Boolean Expressions POJ 2106

Description

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.

Input

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.

Output

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.

Sample Input

( V | V ) & F & ( F| V)

!V | V & V & !F & (F | V ) & (!F | F | !V & V)

(F&F|V|!V&!F&!(F|F&V))

Sample Output

Expression 1: F
Expression 2: V
Expression 3: V

Source

México and Central America 2004

算法

递归，一个Boolean Expression是可以被分解为三个层级，按照运算符的优先级，优先级越高的层级就越低。

Boolean Expression = AndExpression | AndExpression | $\cdots$ | AndExpression

AndExpression = NotExpression & NotExpression & $\cdots$ & NotExpression

NotExpression 有多种情况：

1. ! NotExpression 递归
2. (Boolean Expression) 递归
3. V 返回 true
4. F 返回 false

具体实现时，由于需要在不取出字符的条件下观察输入流的下一个字符，所以使用cin.peek()，但是题目中表示，表达式中可能会随意出现空格，所以需要另外写一个Peek()和Get()函数

AC Code

#include<iostream>

using namespace std;

bool OrExpre();
bool AndExpre();
bool NotExpre();
char Peek();
char Get();

int main()
{
    int I = 1;
    while (Peek() != -1) {
        bool B = OrExpre();
        char c;
        if (B) {
            c = 'V';
        }
        else {
            c = 'F';
        }
        cout << "Expression " << I << ": " << c << endl;
        I++;
    }
    return 0;
}

char Peek()
{
    char c = cin.peek();

    while (c == ' ' || c == '\n') {
        cin.get();
        c = cin.peek();
    }
    return c;
}

char Get()
{
    char c = cin.get();

    while (c == ' ' || c == '\n') {
        c = cin.get();
    }
    return c;
}

bool OrExpre()
{
    bool result = AndExpre(), more = true;

//  cout << "Or Start " << result << endl;
    while (more) {
        char c = Peek();
//      cout << "In OrExpre " << c << endl;
        if (c == '|') {
            Get();
            bool re = AndExpre();
            result |= re;
        }
        else {
            more = false;
        }
//      cout << "Or Loop " << result << endl;
    }
//  cout << "Or " << result << endl;
    return result;
}

bool AndExpre()
{
    bool result = NotExpre(), more = true;

    while (more) {
        char c = Peek();
//      cout << "In AndExpre " << c << endl;
        if (c == '&') {
            Get();
            bool re = NotExpre();
            result &= re;
        }
        else {
            more = false;
        }
    }

    return result;
}

bool NotExpre()
{
    bool result;

    char c = Peek();
//  cout << "In NotExpre " << c << endl;
    if (c == '!') {
        Get();
        result = NotExpre();
//      cout << "result " << result << endl;
        return !result;
    }
    else if (c == '(') {
        Get();
        result = OrExpre();
        Get();
        return result;
    }
    else if (c == 'F') {
        Get();
        return false;
    }
    else {
        Get();
        return true;
    }
}