c++演示表达式的运算过程

设一个判断运算符优先级的函数 char Precede(char a, char b);

根据运算符的不同，自然有不同操作 int operate(int a, char theta, int b);

不同运算符间的如下优先顺序：

实现代码如下：

# include<iostream>
# include<stack>
using namespace std;
int operate(int a, char theta, int b);
char Precede(char a, char b);

int main()
{
	stack<char> operators;// 运算符栈
	stack<int> operands;// 操作数栈
	char num[15];  // 用于存储表达式中连续输入的多位数字
	int result_flag = 1;
	operators.push('#');
	cout << "请输入表达式，并以”#“结尾\n";
	char ch ;
	cin >> ch;
	while (ch != '#' || operators.top()!= '#')
	{
		int i = 0, a, b, byte_flag = 0;
		char theta;
		if (ch<'0' || ch>'9')
		{
			char comp = Precede(operators.top(), ch);
			
			switch (comp)
			{
				
			case '>':
				theta = operators.top();
				cout << "开始执行" << theta << "运算:\n";
				cout << theta << "出操作符栈\n";
				operators.pop();
				b = operands.top();
				cout << b << "出操作数栈\n";
				operands.pop();
				a = operands.top();
				cout << a << "出操作数栈\n";
				operands.pop();
				cout << a << theta << b << "=" << operate(a, theta, b)<<endl;
				cout << operate(a, theta, b) << "进操作数栈\n";
				operands.push(operate(a, theta, b));
				break;
			case '=':  // 左括号判断到右括号，将右括号出栈
				cout << operators.top() << "出栈" << endl;
				operators.pop();
				cin >> ch;
				break;
			case '<':
				cout << ch << "进操作符栈\n";
				operators.push(ch);
				cin >> ch;
				break;
			case '!':
				cout << "输入的表达式存在语法错误\n";
				result_flag = 0;
				cin >> ch;
				break;
			}
			continue;
		}
		while (ch >= '0'&&ch <= '9')
		{
			byte_flag = 1;
			num[i++] = ch;
			cin>>ch;
		}
		if (byte_flag)
		{
			num[i] = '\0';
			cout << atoi(num) << "进操作数栈\n";
			operands.push(atoi(num));
		}
		
	
	}
	if (result_flag)
	cout << "表达式最终结果为：" << operands.top() << endl;
	return 0;
}

int operate(int a, char theta, int b)   // 执行 a  operater b 
{
	if (theta == '+')
		return a + b;
	else if (theta == '-')
		return a - b;
	else if (theta == '*')
		return a*b;
	else if (theta == '/')
		return a / b;
}
char Precede(char a, char b)//比较两个运算符的优先级，a运算符在b左边

{
	if (a == '+' || a == '-')
	{
		if (b == '+' || b == '-' || b == ')' || b == '#')
			return '>';
		else
			return '<';
	}
	else if (a == '*' || a == '/')
	{
		if (b == '(')
			return '<';
		else
			return '>';
	}
	else if (a == '(')
	{
		if (b == '+' || b == '-' || b == '*' || b == '/' || b == '(')
			return '<';
		else if (b == ')')
			return '=';
		else
		{
			return '!'; 
		}
	}
	else if (a == ')')
	{
		if (b == '+' || b == '-' || b == '*' || b == '/' || b == ')' || b == '#')
			return '>';
		else if (b == '(')
		{
			return '!'; 
		}
	}
	else if (a == '#')
	{
		if (b == ')')
		{
			return '!'; 
		}
		else if (b == '#')
			return '=';
		else
			return '<';
	}
}