Boolean Expressions题解

Boolean Expressions

问题重述

描述
The objective of the program you are going to produce is to evaluate boolean expressions as the one shown next:

Expression: ( V | V ) & F & ( F | V )

where V is for True, and F is for False. The expressions may include the following operators: ! for not , & for and, | for or , the use of parenthesis for operations grouping is also allowed.

To perform the evaluation of an expression, it will be considered the priority of the operators, the not having the highest, and the or the lowest. The program must yield V or F , as the result for each expression in the input file.

输入
The expressions are of a variable length, although will never exceed 100 symbols. Symbols may be separated by any number of spaces or no spaces at all, therefore, the total length of an expression, as a number of characters, is unknown.

The number of expressions in the input file is variable and will never be greater than 20. Each expression is presented in a new line, as shown below.

输出
For each test expression, print "Expression " followed by its sequence number, ": ", and the resulting value of the corresponding test expression. Separate the output for consecutive test expressions with a new line.

Use the same format as that shown in the sample output shown below.

思路：
参考MOOC郭炜老师程序设计与算法（二）算法基础 表达式求值讲解
根据 ’ | ’ 、’ &’ 和’ ! ’ 的优先级我们可以将一个表达式拆分，括号是一个子表达式看做整体，所以一个表达式是用’ | ‘连接的几个项，一个项是由’ & ‘连接的几个因子，而一个因子可以是一个符号也可以又是一个括号表达式，同时它们之前可能有若干个’ ! '运算符。我们可以依次写出函数来递归求解。

C++代码：

#include<iostream> 
#include<vector>
using namespace std;
vector<char>arr;//arr用来存储去掉空格的表达式 
char expression_value();
char term_value();
char factor_value();
int mark; //mark用来指示当前字符
char expression_value()//处理表达式 
{
	char result = term_value();//先获得第一个项 
	while(true)         //循环处理所有的'|'符号 
	{
		if(arr[mark] == '|')//是'|'符就处理不是了就跳出循环 
		{
			mark++;       //是的话取下'|'符  
			char value = term_value();//获取'|'的下一项 
			if(result != 'V')//由运算关系知如果result为真直接返回真，若为假返回'|'符后一项的值 
			{
				result = value;
			}
		}
		else
			break;
	}
	return result;
}
char term_value()//处理项 
{
	char result = factor_value();//获得第一个因子 
	while(true)//循环处理所有的'&'符号 
	{
		if(arr[mark] == '&')//是'&'符就处理不是了就跳出循环
		{
			mark++;    //是的话取下'&'符 
			char value = factor_value();//获取'&'的下一个因子 	
			if(result != 'F')//由运算关系知如果result为假直接返回假，若为真返回'&'符后一项的值
			{
				result = value;
			}		
		}
		else
			break;
	}
	return result;
}
char factor_value()//处理因子
{/*因子有两种情况一种是单个的字符真或假，
   另一种是括号表达式同时因子前面可能有若干个'!'*/
	char result;
	int counts = 0;//先用一个counts来存储'!'的个数 
	while(arr[mark]=='!')
	{
		counts++;
		mark++;
	}
	if(arr[mark] == '(')//如果检查到因子第一字符是'('说明它是一个表达式 
	{
		mark++;//拿下'('
		result = expression_value();//用result获取里面的表达式的值递归回去 
		mark++;//拿下')'
	}
	else       //如果不是的话说明它是单个字符直接获取 
	{		
		result = arr[mark];
		mark++;
	}
	if(counts%2)//最后判断'!'符的数量如果是奇数则需要改变前面获得的result值 
	{
		if(result=='V')
			result = 'F';
		else	
			result = 'V';
	}
	return result;
}
int main()
{
	string a;
	int t=0;
	while(getline(cin,a))//多组输入
	{
		t++;			//记录第几组输入 
		mark=0;			//mark初值赋为0 
		arr.resize(0);  //容器初值大小设置为0 
		for(int i=0;i<a.size();i++)//处理一下输入的空格，非空格压入容器 
		{
			if(a[i]!=' ')
				arr.push_back(a[i]);
		}
		printf("Expression %d: %c\n",t,expression_value());//输出结果 
	}		
	return 0;
}

测试执行