C++ 递归算法实现中缀表达式转后缀表达式

以下是使用递归算法实现将中缀表达式转换为后缀表达式的代码：

#include <iostream>
#include <stack>
#include <string>

// 判断字符是否为运算符
bool isOperator(char c) {
    if (c == '+' || c == '-' || c == '*' || c == '/') {
        return true;
    }
    return false;
}

// 判断字符是否为左括号
bool isLeftParenthesis(char c) {
    if (c == '(') {
        return true;
    }
    return false;
}

// 判断字符是否为右括号
bool isRightParenthesis(char c) {
    if (c == ')') {
        return true;
    }
    return false;
}

// 判断运算符的优先级
int getPriority(char op) {
    if (op == '*' || op == '/') {
        return 2;
    } else if (op == '+' || op == '-') {
        return 1;
    }
    return 0;
}

// 将中缀表达式转换为后缀表达式
std::string infixToPostfix(const std::string& infixExpression, int start, int end) {
    if (start > end) {
        return '';
    }

    std::stack<char> operatorStack;
    std::string postfixExpression;

    for (int i = start; i <= end; i++) {
        char c = infixExpression[i];

        if (isOperator(c)) {
            while (!operatorStack.empty() && isOperator(operatorStack.top()) &&
                   getPriority(operatorStack.top()) >= getPriority(c)) {
                postfixExpression += operatorStack.top();
                operatorStack.pop();
            }
            operatorStack.push(c);
        } else if (isLeftParenthesis(c)) {
            operatorStack.push(c);
        } else if (isRightParenthesis(c)) {
            while (!operatorStack.empty() && !isLeftParenthesis(operatorStack.top())) {
                postfixExpression += operatorStack.top();
                operatorStack.pop();
            }
            if (!operatorStack.empty() && isLeftParenthesis(operatorStack.top())) {
                operatorStack.pop();
            } else {
                // 括号不配对，返回空字符串表示出错
                return '';
            }
        } else {
            // 操作数直接添加到后缀表达式中
            postfixExpression += c;
        }
    }

    while (!operatorStack.empty()) {
        if (isLeftParenthesis(operatorStack.top()) || isRightParenthesis(operatorStack.top())) {
            // 括号不配对，返回空字符串表示出错
            return '';
        }
        postfixExpression += operatorStack.top();
        operatorStack.pop();
    }

    return postfixExpression;
}

int main() {
    std::string infixExpression;
    std::cout << '请输入中缀表达式：';
    std::cin >> infixExpression;

    std::string postfixExpression = infixToPostfix(infixExpression, 0, infixExpression.length() - 1);
    if (postfixExpression == '') {
        std::cout << '表达式不合法！' << std::endl;
    } else {
        std::cout << '后缀表达式：' << postfixExpression << std::endl;
    }

    return 0;
}

示例输入和输出与之前的代码相同，这次使用了递归算法实现了将中缀表达式转换为后缀表达式的功能。希望这次的代码满足你的需求。