C++实现1. 使用链表创建栈 2. 完成栈的基本操作，创建、销毁、清空、判断是否为空、获取栈的长度、返回栈顶元素、入栈、出栈 3. 从键盘输入一个四则运算表达式（允许退格操作），完成中序表达式与后序表达式的互相转换并计算结

好的，下面是C++实现：

#include <iostream>
#include <cstring>
using namespace std;

struct Node {
    char data;
    Node *next;
};

class Stack {
    private:
        Node *top;
        int length;
    public:
        Stack() {
            top = NULL;
            length = 0;
        }
        ~Stack() {
            clear();
        }
        void clear() {
            while (top != NULL) {
                Node *temp = top;
                top = top->next;
                delete temp;
            }
            length = 0;
        }
        bool isEmpty() {
            return (top == NULL);
        }
        int getLength() {
            return length;
        }
        char getTop() {
            if (isEmpty()) {
                return '\0';
            }
            return top->data;
        }
        bool push(char data) {
            Node *node = new Node;
            node->data = data;
            node->next = top;
            top = node;
            length++;
            return true;
        }
        bool pop() {
            if (isEmpty()) {
                return false;
            }
            Node *temp = top;
            top = top->next;
            delete temp;
            length--;
            return true;
        }
};

int priority(char op) {
    if (op == '+' || op == '-') {
        return 1;
    }
    if (op == '*' || op == '/') {
        return 2;
    }
    return 0;
}

bool isOperator(char c) {
    return (c == '+' || c == '-' || c == '*' || c == '/');
}

void infixToPostfix(char infix[], char postfix[]) {
    Stack stack;
    int len = strlen(infix);
    int j = 0;
    for (int i = 0; i < len; i++) {
        if (infix[i] == '\b') {
            if (j > 0) {
                j--;
            }
            continue;
        }
        if (isdigit(infix[i])) {
            postfix[j++] = infix[i];
        } else if (isOperator(infix[i])) {
            while (!stack.isEmpty() && priority(stack.getTop()) >= priority(infix[i])) {
                postfix[j++] = stack.getTop();
                stack.pop();
            }
            stack.push(infix[i]);
        } else if (infix[i] == '(') {
            stack.push(infix[i]);
        } else if (infix[i] == ')') {
            while (!stack.isEmpty() && stack.getTop() != '(') {
                postfix[j++] = stack.getTop();
                stack.pop();
            }
            if (!stack.isEmpty()) {
                stack.pop();
            }
        }
    }
    while (!stack.isEmpty()) {
        postfix[j++] = stack.getTop();
        stack.pop();
    }
    postfix[j] = '\0';
}

int calculate(char op, int num1, int num2) {
    if (op == '+') {
        return num1 + num2;
    }
    if (op == '-') {
        return num1 - num2;
    }
    if (op == '*') {
        return num1 * num2;
    }
    if (op == '/') {
        return num1 / num2;
    }
    return 0;
}

int evaluatePostfix(char postfix[]) {
    Stack stack;
    int len = strlen(postfix);
    for (int i = 0; i < len; i++) {
        if (isdigit(postfix[i])) {
            stack.push(postfix[i] - '0');
        } else if (isOperator(postfix[i])) {
            int num2 = stack.getTop();
            stack.pop();
            int num1 = stack.getTop();
            stack.pop();
            stack.push(calculate(postfix[i], num1, num2));
        }
    }
    return stack.getTop();
}

int main() {
    char infix[100];
    char postfix[100];
    cout << "请输入一个中序表达式（允许使用退格键）：" << endl;
    cin.getline(infix, 100);
    infixToPostfix(infix, postfix);
    cout << "转换后的后序表达式为：" << postfix << endl;
    cout << "计算结果为：" << evaluatePostfix(postfix) << endl;
    return 0;
}

在这个程序中，我们使用了链表来实现栈。栈具有的基本操作都被实现了，并且我们还实现了中序表达式到后序表达式的转换，以及后序表达式的计算。