栈应用之计算全括号形式的数值表达式-优快云博客

本文链接：https://blog.youkuaiyun.com/coobj2008/article/details/20704323

本文探讨如何利用栈来判断一个全括号形式的中缀表达式是否正确配对，该表达式仅包含加减乘除二元运算符。

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1.判断表达式括号是否配对

#include <iostream>
#include <stack>

using namespace std;

bool isBalanced(const string& expression) {
	const char left = '(', right = ')';
	bool flag = true;
	stack<char> chstack;
	char ch;
	for(int i = 0; i < expression.size(); i++) {
		ch = expression[i];
		if(ch == '(')
			chstack.push(ch);
		else if(ch == ')' && !chstack.empty())
			chstack.pop();
		else if(ch == ')' && chstack.empty()) {
			flag = false;
			break;
		}
	}
	return (chstack.empty() && flag);
}

2.计算数值表达式

使用条件：（1）表达式使用全括号形式，中缀表达式（2）表达式中只能出现‘+’、‘-’、‘*’、‘/'等二元操作符，不能出现取反等一元操作符，即为非负数

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

using namespace std;

void evaluate_top(stack<double>& nums, stack<char>& operations) {
	double operd2 = nums.top();
	nums.pop();
	double operd1 = nums.top();
	nums.pop();
	switch(operations.top()) {
		case '+' : nums.push(operd1 + operd2);
					break;
		case '-' : nums.push(operd1 - operd2);
					break;
		case '*' : nums.push(operd1 * operd2);
					break;
		case '/' : nums.push(operd1 / operd2);
					break;
	}
	operations.pop();
}

double read_and_evaluate(istream &ins) {
	stack<char> chstack;
	stack<double> dstack;
	const char DECIMAL = '.', RIGHT_PAR = ')';
	double num;
	char ch;
	while(ins && ins.peek()!='\n') {
		if(isdigit(ins.peek()) || ins.peek() == DECIMAL) {
			ins >> num;
			dstack.push(num);
		}
		else if((ins.peek() == '+') || (ins.peek() == '-') || (ins.peek() == '*') || (ins.peek() == '/')) {
			ins >> ch;
			chstack.push(ch);
		}
		else if(ins.peek() == RIGHT_PAR) {
			ins.ignore();
			evaluate_top(dstack, chstack);	
		}
		else 
			ins.ignore();
	}
	return dstack.top();	
}

int main() {
	cout << "Type a fully parethesized arithmetic expression:" << endl;
	double result = read_and_evaluate(cin);
	cout << "That evaluates to " << result << endl;
	return 0;
}