本文使用C++实现Shunting-yard算法，将中缀表达式转换为后缀表达式，然后使用后缀表达式计算结果，实现了目前支持以下

• 四则运算（+、-、*、/）
• 开平方（^）
• 取基数为 10 的对数（L）
• 小括号

的组合，实现代码如下

#include <iostream>  
#include <stack>  
#include <string>  
#include <vector>  
#include <cctype>
#include <math.h>/*** @brief getPrecedence 判断优先级* @param op 操作符* @return 0是特殊的，最高优先级，其他的数字越大，优先级越高*/
int getPrecedence(char op) {if (op == '+' || op == '-') {return 1;}else if (op == '*' || op == '/') {return 2;}else if (op == '^'){return 3;}else {return 0;}
}/*** @brief isOperator 判断字符是否是运算符* @param c* @return 是返回true*/
bool isOperator(char c) {return c == '+' || c == '-' || c == '*' || c == '/' || c == '^';
}/*** @brief shuntingYard Shunting-yard 算法*  用于将中缀表达式（如 "3 + 4 * 2"）转换为后缀表达式（逆波兰表示法，如 "3 4 2 * +"）的算法* @param expression 中缀表达式* @return 后缀表达式*/
std::vector<std::string> shuntingYard(const std::string& expression) {std::stack<std::string> operators;std::vector<std::string> output;for (size_t i = 0; i < expression.length(); ++i) {char c = expression[i];if (std::isspace(c)) {continue; // Skip whitespace  }else if (isdigit(c) || (c == '.' && (i == 0 || !isdigit(expression[i - 1])))) {std::string number;while (i < expression.length() && (isdigit(expression[i]) || expression[i] == '.')) {number += expression[i++];}output.push_back(number);--i; // Because the for loop also increments i  }else if (isOperator(c)) {while (!operators.empty() && getPrecedence(c) <= getPrecedence(operators.top()[0])) {output.push_back(operators.top());operators.pop();}operators.push(std::string(1, c));}else if (c == '(') {operators.push("(");}else if (c == ')') {while (!operators.empty() && operators.top() != "(") {output.push_back(operators.top());operators.pop();}if (!operators.empty()) {operators.pop(); // Remove the '(' from the stack  }}else if (c == 'L'){operators.push("L");}else {std::cerr << "Error: Unexpected character '" << c << "'" << std::endl;return {};}}// Push any remaining operators to the output  while (!operators.empty()) {output.push_back(operators.top());operators.pop();}return output;
}/*** @brief evaluatePostfix 计算后缀表达式的结果* @param postfix 后缀表达式* @return 计算结果*/
double evaluatePostfix(const std::vector<std::string>& postfix) {std::stack<double> values;for (const std::string& token : postfix) {if (isOperator(token[0])) {double val2 = values.top(); values.pop();// 防止表达式中有负数导致程序崩溃double val1 = 0.0;if (values.size() > 0){val1 = values.top();values.pop();}double result;switch (token[0]) {case '+': result = val1 + val2; break;case '-': result = val1 - val2; break;case '*': result = val1 * val2; break;case '/':if (val2 == 0) throw std::invalid_argument("Division by zero");result = val1 / val2; break;case '^': result = pow(val1, val2); break;default: throw std::invalid_argument("Invalid operator");}// 显示计算过程std::cout << val1 << token[0] << val2 << "=" << result << std::endl;values.push(result);}else if (token[0] == 'L'){double val = values.top(); values.pop();double result = log10(val);values.push(result);std::cout << "Log10(" << val << ")=" << result << std::endl;}else {values.push(std::stod(token));}}return values.top();
}int main() {std::string infix;std::cout << "Enter an infix expression: ";std::getline(std::cin, infix);while (infix.size() > 0){try{std::vector<std::string> postfix = shuntingYard(infix);// 打印后缀表达式用于验证  std::cout << "Postfix expression: ";for (const auto& token : postfix) {std::cout << token << " ";}std::cout << std::endl;double result = evaluatePostfix(postfix);std::cout << "Result: " << result << std::endl;}catch (const std::exception& e) {std::cerr << "Error: " << e.what() << std::endl;}infix = "";std::cout << "Enter an infix expression: ";std::getline(std::cin, infix);}return 0;
}