Question

Write a program to check given expression is valid or not.The expression consists of paranthsis like  [{( if valid then convert into postfix expression and after conversion then evaluate postfix expession(using stack) and do not use build in stack. Use the c++ laguage.

Answer 1

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

using namespace std;

// Function to convert Infix expression to postfix
string InfixToPostfix(string expression);

// Function to verify whether an operator has higher precedence over other
int HasHigherPrecedence(char operator1, char operator2);

// Function to verify whether a character is operator symbol or not.
bool IsOperator(char C);

// Function to verify whether a character is alphanumeric chanaracter
//(letter or numeric digit) or not.
bool IsOperand(char C);

// Function to check whether a char is an opening parenthesis i.e '(' or '{' or '['
bool IsOpeningParentheses(char C);

// Function to check whether a char is an closing parenthesis i.e ')' or '}' or ']'
bool IsClosingParentheses(char C);

int main()
{
        string expression;
        cout<<"Enter Infix Expression \n";
        getline(cin,expression);
        string postfix = InfixToPostfix(expression);
        cout<<"Output = "<<postfix<<"\n";
}

// Function to evaluate Postfix expression and return output
string InfixToPostfix(string expression)
{
        // Declaring a Stack from Standard template library in C++.
        stack<char> S;
        string postfix = ""; // Initialize postfix as empty string.
        for(int i = 0;i< expression.length();i++) {

                // Scanning each character from left.
                // If character is a delimiter, move on.
                if(expression[i] == ' ' || expression[i] == ',') continue;

                // Else if character is an operand then just append it in res string
                else if(IsOperand(expression[i]))
                {
                        postfix +=expression[i];
                }

                //If character is operator, check for Higher precedence operator in Stack top
                //till first opening bracket and pop all such operators
                //Finally push the current operator on the Stack
                else if(IsOperator(expression[i]))
                {
                        while(!S.empty() && !IsOpeningParentheses(S.top())
                        && HasHigherPrecedence(S.top(),expression[i]))
                        {
                                postfix+= S.top();
                                S.pop();
                        }
                        S.push(expression[i]);
                }

                //If opening Parentheses simply push it on the Stack
                else if(IsOpeningParentheses(expression[i]))
                {
                        S.push(expression[i]);
                }

        //If Closing Parentheses then pop all the operators and append to res string
        // until Stack top is opening Parentheses and finally one extra pop for Opening Parentheses
                else if(IsClosingParentheses(expression[i]))
                {
                        while(!S.empty() && !IsOpeningParentheses(S.top())) {
                                postfix += S.top();
                                S.pop();
                        }
                        S.pop();
                }
        }

    //Finally pop and append all operators till Stack is not empty
        while(!S.empty()) {
                postfix += S.top();
                S.pop();
        }

        return postfix;
}

// Function to verify whether a character is english letter or numeric digit.
// We are assuming in this solution that operand will be a single character
bool IsOperand(char C)
{
        if(C >= '0' && C <= '9') return true;
        if(C >= 'a' && C <= 'z') return true;
        if(C >= 'A' && C <= 'Z') return true;
        return false;
}

// Function to verify whether a character is operator symbol or not.
bool IsOperator(char C)
{
        if(C == '+' || C == '-' || C == '*' || C == '/' || C== '^')
                return true;

        return false;
}

bool IsOpeningParentheses(char C)
{
    if(C == '(' || C == '{' || C=='[')
        return true ;
    return false;
}

bool IsClosingParentheses(char C)
{
    if(C == ')' || C == '}' || C==']')
        return true ;
    return false;
}
// Function to verify whether an operator is right associative or not.
int IsRightAssociative(char op)
{
        if(op == '^') return true;
        return false;
}

// Function to get weight of an operator. An operator with higher weight will have higher precedence.
int GetOperatorWeight(char op)
{
        int weight = -1;
        switch(op)
        {
        case '+':
        case '-':
                weight = 1;
                break ;
        case '*':
        case '/':
                weight = 2;
                break ;
        case '^':
                weight = 3;
                break;
        }
        return weight;
}

// Function to perform an operation and return output.
int HasHigherPrecedence(char op1, char op2)
{
        int op1Weight = GetOperatorWeight(op1);
        int op2Weight = GetOperatorWeight(op2);

        // If operators have equal precedence, return true if they are left associative.
        // return false, if right associative.
        // if operator is left-associative, left one should be given priority.
        if(op1Weight == op2Weight)
        {
                if(IsRightAssociative(op1)) return false;
                else return true;
        }
        return op1Weight > op2Weight ?  true: false;
}

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