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 原理：

数据栈：有数据就直接入栈

运算符栈：设遍历到当前的运算符位e，如果栈不为空，比较栈顶与当前运算符优先级e，当栈顶运算符优先级大于或者等于e的优先级，则出栈，并将两个数据栈的数据出栈，计算出对应的数据，加入到数据栈中，否则将运算符入栈

#include <iostream>
#include <unordered_map>
#include <stack>
#include <functional>
#include <string>#define MAX_PRI INT_MAXusing namespace std;
int main() {//数据栈stack<double> _data;   //运算符栈stack<char> _operator;   //运算符优先级unordered_map<char, int> pri{ {'+', 0}, {'-', 0}, {'*', 1}, {'/', 1}, {'^', 2}, {'(', MAX_PRI }, {')', MAX_PRI}};unordered_map<char, function<double(double, double)>> func{{'+', [](double x, double y) -> double { return x + y; }},{'-', [](double x, double y) -> double { return x - y; }},  {'*', [](double x, double y) -> double { return x * y; }},{'/', [](double x, double y) -> double { return x / y; }},{'^', [](double x, double y) -> double { return pow(x, y); }}};string exp;cin >> exp;auto calculate = [&_data, &_operator, &func]() {char op = _operator.top();_operator.pop();double x = _data.top();_data.pop();double y = _data.top();_data.pop();_data.push(func[op](y, x));   //运算顺序与出栈顺序相反};auto stringtonum = [&exp, &pri](int& i) -> double {int j = i + 1;while (j < exp.length() && pri.find(exp[j]) == pri.end()) j++;double num = stod(exp.substr(i, j - i));i = j - 1;   return num;};for (int i = 0; i < exp.length(); ++i) {char e = exp[i];if (pri.find(e) == pri.end()) {   //当前字符不是运算符，则切割数字_data.push(stringtonum(i));} else if (e == '(') {_operator.push('(');} else if (e == ')') {while (_operator.top() != '(') {calculate();}_operator.pop();} else {//当前运算符优先级<=栈顶运算符优先级，则出栈计算while (!_operator.empty() && pri[_operator.top()] >= pri[e] && _operator.top() != '(') {calculate();}_operator.push(e);}}while (!_operator.empty()) {calculate();}cout << _data.top() << endl;
}