Stack *s) {
    if (s->top != NULL) {
        Node *temp = s->top;
        int value = temp->data;
        s->top = temp->next;
        free(temp);
        return value;
    }
    return -1;
}

队列的模拟实现

队列是先进先出（FIFO）的数据结构，核心操作包括入队（enqueue）、出队（dequeue）和查看队首元素（front）。同样可通过数组或链表实现。

数组实现循环队列
使用固定大小的数组和两个指针（front和rear）模拟循环队列。入队时移动rear指针，出队时移动front指针，利用取模运算处理边界。

#define QUEUE_SIZE 100

typedef struct {
    int data[QUEUE_SIZE];
    int front, rear;
} Queue;

void enqueue(Queue *q, int value) {
    if ((q->rear + 1) % QUEUE_SIZE != q->front) {
        q->data[q->rear] = value;
        q->rear = (q->rear + 1) % QUEUE_SIZE;
    }
}

int dequeue(Queue *q) {
    if (q->front != q->rear) {
        int value = q->data[q->front];
        q->front = (q->front + 1) % QUEUE_SIZE;
        return value;
    }
    return -1; // 队空标志
}

链表实现队列
使用带头尾指针的单链表。入队在尾部插入节点，出队从头部删除节点。动态内存分配避免空间浪费。

typedef struct QNode {
    int data;
    struct QNode *next;
} QNode;

typedef struct {
    QNode *front, *rear;
} Queue;

void enqueue(Queue *q, int value) {
    QNode *newNode = (QNode *)malloc(sizeof(QNode));
    newNode->data = value;
    newNode->next = NULL;
    if (q->rear == NULL) {
        q->front = q->rear = newNode;
    } else {
        q->rear->next = newNode;
        q->rear = newNode;
    }
}

int dequeue(Queue *q) {
    if (q->front != NULL) {
        QNode *temp = q->front;
        int value = temp->data;
        q->front = temp->next;
        if (q->front == NULL) q->rear = NULL;
        free(temp);
        return value;
    }
    return -1;
}

复杂度分析

• 栈
  数组和链表实现的压栈、弹栈操作均为 $O(1)$ 时间复杂度。数组实现有固定容量限制，链表实现空间更灵活但需处理动态内存。

• 队列
  循环队列的入队出队为 $O(1)$，链表实现同样为 $O(1)$。循环队列需处理满队条件，链表实现需维护头尾指针。

应用场景对比

• 栈
  函数调用栈、表达式求值（如括号匹配）、回溯算法（如DFS）。

• 队列
  任务调度（如CPU轮转）、缓冲区管理（如打印队列）、广度优先搜索（BFS）。

通过模拟实现可深入理解两种结构的差异：栈的LIFO特性适合反向处理，队列的FIFO特性适合顺序调度。实际开发中可根据需求选择底层实现方式。

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