C++ || Multi Digit, Decimal & Negative Number Infix To Postfix Conversion & Evaluation

January 31, 2014 admin 1 Comment

Click Here For Updated Version Of Program

The following is sample code which demonstrates the implementation of a multi digit, decimal, and negative number infix to postfix converter and evaluator using a Finite State Machine

REQUIRED KNOWLEDGE FOR THIS PROGRAM

How To Convert Infix To Postfix How To Evaluate A Postfix Expression What Is A Finite State Machine?

Using a Finite State Machine, the program demonstrated on this page has the ability to convert and evaluate a single digit, multi digit, decimal number, and/or negative number infix equation. So for example, if the the infix equation of (19.87 * -2) was entered into the program, the converted postfix expression of 19.87 ~2* would display to the screen, as well as the final evaluated answer of -39.74.

NOTE: In this program, negative numbers are represented by the “~” symbol on the postfix string. This is used to differentiate between a negative number and a subtraction symbol.

This program has the following flow of control:

• Get an infix expression from the user • Convert the infix expression to postfix • Use a Finite State Machine to isolate all of the math operators, multi digit, decimal, negative and single digit numbers that are found in the postfix expression • Evaluate the postfix expression using the tokens found from the above step • Display the evaluated answer to the screen

The above steps are implemented below.





		
		
			Multi Digit Infix To Postfix Conversion & Evaluation
			
C++
			
			// ============================================================================
//   Author:  Kenneth Perkins
//   Taken From: http://programmingnotes.org/
//   Date:  Jan 31, 2014
//   File: InToPostEval.cpp
//   Description: The following demonstrates the implementation of an infix to
//     postfix converter and evaluator. Using a Finite State Machine, this
//     program has the ability to convert and evaluate multi digit, decimal,
//     negative and positive values.
// ============================================================================
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <cctype>
#include <string>
#include <vector>
#include <stack>
#include <algorithm>
using namespace std;

/* This holds the transition states for our Finite State Machine
    -- They are placed in numerical order for easy understanding within
        the FSM array, which is located below */

enum FSM_TRANSITIONS
{
    REJECT = 0,
    INTEGER,
    REAL,
    NEGATIVE,
    OPERATOR,
    UNKNOWN,
    SPACE
};

/* This is the Finite State Machine
    -- The zero represents a place holder, so the row in the array
            starts on row 1 instead of 0

                           integer,  real,  negative, operator, unknown, space */
int stateTable[][7] = { {0, INTEGER,  REAL, NEGATIVE, OPERATOR,  UNKNOWN,  SPACE},
/* STATE 1 */   {INTEGER,  INTEGER,  REAL,   REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 2 */   {REAL,       REAL,  REJECT,  REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 3 */   {NEGATIVE, INTEGER,  REAL,   REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 4 */   {OPERATOR,  REJECT, REJECT,  REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 5 */   {UNKNOWN,   REJECT, REJECT,  REJECT,  REJECT,   UNKNOWN, REJECT},
/* STATE 6 */   {SPACE,     REJECT, REJECT,  REJECT,  REJECT,   REJECT,  REJECT} };

// function prototypes
void DisplayDirections();
string ConvertInfixToPostfix(string infix);
bool IsMathOperator(char token);
int OrderOfOperations(char token);
vector<string> Lexer(string postfix);
int Get_FSM_Col(char& currentChar);
double EvaluatePostfix(const vector<string>& postfix);
double Calculate(char token, double op1, double op2);

int main()
{
    // declare variables
    string infix = "";
    string postfix = "";
    double answer = 0;
    vector<string> tokens;

    // display directions to user
    DisplayDirections();

    // get data from user
    cout << "\nPlease enter an Infix expression: ";
    getline(cin, infix);

    postfix = ConvertInfixToPostfix(infix);

    // use the "Lexer" function to isolate multi digit, negative and decimal
    // numbers, aswell as single digit numbers and math operators
    tokens = Lexer(postfix);

    // display the found tokens to the screen
    //for (unsigned x = 0; x < tokens.size(); ++x)
    //{
    //    cout<<tokens.at(x)<<endl;
    //}

    cout << "\nThe Infix expression = " << infix;
    cout << "\nThe Postfix expression = " << postfix << endl;

    answer = EvaluatePostfix(tokens);

    cout << "\nFinal answer = " << answer << endl;

    cin.get();
    return 0;
}// end of main

void DisplayDirections()
{// this function displays instructions to the screen
    cout << "\n==== Infix To Postfix Conversion & Evaluation ====\n"
        << "\nMath Operators:\n"
        << "+ || Addition\n"
        << "- || Subtraction\n"
        << "* || Multiplication\n"
        << "/ || Division\n"
        << "% || Modulus\n"
        << "^ || Power\n"
        << "$ || Square Root\n"
        << "s || Sine\n"
        << "c || Cosine\n"
        << "t || Tangent\n"
        << "- || Negative Number\n"
        << "Sample Infix Equation: ((s(-4^5)*1.4)/($(23+2)--2.8))*(c(1%2)/(7.28*.1987)^(t23))\n";
    // ((sin(-4^5)*1.4)/(sqrt(23+2)--2.8))*(cos(1%2)/(7.28*.1987)^(tan(23)))
}// end of DisplayDirections

string ConvertInfixToPostfix(string infix)
{// this function converts an infix expression to postfix
    // declare function variables
    string postfix;
    stack<char> charStack;

    // remove all whitespace from the string
    infix.erase(std::remove_if(infix.begin(), infix.end(), [](char c) {
        return std::isspace(static_cast<unsigned char>(c));
    }), infix.end());

    // automatically convert negative numbers to have the ~ symbol
    for (unsigned x = 0; x < infix.length(); ++x) {
        if (infix[x] != '-') {
            continue;
        } else if (x + 1 < infix.length() && IsMathOperator(infix[x + 1])) {
            continue;
        }
        if (x == 0 || infix[x - 1] == '(' || IsMathOperator(infix[x - 1])) {
            infix[x] = '~';
        }
    }

    // loop thru array until there is no more data
    for (unsigned x = 0; x < infix.length(); ++x)
    {
        // place numbers (standard, decimal, & negative)
        // numbers onto the 'postfix' string
        if ((isdigit(infix[x])) || (infix[x] == '.') || (infix[x] == '~'))
        {
            postfix += infix[x];
        }
        else if (isspace(infix[x]))
        {
            continue;
        }
        else if (IsMathOperator(infix[x]))
        {
            postfix += " ";
            // use the 'OrderOfOperations' function to check equality
            // of the math operator at the top of the stack compared to
            // the current math operator in the infix string
            while ((!charStack.empty()) &&
                (OrderOfOperations(charStack.top()) >= OrderOfOperations(infix[x])))
            {
                // place the math operator from the top of the
                // stack onto the postfix string and continue the
                // process until complete
                postfix += charStack.top();
                charStack.pop();
            }
            // push the remaining math operator onto the stack
            charStack.push(infix[x]);
        }
        // push outer parentheses onto stack
        else if (infix[x] == '(')
        {
            charStack.push(infix[x]);
        }
        else if (infix[x] == ')')
        {
            // pop the current math operator from the stack
            while ((!charStack.empty()) && (charStack.top() != '('))
            {
                // place the math operator onto the postfix string
                postfix += charStack.top();
                // pop the next operator from the stack and
                // continue the process until complete
                charStack.pop();
            }

            if (!charStack.empty()) // pop '(' symbol off the stack
            {
                charStack.pop();
            }
            else // no matching '('
            {
                cout << "\nPARENTHESES MISMATCH #1\n";
                exit(1);
            }
        }
        else
        {
            cout << "\nINVALID INPUT #1\n";
            exit(1);
        }
    }

    // place any remaining math operators from the stack onto
    // the postfix array
    while (!charStack.empty())
    {
        postfix += charStack.top();
        charStack.pop();
    }

    return postfix;
}// end of ConvertInfixToPostfix

bool IsMathOperator(char token)
{// this function checks if operand is a math operator
    switch (tolower(token))
    {
    case '+': case '-': case '*': case '/':
    case '%': case '^': case '$': case 'c':
    case 's': case 't':
        return true;
        break;
    default:
        return false;
        break;
    }
}// end of IsMathOperator

int OrderOfOperations(char token)
{// this function returns the priority of each math operator
    int priority = 0;
    switch (tolower(token))
    {
    case 'c': case 's': case 't':
        priority = 5;
        break;
    case '^': case '$':
        priority = 4;
        break;
    case '*': case '/': case '%':
        priority = 3;
        break;
    case '-':
        priority = 2;
        break;
    case '+':
        priority = 1;
        break;
    }
    return priority;
}// end of OrderOfOperations

vector<string> Lexer(string postfix)
{// this function parses a postfix string using an FSM to generate
 //  each individual token in the expression
    vector<string> tokens;
    char currentChar = ' ';
    int col = REJECT;
    int currentState = REJECT;
    string currentToken = "";

    // use an FSM to parse multidigit and decimal numbers
    // also does error check for invalid input of decimals
    for (unsigned x = 0; x < postfix.length();)
    {
        currentChar = postfix[x];

        // get the column number for the current character
        col = Get_FSM_Col(currentChar);

        // exit if the real number has multiple periods "."
        // in the expression (i.e: 19.3427.23)
        if ((currentState == REAL) && (col == REAL))
        {
            cerr << "\nINVALID INPUT #2\n";
            exit(1);
        }
        /* ========================================================

            THIS IS WHERE WE CHECK THE FINITE STATE MACHINE TABLE
               USING THE "col" VARIABLE FROM ABOVE ^

          ========================================================= */

          // get the current state of our machine
        currentState = stateTable[currentState][col];

        /* ===================================================

          THIS IS WHERE WE CHECK FOR A SUCCESSFUL PARSE
           - If the current state in our machine == REJECT
             (the starting state), then we have successfully parsed
             a token, which is returned to its caller

            - ELSE we continue trying to find a successful token

            =================================================== */
        if (currentState == REJECT)
        {
            if (currentToken != " ") // we dont care about whitespace
            {
                tokens.push_back(currentToken);
            }
            currentToken = "";
        }
        else
        {
            currentToken += currentChar;
            ++x;
        }

    }
    // this ensures the last token gets saved when
    // we reach the end of the postfix string buffer
    if (currentToken != " ") // we dont care about whitespace
    {
        tokens.push_back(currentToken);
    }
    return tokens;
}// end of Lexer

int Get_FSM_Col(char& currentChar)
{// this function determines the state of the type of character being examined
    // check for whitespace
    if (isspace(currentChar))
    {
        return SPACE;
    }

    // check for integer numbers
    else if (isdigit(currentChar))
    {
        return INTEGER;
    }

    // check for real numbers
    else if (currentChar == '.')
    {
        return REAL;
    }

    // check for negative numbers
    else if (currentChar == '~')
    {
        currentChar = '-';
        return NEGATIVE;
    }

    // check for math operators
    else if (IsMathOperator(currentChar))
    {
        return OPERATOR;
    }
    return UNKNOWN;
}// end of Get_FSM_Col

double EvaluatePostfix(const vector<string>& postfix)
{// this function evaluates a postfix expression
    // declare function variables
    double op1 = 0;
    double op2 = 0;
    double answer = 0;
    stack<double> doubleStack;

    cout << "\nCalculations:\n";

    // loop thru array until there is no more data
    for (unsigned x = 0; x < postfix.size(); ++x)
    {
        // push numbers onto the stack
        if ((isdigit(postfix[x][0])) || (postfix[x][0] == '.'))
        {
            doubleStack.push(atof(postfix[x].c_str()));
        }
        // push negative numbers onto the stack
        else if ((postfix[x].length() > 1) && ((postfix[x][0] == '-') &&
            (isdigit(postfix[x][1]) || (postfix[x][1] == '.'))))
        {
            doubleStack.push(atof(postfix[x].c_str()));
        }
        // if expression is a math operator, pop numbers from stack
        // & send the popped numbers to the 'Calculate' function
        else if (IsMathOperator(postfix[x][0]) && (!doubleStack.empty()))
        {
            char token = tolower(postfix[x][0]);

            // if expression is square root, sin, cos,
            // or tan operation only pop stack once
            if (token == '$' || token == 's' || token == 'c' || token == 't')
            {
                op2 = 0;
                op1 = doubleStack.top();
                doubleStack.pop();
                answer = Calculate(token, op1, op2);
                doubleStack.push(answer);
            }
            else if (doubleStack.size() > 1)
            {
                op2 = doubleStack.top();
                doubleStack.pop();
                op1 = doubleStack.top();
                doubleStack.pop();
                answer = Calculate(token, op1, op2);
                doubleStack.push(answer);
            }
        }
        else // this should never execute, & if it does, something went really wrong
        {
            cout << "\nINVALID INPUT #3\n";
            exit(1);
        }
    }
    // pop the final answer from the stack, and return to main
    if (!doubleStack.empty())
    {
        answer = doubleStack.top();
    }
    return answer;
}// end of EvaluatePostfix

double Calculate(char token, double op1, double op2)
{// this function carries out the actual math process
    double ans = 0;
    switch (tolower(token))
    {
    case '+':
        cout << op1 << token << op2 << " = ";
        ans = op1 + op2;
        break;
    case '-':
        cout << op1 << token << op2 << " = ";
        ans = op1 - op2;
        break;
    case '*':
        cout << op1 << token << op2 << " = ";
        ans = op1 * op2;
        break;
    case '/':
        cout << op1 << token << op2 << " = ";
        ans = op1 / op2;
        break;
    case '%':
        cout << op1 << token << op2 << " = ";
        ans = ((int)op1 % (int)op2) + modf(op1, &op2);
        break;
    case '^':
        cout << op1 << token << op2 << " = ";
        ans = pow(op1, op2);
        break;
    case '$':
        cout << char(251) << op1 << " = ";
        ans = sqrt(op1);
        break;
    case 'c':
        cout << "cos(" << op1 << ") = ";
        ans = cos(op1);
        break;
    case 's':
        cout << "sin(" << op1 << ") = ";
        ans = sin(op1);
        break;
    case 't':
        cout << "tan(" << op1 << ") = ";
        ans = tan(op1);
        break;
    default:
        ans = 0;
        break;
    }
    cout << ans << endl;
    return ans;
}// http://programmingnotes.org/
			
				
					
				
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						// ============================================================================
//   Author:  Kenneth Perkins
//   Taken From: http://programmingnotes.org/
//   Date:  Jan 31, 2014
//   File: InToPostEval.cpp
//   Description: The following demonstrates the implementation of an infix to
//     postfix converter and evaluator. Using a Finite State Machine, this
//     program has the ability to convert and evaluate multi digit, decimal,
//     negative and positive values.
// ============================================================================
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <cctype>
#include <string>
#include <vector>
#include <stack>
#include <algorithm>
using namespace std;
 
/* This holds the transition states for our Finite State Machine
    -- They are placed in numerical order for easy understanding within
        the FSM array, which is located below */
 
enum FSM_TRANSITIONS
{
    REJECT = 0,
    INTEGER,
    REAL,
    NEGATIVE,
    OPERATOR,
    UNKNOWN,
    SPACE
};
 
/* This is the Finite State Machine
    -- The zero represents a place holder, so the row in the array
            starts on row 1 instead of 0
 
                           integer,  real,  negative, operator, unknown, space */
int stateTable[][7] = { {0, INTEGER,  REAL, NEGATIVE, OPERATOR,  UNKNOWN,  SPACE},
/* STATE 1 */   {INTEGER,  INTEGER,  REAL,   REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 2 */   {REAL,       REAL,  REJECT,  REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 3 */   {NEGATIVE, INTEGER,  REAL,   REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 4 */   {OPERATOR,  REJECT, REJECT,  REJECT,  REJECT,   REJECT,  REJECT},
/* STATE 5 */   {UNKNOWN,   REJECT, REJECT,  REJECT,  REJECT,   UNKNOWN, REJECT},
/* STATE 6 */   {SPACE,     REJECT, REJECT,  REJECT,  REJECT,   REJECT,  REJECT} };
 
// function prototypes
void DisplayDirections();
string ConvertInfixToPostfix(string infix);
bool IsMathOperator(char token);
int OrderOfOperations(char token);
vector<string> Lexer(string postfix);
int Get_FSM_Col(char& currentChar);
double EvaluatePostfix(const vector<string>& postfix);
double Calculate(char token, double op1, double op2);
 
int main()
{
    // declare variables
    string infix = "";
    string postfix = "";
    double answer = 0;
    vector<string> tokens;
 
    // display directions to user
    DisplayDirections();
 
    // get data from user
    cout << "\nPlease enter an Infix expression: ";
    getline(cin, infix);
 
    postfix = ConvertInfixToPostfix(infix);
 
    // use the "Lexer" function to isolate multi digit, negative and decimal
    // numbers, aswell as single digit numbers and math operators
    tokens = Lexer(postfix);
 
    // display the found tokens to the screen
    //for (unsigned x = 0; x < tokens.size(); ++x)
    //{
    //    cout<<tokens.at(x)<<endl;
    //}
 
    cout << "\nThe Infix expression = " << infix;
    cout << "\nThe Postfix expression = " << postfix << endl;
 
    answer = EvaluatePostfix(tokens);
 
    cout << "\nFinal answer = " << answer << endl;
 
    cin.get();
    return 0;
}// end of main
 
void DisplayDirections()
{// this function displays instructions to the screen
    cout << "\n==== Infix To Postfix Conversion & Evaluation ====\n"
        << "\nMath Operators:\n"
        << "+ || Addition\n"
        << "- || Subtraction\n"
        << "* || Multiplication\n"
        << "/ || Division\n"
        << "% || Modulus\n"
        << "^ || Power\n"
        << "$ || Square Root\n"
        << "s || Sine\n"
        << "c || Cosine\n"
        << "t || Tangent\n"
        << "- || Negative Number\n"
        << "Sample Infix Equation: ((s(-4^5)*1.4)/($(23+2)--2.8))*(c(1%2)/(7.28*.1987)^(t23))\n";
    // ((sin(-4^5)*1.4)/(sqrt(23+2)--2.8))*(cos(1%2)/(7.28*.1987)^(tan(23)))
}// end of DisplayDirections
 
string ConvertInfixToPostfix(string infix)
{// this function converts an infix expression to postfix
    // declare function variables
    string postfix;
    stack<char> charStack;
 
    // remove all whitespace from the string
    infix.erase(std::remove_if(infix.begin(), infix.end(), [](char c) {
        return std::isspace(static_cast<unsigned char>(c));
    }), infix.end());
 
    // automatically convert negative numbers to have the ~ symbol
    for (unsigned x = 0; x < infix.length(); ++x) {
        if (infix[x] != '-') {
            continue;
        } else if (x + 1 < infix.length() && IsMathOperator(infix[x + 1])) {
            continue;
        }
        if (x == 0 || infix[x - 1] == '(' || IsMathOperator(infix[x - 1])) {
            infix[x] = '~';
        }
    }
 
    // loop thru array until there is no more data
    for (unsigned x = 0; x < infix.length(); ++x)
    {
        // place numbers (standard, decimal, & negative)
        // numbers onto the 'postfix' string
        if ((isdigit(infix[x])) || (infix[x] == '.') || (infix[x] == '~'))
        {
            postfix += infix[x];
        }
        else if (isspace(infix[x]))
        {
            continue;
        }
        else if (IsMathOperator(infix[x]))
        {
            postfix += " ";
            // use the 'OrderOfOperations' function to check equality
            // of the math operator at the top of the stack compared to
            // the current math operator in the infix string
            while ((!charStack.empty()) &&
                (OrderOfOperations(charStack.top()) >= OrderOfOperations(infix[x])))
            {
                // place the math operator from the top of the
                // stack onto the postfix string and continue the
                // process until complete
                postfix += charStack.top();
                charStack.pop();
            }
            // push the remaining math operator onto the stack
            charStack.push(infix[x]);
        }
        // push outer parentheses onto stack
        else if (infix[x] == '(')
        {
            charStack.push(infix[x]);
        }
        else if (infix[x] == ')')
        {
            // pop the current math operator from the stack
            while ((!charStack.empty()) && (charStack.top() != '('))
            {
                // place the math operator onto the postfix string
                postfix += charStack.top();
                // pop the next operator from the stack and
                // continue the process until complete
                charStack.pop();
            }
 
            if (!charStack.empty()) // pop '(' symbol off the stack
            {
                charStack.pop();
            }
            else // no matching '('
            {
                cout << "\nPARENTHESES MISMATCH #1\n";
                exit(1);
            }
        }
        else
        {
            cout << "\nINVALID INPUT #1\n";
            exit(1);
        }
    }
 
    // place any remaining math operators from the stack onto
    // the postfix array
    while (!charStack.empty())
    {
        postfix += charStack.top();
        charStack.pop();
    }
 
    return postfix;
}// end of ConvertInfixToPostfix
 
bool IsMathOperator(char token)
{// this function checks if operand is a math operator
    switch (tolower(token))
    {
    case '+': case '-': case '*': case '/':
    case '%': case '^': case '$': case 'c':
    case 's': case 't':
        return true;
        break;
    default:
        return false;
        break;
    }
}// end of IsMathOperator
 
int OrderOfOperations(char token)
{// this function returns the priority of each math operator
    int priority = 0;
    switch (tolower(token))
    {
    case 'c': case 's': case 't':
        priority = 5;
        break;
    case '^': case '$':
        priority = 4;
        break;
    case '*': case '/': case '%':
        priority = 3;
        break;
    case '-':
        priority = 2;
        break;
    case '+':
        priority = 1;
        break;
    }
    return priority;
}// end of OrderOfOperations
 
vector<string> Lexer(string postfix)
{// this function parses a postfix string using an FSM to generate
 //  each individual token in the expression
    vector<string> tokens;
    char currentChar = ' ';
    int col = REJECT;
    int currentState = REJECT;
    string currentToken = "";
 
    // use an FSM to parse multidigit and decimal numbers
    // also does error check for invalid input of decimals
    for (unsigned x = 0; x < postfix.length();)
    {
        currentChar = postfix[x];
 
        // get the column number for the current character
        col = Get_FSM_Col(currentChar);
 
        // exit if the real number has multiple periods "."
        // in the expression (i.e: 19.3427.23)
        if ((currentState == REAL) && (col == REAL))
        {
            cerr << "\nINVALID INPUT #2\n";
            exit(1);
        }
        /* ========================================================
 
            THIS IS WHERE WE CHECK THE FINITE STATE MACHINE TABLE
               USING THE "col" VARIABLE FROM ABOVE ^
 
          ========================================================= */
 
          // get the current state of our machine
        currentState = stateTable[currentState][col];
 
        /* ===================================================
 
          THIS IS WHERE WE CHECK FOR A SUCCESSFUL PARSE
           - If the current state in our machine == REJECT
             (the starting state), then we have successfully parsed
             a token, which is returned to its caller
 
            - ELSE we continue trying to find a successful token
 
            =================================================== */
        if (currentState == REJECT)
        {
            if (currentToken != " ") // we dont care about whitespace
            {
                tokens.push_back(currentToken);
            }
            currentToken = "";
        }
        else
        {
            currentToken += currentChar;
            ++x;
        }
 
    }
    // this ensures the last token gets saved when
    // we reach the end of the postfix string buffer
    if (currentToken != " ") // we dont care about whitespace
    {
        tokens.push_back(currentToken);
    }
    return tokens;
}// end of Lexer
 
int Get_FSM_Col(char& currentChar)
{// this function determines the state of the type of character being examined
    // check for whitespace
    if (isspace(currentChar))
    {
        return SPACE;
    }
 
    // check for integer numbers
    else if (isdigit(currentChar))
    {
        return INTEGER;
    }
 
    // check for real numbers
    else if (currentChar == '.')
    {
        return REAL;
    }
 
    // check for negative numbers
    else if (currentChar == '~')
    {
        currentChar = '-';
        return NEGATIVE;
    }
 
    // check for math operators
    else if (IsMathOperator(currentChar))
    {
        return OPERATOR;
    }
    return UNKNOWN;
}// end of Get_FSM_Col
 
double EvaluatePostfix(const vector<string>& postfix)
{// this function evaluates a postfix expression
    // declare function variables
    double op1 = 0;
    double op2 = 0;
    double answer = 0;
    stack<double> doubleStack;
 
    cout << "\nCalculations:\n";
 
    // loop thru array until there is no more data
    for (unsigned x = 0; x < postfix.size(); ++x)
    {
        // push numbers onto the stack
        if ((isdigit(postfix[x][0])) || (postfix[x][0] == '.'))
        {
            doubleStack.push(atof(postfix[x].c_str()));
        }
        // push negative numbers onto the stack
        else if ((postfix[x].length() > 1) && ((postfix[x][0] == '-') &&
            (isdigit(postfix[x][1]) || (postfix[x][1] == '.'))))
        {
            doubleStack.push(atof(postfix[x].c_str()));
        }
        // if expression is a math operator, pop numbers from stack
        // & send the popped numbers to the 'Calculate' function
        else if (IsMathOperator(postfix[x][0]) && (!doubleStack.empty()))
        {
            char token = tolower(postfix[x][0]);
 
            // if expression is square root, sin, cos,
            // or tan operation only pop stack once
            if (token == '$' || token == 's' || token == 'c' || token == 't')
            {
                op2 = 0;
                op1 = doubleStack.top();
                doubleStack.pop();
                answer = Calculate(token, op1, op2);
                doubleStack.push(answer);
            }
            else if (doubleStack.size() > 1)
            {
                op2 = doubleStack.top();
                doubleStack.pop();
                op1 = doubleStack.top();
                doubleStack.pop();
                answer = Calculate(token, op1, op2);
                doubleStack.push(answer);
            }
        }
        else // this should never execute, & if it does, something went really wrong
        {
            cout << "\nINVALID INPUT #3\n";
            exit(1);
        }
    }
    // pop the final answer from the stack, and return to main
    if (!doubleStack.empty())
    {
        answer = doubleStack.top();
    }
    return answer;
}// end of EvaluatePostfix
 
double Calculate(char token, double op1, double op2)
{// this function carries out the actual math process
    double ans = 0;
    switch (tolower(token))
    {
    case '+':
        cout << op1 << token << op2 << " = ";
        ans = op1 + op2;
        break;
    case '-':
        cout << op1 << token << op2 << " = ";
        ans = op1 - op2;
        break;
    case '*':
        cout << op1 << token << op2 << " = ";
        ans = op1 * op2;
        break;
    case '/':
        cout << op1 << token << op2 << " = ";
        ans = op1 / op2;
        break;
    case '%':
        cout << op1 << token << op2 << " = ";
        ans = ((int)op1 % (int)op2) + modf(op1, &op2);
        break;
    case '^':
        cout << op1 << token << op2 << " = ";
        ans = pow(op1, op2);
        break;
    case '$':
        cout << char(251) << op1 << " = ";
        ans = sqrt(op1);
        break;
    case 'c':
        cout << "cos(" << op1 << ") = ";
        ans = cos(op1);
        break;
    case 's':
        cout << "sin(" << op1 << ") = ";
        ans = sin(op1);
        break;
    case 't':
        cout << "tan(" << op1 << ") = ";
        ans = tan(op1);
        break;
    default:
        ans = 0;
        break;
    }
    cout << ans << endl;
    return ans;
}// http://programmingnotes.org/

QUICK NOTES:
The highlighted lines are sections of interest to look out for.

The code is heavily commented, so no further insight is necessary. If you have any questions, feel free to leave a comment below.

The following is sample output.

====== RUN 1 ====== ==== Infix To Postfix Conversion & Evaluation ====
Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root s || Sine c || Cosine t || Tangent ~ || Negative Number Sample Infix Equation: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23)) Please enter an Infix expression: 12/3*9 The Infix expression = 12/3*9 The Postfix expression = 12 3 /9* Calculations: 12/3 = 4 4*9 = 36 Final answer = 36 ====== RUN 2 ====== ==== Infix To Postfix Conversion & Evaluation ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root s || Sine c || Cosine t || Tangent ~ || Negative Number Sample Infix Equation: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23)) Please enter an Infix expression: -150.89996 - 87.56643 The Infix expression = -150.89996 - 87.56643 The Postfix expression = ~150.89996 87.56643- Calculations: -150.9-87.5664 = -238.466 Final answer = -238.466 ====== RUN 3 ====== ==== Infix To Postfix Conversion & Evaluation ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root s || Sine c || Cosine t || Tangent ~ || Negative Number Sample Infix Equation: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23)) Please enter an Infix expression: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23)) The Infix expression = ((s(-4^5)*1.4)/($(23+2)--2.8))*(c(1%2)/(7.28*.1987)^(t23)) The Postfix expression = ~4 5^ s1.4* 23 2+ $~2.8-/ 1 2% c7.28 .1987* 23t^/* Calculations: -4^5 = -1024 sin(-1024) = 0.158533 0.158533*1.4 = 0.221947 23+2 = 25 √25 = 5 5--2.8 = 7.8 0.221947/7.8 = 0.0284547 1%2 = 1 cos(1) = 0.540302 7.28*0.1987 = 1.44654 tan(23) = 1.58815 1.44654^1.58815 = 1.79733 0.540302/1.79733 = 0.300614 0.0284547*0.300614 = 0.00855389 Final answer = 0.00855389 ====== RUN 4 ====== ==== Infix To Postfix Conversion & Evaluation ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root s || Sine c || Cosine t || Tangent - || Negative Number Sample Infix Equation: ((s(-4^5)*1.4)/($(23+2)--2.8))*(c(1%2)/(7.28*.1987)^(t23)) Please enter an Infix expression: (1987 + 1991) * -1 The Infix expression = (1987 + 1991) * -1 The Postfix expression = 1987 1991+ ~1* Calculations: 1987+1991 = 3978 3978*-1 = -3978 Final answer = -3978

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Posted in: Advanced, C++ Tags: array, c++, for loop, if/else, infix, postfix, template, While Loop

One Response to C++ || Multi Digit, Decimal & Negative Number Infix To Postfix Conversion & Evaluation

Dharam Singh Thakur says:

August 9, 2014 at 8:28 pm

How do I evaluate a postfix epression having negative numbers? – Quora

Go to this link ……http://programmingnotes.freeweq….

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C++ || Multi Digit, Decimal & Negative Number Infix To Postfix Conversion & Evaluation

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