用栈解释四则运算

    四则运算是先乘除后加减，如果输入一条带有加减乘除的式子，可以用两个栈分别储存数字和运算符，然后用个for循环先对该式子进行遍历，将数字和运算符分开存储，并比对运算符的优先级进行计算，然后再将运算结果放到数字栈中进行下一步运算，最后输出结果。

1、逻辑思维导图

2、代码

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

using namespace std;

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

double calculate(double n1, double n2, char o)
{
	switch (o)
	{
	case'+':return n1 + n2;
		break;
	case'-':return n1 - n2;
		break;
	case'*':return n1 * n2;
		break;
	case'/':return n1 / n2;
		break;
	}
	return 0;
}

double evaluateExpression(const string& expression)
{
	stack<double>numbers;
	stack<char>operation;
	for (int i = 0; i < expression.length(); i++)
	{
		if (expression[i] == ' ')
		{
			continue;
		}
		else if (isdigit(expression[i]))
		{
			double val = 0;
			while (i < expression.length() && isdigit(expression[i]))
			{
				val = val * 10 + expression[i] - '0';
				i++;
			}
			numbers.push(val);
			i--;
		}
		else
		{
			while (!operation.empty() && getPriority(operation.top()) >= getPriority(expression[i]))
			{
				double val2 = numbers.top();
				numbers.pop();
				double val1 = numbers.top();
				numbers.pop();
				char op = operation.top();
				operation.pop();
				numbers.push(calculate(val1, val2, op));
			}
			operation.push(expression[i]);
		}
	}
	while (!operation.empty())
	{
		double val2 = numbers.top();
		numbers.pop();
		double val1 = numbers.top();
		numbers.pop();
		char op = operation.top();
		operation.pop();
		numbers.push(calculate(val1, val2, op));
	}
	return numbers.top();
}
int main() 
{
	string expression = "12*2+12/6-1";
	double result = evaluateExpression(expression);
	cout<< "result=" <<result<< endl;
	return 0;
}

3、运行结果