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

February 05, 2021 admin No comments

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

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.

REQUIRED KNOWLEDGE FOR THIS PROGRAM

How To Convert Infix To Postfix How To Evaluate A Postfix Expression

1. Overview

The program demonstrated on this page is different from a previous implementation of the same type in that this version does not use a Finite State Machine during the conversion process, which simplifies the implemetation!

This program has the following flow of control:

• Get an infix expression from the user • Convert the infix expression to postfix & 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 by breaking the infix string into tokens found from the above step • Display the evaluated answer to the screen

The above steps are implemented below.

2. Infix To Posfix Conversion & Evaluation





		
		
			Multi Digit Infix To Postfix Conversion & Evaluation
			
C++
			
			// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Jan 31, 2014
//    Updated: Feb 5, 2021
//    Taken From: http://programmingnotes.org/
//    File: InToPostEval.cpp
//    Description: The following demonstrates the implementation of an infix to
//      postfix converter and evaluator. 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>
#include <exception>
#include <stdexcept>

// function prototypes
void displayDirections();
std::string convertInfixToPostfix(std::string infix);
bool isMathOperator(char token);
int orderOfOperations(char token);
double evaluatePostfix(const std::string& postfix);
double calculate(char mathOperator, double value1, double value2);
bool isNumeric(char value);
bool isNumeric(std::string value);
std::vector<std::string> split(const std::string& source, const std::string& delimiters = " ");
std::string replaceAll(const std::string& source
    , const std::string& oldValue, const std::string& newValue);

int main() {
    // declare variables
    std::string infix = "";

    // display directions to user
    displayDirections();

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

        // convert infix to postfix
        std::string postfix = convertInfixToPostfix(infix);

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

        // evaluate the postfix string
        double answer = evaluatePostfix(postfix);

        std::cout << "\nFinal answer = " << answer << std::endl;
    } catch (std::exception& e) {
        std::cout << "\nAn error occurred: " + std::string(e.what()) << std::endl;
    }

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

void displayDirections() {
// this function displays instructions to the screen
    std::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

std::string convertInfixToPostfix(std::string infix) {
// this function converts an infix expression to postfix
        // declare function variables
    std::string postfix;
    std::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());

    // negate equations marked with '--'
    infix = replaceAll(infix, "(--", "(");

    // automatically convert negative numbers to have the ~ symbol.
    // this is done so we can distinguish negative numbers and the subtraction symbol
    for (unsigned x = 0; x < infix.length(); ++x) {
        if (infix[x] != '-') {
            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 (isNumeric(infix[x])) {
            if (postfix.length() > 0 && !isNumeric(postfix.back())) {
                if (!std::isspace(postfix.back())) {
                    postfix += " ";
                }
            }
            postfix += infix[x];

        } else if (std::isspace(infix[x])) {
            continue;

        } else if (isMathOperator(infix[x])) {
            if (postfix.length() > 0 && !std::isspace(postfix.back())) {
                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
                if (postfix.length() > 0 && !std::isspace(postfix.back())) {
                    postfix += " ";
                }
                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() != '(')) {
                if (postfix.length() > 0 && !std::isspace(postfix.back())) {
                    postfix += " ";
                }
                // 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();
            }

            // pop '(' symbol off the stack
            if (!charStack.empty()) {
                charStack.pop();
            } else {
                // no matching '('
                throw std::invalid_argument{ "PARENTHESES MISMATCH" };
            }
        } else {
            throw std::invalid_argument{ "INVALID INPUT" };
        }
    }

    // place any remaining math operators from the stack onto
    // the postfix array
    while (!charStack.empty()) {
        if (charStack.top() == '(' || charStack.top() == ')') {
            throw std::invalid_argument{ "PARENTHESES MISMATCH" };
        }
        if (postfix.length() > 0 && !std::isspace(postfix.back())) {
            postfix += " ";
        }
        postfix += charStack.top();
        charStack.pop();
    }

    // replace all '~' symbols with a minus sign
    postfix = replaceAll(postfix, "~", "-");

    return postfix;
}// end of convertInfixToPostfix

bool isMathOperator(char token) {
// this function checks if operand is a math operator
    switch (std::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 (std::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

double evaluatePostfix(const std::string& postfix) {
// this function evaluates a postfix expression
    // declare function variables
    double answer = 0;
    std::stack<double> doubleStack;

    // split string into tokens to isolate multi digit, negative and decimal
    // numbers, aswell as single digit numbers and math operators
    auto tokens = split(postfix);

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

    std::cout << "\nCalculations:\n";

    // loop thru array until there is no more data
    for (unsigned x = 0; x < tokens.size(); ++x) {
        auto token = tokens[x];

        // push numbers & negative numbers onto the stack
        if (isNumeric(token)) {
            doubleStack.push(std::atof(token.c_str()));
        }
        // if expression is a math operator, pop numbers from stack
        // & send the popped numbers to the 'calculate' function
        else if (isMathOperator(token[0]) && (!doubleStack.empty())) {
            double value1 = 0;
            double value2 = 0;
            char mathOperator = static_cast<unsigned char>(std::tolower(token[0]));

            // if expression is square root, sin, cos,
            // or tan operation only pop stack once
            if (mathOperator == '$' || mathOperator == 's' || mathOperator == 'c' || mathOperator == 't') {
                value2 = 0;
                value1 = doubleStack.top();
                doubleStack.pop();
                answer = calculate(mathOperator, value1, value2);
                doubleStack.push(answer);

            } else if (doubleStack.size() > 1) {
                value2 = doubleStack.top();
                doubleStack.pop();
                value1 = doubleStack.top();
                doubleStack.pop();
                answer = calculate(mathOperator, value1, value2);
                doubleStack.push(answer);
            }
        } else {
            // this should never execute, & if it does, something went really wrong
            throw std::invalid_argument{ "INVALID POSTFIX STRING" };
        }
    }
    // 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 mathOperator, double value1, double value2) {
// this function carries out the actual math process
    double ans = 0;
    switch (std::tolower(mathOperator)) {
        case '+':
            std::cout << value1 << mathOperator << value2;
            ans = value1 + value2;
            break;
        case '-':
            std::cout << value1 << mathOperator << value2;
            ans = value1 - value2;
            break;
        case '*':
            std::cout << value1 << mathOperator << value2;
            ans = value1 * value2;
            break;
        case '/':
            std::cout << value1 << mathOperator << value2;
            ans = value1 / value2;
            break;
        case '%':
            std::cout << value1 << mathOperator << value2;
            ans = ((int)value1 % (int)value2) + std::modf(value1, &value2);
            break;
        case '^':
            std::cout << value1 << mathOperator << value2;
            ans = std::pow(value1, value2);
            break;
        case '$':
            std::cout << char(251) << value1;
            ans = std::sqrt(value1);
            break;
        case 'c':
            std::cout << "cos(" << value1 << ")";
            ans = std::cos(value1);
            break;
        case 's':
            std::cout << "sin(" << value1 << ")";
            ans = std::sin(value1);
            break;
        case 't':
            std::cout << "tan(" << value1 << ")";
            ans = std::tan(value1);
            break;
        default:
            ans = 0;
            break;
    }
    std::cout << " = " << ans << std::endl;
    return ans;
}// end of calculate

std::vector<std::string> split(const std::string& source, const std::string& delimiters) {
    std::size_t prev = 0;
    std::size_t currentPos = 0;
    std::vector<std::string> results;

    while ((currentPos = source.find_first_of(delimiters, prev)) != std::string::npos) {
        if (currentPos > prev) {
            results.push_back(source.substr(prev, currentPos - prev));
        }
        prev = currentPos + 1;
    }
    if (prev < source.length()) {
        results.push_back(source.substr(prev, std::string::npos));
    }
    return results;
}// end of split

std::string replaceAll(const std::string& source
    , const std::string& oldValue, const std::string& newValue) {
    if (oldValue.empty()) {
        return source;
    }
    std::string newString;
    newString.reserve(source.length());
    std::size_t lastPos = 0;
    std::size_t findPos;
    while (std::string::npos != (findPos = source.find(oldValue, lastPos))) {
        newString.append(source, lastPos, findPos - lastPos);
        newString += newValue;
        lastPos = findPos + oldValue.length();
    }
    newString += source.substr(lastPos);
    return newString;
}// end of replaceAll

bool isNumeric(char value) {
    return std::isdigit(value) || value == '.' || value == '~';
}// end of isNumeric

bool isNumeric(std::string value) {
    for (unsigned index = 0; index < value.length(); ++index) {
        if (index == 0 && value[index] == '-' && value.length() > 1) {
            continue;
        }
        if (!isNumeric(value[index])) {
            return false;
        }
    }
    return true;
}// http://programmingnotes.org/
			
				
					
				
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						// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Jan 31, 2014
//    Updated: Feb 5, 2021
//    Taken From: http://programmingnotes.org/
//    File: InToPostEval.cpp
//    Description: The following demonstrates the implementation of an infix to
//      postfix converter and evaluator. 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>
#include <exception>
#include <stdexcept>
 
// function prototypes
void displayDirections();
std::string convertInfixToPostfix(std::string infix);
bool isMathOperator(char token);
int orderOfOperations(char token);
double evaluatePostfix(const std::string& postfix);
double calculate(char mathOperator, double value1, double value2);
bool isNumeric(char value);
bool isNumeric(std::string value);
std::vector<std::string> split(const std::string& source, const std::string& delimiters = " ");
std::string replaceAll(const std::string& source
    , const std::string& oldValue, const std::string& newValue);
 
int main() {
    // declare variables
    std::string infix = "";
 
    // display directions to user
    displayDirections();
 
    try {
        // get data from user
        std::cout << "\nPlease enter an Infix expression: ";
        std::getline(std::cin, infix);
 
        // convert infix to postfix
        std::string postfix = convertInfixToPostfix(infix);
 
        std::cout << "\nThe Infix expression = " << infix;
        std::cout << "\nThe Postfix expression = " << postfix << std::endl;
 
        // evaluate the postfix string
        double answer = evaluatePostfix(postfix);
 
        std::cout << "\nFinal answer = " << answer << std::endl;
    } catch (std::exception& e) {
        std::cout << "\nAn error occurred: " + std::string(e.what()) << std::endl;
    }
 
    std::cin.get();
    return 0;
}// end of main
 
void displayDirections() {
// this function displays instructions to the screen
    std::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
 
std::string convertInfixToPostfix(std::string infix) {
// this function converts an infix expression to postfix
        // declare function variables
    std::string postfix;
    std::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());
 
    // negate equations marked with '--'
    infix = replaceAll(infix, "(--", "(");
 
    // automatically convert negative numbers to have the ~ symbol.
    // this is done so we can distinguish negative numbers and the subtraction symbol
    for (unsigned x = 0; x < infix.length(); ++x) {
        if (infix[x] != '-') {
            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 (isNumeric(infix[x])) {
            if (postfix.length() > 0 && !isNumeric(postfix.back())) {
                if (!std::isspace(postfix.back())) {
                    postfix += " ";
                }
            }
            postfix += infix[x];
 
        } else if (std::isspace(infix[x])) {
            continue;
 
        } else if (isMathOperator(infix[x])) {
            if (postfix.length() > 0 && !std::isspace(postfix.back())) {
                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
                if (postfix.length() > 0 && !std::isspace(postfix.back())) {
                    postfix += " ";
                }
                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() != '(')) {
                if (postfix.length() > 0 && !std::isspace(postfix.back())) {
                    postfix += " ";
                }
                // 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();
            }
 
            // pop '(' symbol off the stack
            if (!charStack.empty()) {
                charStack.pop();
            } else {
                // no matching '('
                throw std::invalid_argument{ "PARENTHESES MISMATCH" };
            }
        } else {
            throw std::invalid_argument{ "INVALID INPUT" };
        }
    }
 
    // place any remaining math operators from the stack onto
    // the postfix array
    while (!charStack.empty()) {
        if (charStack.top() == '(' || charStack.top() == ')') {
            throw std::invalid_argument{ "PARENTHESES MISMATCH" };
        }
        if (postfix.length() > 0 && !std::isspace(postfix.back())) {
            postfix += " ";
        }
        postfix += charStack.top();
        charStack.pop();
    }
 
    // replace all '~' symbols with a minus sign
    postfix = replaceAll(postfix, "~", "-");
 
    return postfix;
}// end of convertInfixToPostfix
 
bool isMathOperator(char token) {
// this function checks if operand is a math operator
    switch (std::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 (std::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
 
double evaluatePostfix(const std::string& postfix) {
// this function evaluates a postfix expression
    // declare function variables
    double answer = 0;
    std::stack<double> doubleStack;
 
    // split string into tokens to isolate multi digit, negative and decimal
    // numbers, aswell as single digit numbers and math operators
    auto tokens = split(postfix);
 
    // display the found tokens to the screen
    //for (unsigned x = 0; x < tokens.size(); ++x) {
    //    std::cout<< tokens.at(x) << std::endl;
    //}
 
    std::cout << "\nCalculations:\n";
 
    // loop thru array until there is no more data
    for (unsigned x = 0; x < tokens.size(); ++x) {
        auto token = tokens[x];
 
        // push numbers & negative numbers onto the stack
        if (isNumeric(token)) {
            doubleStack.push(std::atof(token.c_str()));
        }
        // if expression is a math operator, pop numbers from stack
        // & send the popped numbers to the 'calculate' function
        else if (isMathOperator(token[0]) && (!doubleStack.empty())) {
            double value1 = 0;
            double value2 = 0;
            char mathOperator = static_cast<unsigned char>(std::tolower(token[0]));
 
            // if expression is square root, sin, cos,
            // or tan operation only pop stack once
            if (mathOperator == '$' || mathOperator == 's' || mathOperator == 'c' || mathOperator == 't') {
                value2 = 0;
                value1 = doubleStack.top();
                doubleStack.pop();
                answer = calculate(mathOperator, value1, value2);
                doubleStack.push(answer);
 
            } else if (doubleStack.size() > 1) {
                value2 = doubleStack.top();
                doubleStack.pop();
                value1 = doubleStack.top();
                doubleStack.pop();
                answer = calculate(mathOperator, value1, value2);
                doubleStack.push(answer);
            }
        } else {
            // this should never execute, & if it does, something went really wrong
            throw std::invalid_argument{ "INVALID POSTFIX STRING" };
        }
    }
    // 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 mathOperator, double value1, double value2) {
// this function carries out the actual math process
    double ans = 0;
    switch (std::tolower(mathOperator)) {
        case '+':
            std::cout << value1 << mathOperator << value2;
            ans = value1 + value2;
            break;
        case '-':
            std::cout << value1 << mathOperator << value2;
            ans = value1 - value2;
            break;
        case '*':
            std::cout << value1 << mathOperator << value2;
            ans = value1 * value2;
            break;
        case '/':
            std::cout << value1 << mathOperator << value2;
            ans = value1 / value2;
            break;
        case '%':
            std::cout << value1 << mathOperator << value2;
            ans = ((int)value1 % (int)value2) + std::modf(value1, &value2);
            break;
        case '^':
            std::cout << value1 << mathOperator << value2;
            ans = std::pow(value1, value2);
            break;
        case '$':
            std::cout << char(251) << value1;
            ans = std::sqrt(value1);
            break;
        case 'c':
            std::cout << "cos(" << value1 << ")";
            ans = std::cos(value1);
            break;
        case 's':
            std::cout << "sin(" << value1 << ")";
            ans = std::sin(value1);
            break;
        case 't':
            std::cout << "tan(" << value1 << ")";
            ans = std::tan(value1);
            break;
        default:
            ans = 0;
            break;
    }
    std::cout << " = " << ans << std::endl;
    return ans;
}// end of calculate
 
std::vector<std::string> split(const std::string& source, const std::string& delimiters) {
    std::size_t prev = 0;
    std::size_t currentPos = 0;
    std::vector<std::string> results;
 
    while ((currentPos = source.find_first_of(delimiters, prev)) != std::string::npos) {
        if (currentPos > prev) {
            results.push_back(source.substr(prev, currentPos - prev));
        }
        prev = currentPos + 1;
    }
    if (prev < source.length()) {
        results.push_back(source.substr(prev, std::string::npos));
    }
    return results;
}// end of split
 
std::string replaceAll(const std::string& source
    , const std::string& oldValue, const std::string& newValue) {
    if (oldValue.empty()) {
        return source;
    }
    std::string newString;
    newString.reserve(source.length());
    std::size_t lastPos = 0;
    std::size_t findPos;
    while (std::string::npos != (findPos = source.find(oldValue, lastPos))) {
        newString.append(source, lastPos, findPos - lastPos);
        newString += newValue;
        lastPos = findPos + oldValue.length();
    }
    newString += source.substr(lastPos);
    return newString;
}// end of replaceAll
 
bool isNumeric(char value) {
    return std::isdigit(value) || value == '.' || value == '~';
}// end of isNumeric
 
bool isNumeric(std::string value) {
    for (unsigned index = 0; index < value.length(); ++index) {
        if (index == 0 && value[index] == '-' && value.length() > 1) {
            continue;
        }
        if (!isNumeric(value[index])) {
            return false;
        }
    }
    return true;
}// 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 ^ s 1.4 * 23 2 + $ -2.8 - / 1 2 % c 7.28 .1987 * 23 t ^ / * 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 ====== RUN 5 ====== ==== 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: (1+(2*((3+(4*5))*6))) The Infix expression = (1+(2*((3+(4*5))*6))) The Postfix expression = 1 2 3 4 5 * + 6 * * + Calculations: 4*5 = 20 3+20 = 23 23*6 = 138 2*138 = 276 1+276 = 277 Final answer = 277

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

C++ || Stack Based Postfix Evaluation (Single Digit)

March 24, 2012 admin No comments

This page consists of another homework assignment which was presented in a C++ Data Structures course. While the previously discussed program dealt with converting Infix expressions to Postfix, this program will demonstrate exactly how to evaluate them.

NOTE: Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

REQUIRED KNOWLEDGE FOR THIS PROGRAM

What Is Postfix? How To Convert Infix To Postfix Equations Stack Data Structure Cin.getline How To Evaluate Postfix Expressions The Order Of Operations #include "ClassStackType.h"

The title of this page is called – “Stack Based Postfix Evaluation (Single Digit).” Why “single digit?” The program demonstrated on this page has the ability to evaluate a postfix equation, but it only has the ability to evaluate single digit values. What do I mean by that? Consider the infix equation: 5+2. When that expression is converted to postfix, it will come out to be: 52+, and the answer will be 7 (5+2=7). But what if we have an equation like 12+2? When that expression is converted to postfix, it will come out to be: 122+. The postfix conversion is correct, but when you try to evaluate the expression, we do not know if the math operation should be 12+2 or 1+22, it can be read either way.

Question: So why is this program being displayed if it only works for single digits?
Answer: Because it demonstrates the process of evaluating postfix equations very well.

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

Before we get into things, here is a helpful algorithm for evaluating a postfix expression in pseudo code:





		
		
			// An algorithm for postfix evaluation.
// For example,  (1 + 2) / (5 + 6) translates to  1 2 + 5 6 + /
// which equals the result of 0.272727
// Valid operands are single digits: 0-9
// Valid operators are: +, -, *, /, ^, $
// Highest precedence: ^, $
// Lowest precedence: +,-
// the operators ')' and '('never goes on stack.

double EvaluatePostfix(string postfix)
{
  while there is input
  {
    if input is a number
        push current number on stack
    else if input is a math operator and stack is not empty
        set operand2 to the top of the operand stack
            pop the stack
        set operand1 to the top of the operand stack
            pop the stack
        apply the math operation that represents to operand1 and operand2
            push the result onto the stack
    else error
  }
  // When the loop is finished, the operand stack will contain one item,
  // the result of evaluating the expression
  pop the stack
  return the answer to the caller
}// http://programmingnotes.org/
			
				
					
				
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						// An algorithm for postfix evaluation.
// For example,  (1 + 2) / (5 + 6) translates to  1 2 + 5 6 + /
// which equals the result of 0.272727
// Valid operands are single digits: 0-9
// Valid operators are: +, -, *, /, ^, $
// Highest precedence: ^, $
// Lowest precedence: +,-
// the operators ')' and '('never goes on stack.
 
double EvaluatePostfix(string postfix)
{
  while there is input
  {
    if input is a number
        push current number on stack
    else if input is a math operator and stack is not empty
        set operand2 to the top of the operand stack
            pop the stack
        set operand1 to the top of the operand stack
            pop the stack
        apply the math operation that represents to operand1 and operand2
            push the result onto the stack
    else error
  }
  // When the loop is finished, the operand stack will contain one item,
  // the result of evaluating the expression
  pop the stack
  return the answer to the caller
}// http://programmingnotes.org/

Once you understand the process of converting from infix to postfix, adding the ability to evaluate multiple digits within this program should be doable.

======= POSTFIX EVALUATION =======

This program uses a custom template.h class. To obtain the code for that class, click here.





		
		
			Postfix Evaluation (Single Digit)
			
C++
			
			// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Mar 24, 2012
//    Taken From: http://programmingnotes.org/
//    File:  PostfixEvaluation.cpp
//    Description: Demonstrate the use of a stack based postfix evaluation.
// ============================================================================
#include <iostream>
#include <cstdlib>
#include <cmath>
#include "ClassStackType.h"
using namespace std;

// function prototypes
void DisplayDirections();
double EvaluatePostfix(char* postfix);
bool IsMathOperator(char token);
double DoMath(double op1, double op2, char token);

int main()
{
     // declare variables
     char expression[50]; // array holding the postfix data
     double answer = 0;

     // display directions to user
     DisplayDirections();

     // get data from user
     cout<<"\nPlease enter a postfix expression: ";
     cin.getline(expression, sizeof(expression));

     cout <<"\nThe postfix expression = "<<expression<<endl;

     cout<<"\nCalculations:\n";

     answer = EvaluatePostfix(expression);

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

     return 0;
}// end of main

void DisplayDirections()
{
     cout << "\n==== Postfix Evaluation ====\n"
         <<"\nMath Operators:\n"
         <<"+ || Addition\n"
         <<"- || Subtraction\n"
         <<"* || Multiplication\n"
         <<"/ || Division\n"
         <<"% || Modulus\n"
         <<"^ || Power\n"
         <<"$ || Square Rootn\n"
         <<"Sample Postfix Equation: 45^14*232+$2-/12%24*/* \n";
}// end of DisplayDirections

double EvaluatePostfix(char* postfix)
{
    // declare function variables
    int counter = 0;
    int currentNum = 0;
    char token = 'a';
    double op1 = 0;
    double op2 = 0;
    double answer = 0;
    StackType<double> doubleStack;

    // loop thru array until there is no more data
    while(postfix[counter] != '\0')
    {
        // push numbers onto the stack
        if(isdigit(postfix[counter]))
        {
            currentNum = postfix[counter] - '0';
            doubleStack.Push(currentNum);
        }
        else if(isspace(postfix[counter]))
        {
            // DO NOTHING
        }
        // if expression is a math operator, pop numbers from stack
        // & send the popped numbers to the 'DoMath' function
        else if((IsMathOperator(postfix[counter])) && (!doubleStack.IsEmpty()))
        {
            token = postfix[counter];

            // if expression is square root operation
            // only pop stack once
            if(token == '$')
            {
                op2 = 0;
                op1 = doubleStack.Top();
                doubleStack.Pop();

                answer = DoMath(op1,op2,token);
                doubleStack.Push(answer);
            }
            else
            {
                op2 = doubleStack.Top();
                doubleStack.Pop();
                op1 = doubleStack.Top();
                doubleStack.Pop();

                answer = DoMath(op1,op2,token);
                doubleStack.Push(answer);
            }
        }
        else
        {
            cout<<"\nINVALID INPUT\n";
            exit(1);
        }
        ++counter;
    }
    // pop the final answer from the stack, and return to main
    answer = doubleStack.Top();
    doubleStack.Pop();

    return answer;
}// end of EvaluatePostfix

bool IsMathOperator(char token)
{// this function checks if operand is a math operator
     switch(token)
     {
        case '+':
            return true;
            break;
        case '-':
            return true;
            break;
        case '*':
            return true;
            break;
        case '/':
            return true;
            break;
        case '%':
            return true;
            break;
        case '^':
            return true;
            break;
        case '$':
            return true;
            break;
        default:
            return false;
            break;
     }
}// end of IsMathOperator

double DoMath(double op1, double op2, char token)
{// this function carries out the actual math process
    double ans = 0;
    switch(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;
            break;
        case '^':
            cout<<op1<<token<<op2<<" = ";
            ans = pow(op1, op2);
            break;
        case '$':
            cout<<char(251)<<op1<<" = ";
            ans = sqrt(op1);
            break;
        default:
            ans = 0;
            break;
    }
    cout<<ans<<endl;
    return ans;
}// http://programmingnotes.org/
			
				
					
				
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						// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Mar 24, 2012
//    Taken From: http://programmingnotes.org/
//    File:  PostfixEvaluation.cpp
//    Description: Demonstrate the use of a stack based postfix evaluation.
// ============================================================================
#include <iostream>
#include <cstdlib>
#include <cmath>
#include "ClassStackType.h"
using namespace std;
 
// function prototypes
void DisplayDirections();
double EvaluatePostfix(char* postfix);
bool IsMathOperator(char token);
double DoMath(double op1, double op2, char token);
 
int main()
{
     // declare variables
     char expression[50]; // array holding the postfix data
     double answer = 0;
 
     // display directions to user
     DisplayDirections();
 
     // get data from user
     cout<<"\nPlease enter a postfix expression: ";
     cin.getline(expression, sizeof(expression));
 
     cout <<"\nThe postfix expression = "<<expression<<endl;
 
     cout<<"\nCalculations:\n";
 
     answer = EvaluatePostfix(expression);
 
     cout<<"\nFinal answer = "<<answer<<endl;
 
     return 0;
}// end of main
 
void DisplayDirections()
{
     cout << "\n==== Postfix Evaluation ====\n"
         <<"\nMath Operators:\n"
         <<"+ || Addition\n"
         <<"- || Subtraction\n"
         <<"* || Multiplication\n"
         <<"/ || Division\n"
         <<"% || Modulus\n"
         <<"^ || Power\n"
         <<"$ || Square Rootn\n"
         <<"Sample Postfix Equation: 45^14*232+$2-/12%24*/* \n";
}// end of DisplayDirections
 
double EvaluatePostfix(char* postfix)
{
    // declare function variables
    int counter = 0;
    int currentNum = 0;
    char token = 'a';
    double op1 = 0;
    double op2 = 0;
    double answer = 0;
    StackType<double> doubleStack;
 
    // loop thru array until there is no more data
    while(postfix[counter] != '\0')
    {
        // push numbers onto the stack
        if(isdigit(postfix[counter]))
        {
            currentNum = postfix[counter] - '0';
            doubleStack.Push(currentNum);
        }
        else if(isspace(postfix[counter]))
        {
            // DO NOTHING
        }
        // if expression is a math operator, pop numbers from stack
        // & send the popped numbers to the 'DoMath' function
        else if((IsMathOperator(postfix[counter])) && (!doubleStack.IsEmpty()))
        {
            token = postfix[counter];
 
            // if expression is square root operation
            // only pop stack once
            if(token == '$')
            {
                op2 = 0;
                op1 = doubleStack.Top();
                doubleStack.Pop();
 
                answer = DoMath(op1,op2,token);
                doubleStack.Push(answer);
            }
            else
            {
                op2 = doubleStack.Top();
                doubleStack.Pop();
                op1 = doubleStack.Top();
                doubleStack.Pop();
 
                answer = DoMath(op1,op2,token);
                doubleStack.Push(answer);
            }
        }
        else
        {
            cout<<"\nINVALID INPUT\n";
            exit(1);
        }
        ++counter;
    }
    // pop the final answer from the stack, and return to main
    answer = doubleStack.Top();
    doubleStack.Pop();
 
    return answer;
}// end of EvaluatePostfix
 
bool IsMathOperator(char token)
{// this function checks if operand is a math operator
     switch(token)
     {
        case '+':
            return true;
            break;
        case '-':
            return true;
            break;
        case '*':
            return true;
            break;
        case '/':
            return true;
            break;
        case '%':
            return true;
            break;
        case '^':
            return true;
            break;
        case '$':
            return true;
            break;
        default:
            return false;
            break;
     }
}// end of IsMathOperator
 
double DoMath(double op1, double op2, char token)
{// this function carries out the actual math process
    double ans = 0;
    switch(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;
            break;
        case '^':
            cout<<op1<<token<<op2<<" = ";
            ans = pow(op1, op2);
            break;
        case '$':
            cout<<char(251)<<op1<<" = ";
            ans = sqrt(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.

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

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

Once compiled, you should get this as your output
(Note: the code was compile three separate times to display different output)

====== RUN 1 ======
==== Postfix Evaluation ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root Sample Postfix Equation: 45^14*232+$2-/12%24*/* Please enter a postfix expression: 1 2 + 5 6 + / The postfix expression = 1 2 + 5 6 + / Calculations: 1+2 = 3 5+6 = 11 3/11 = 0.272727 Final answer = 0.272727 ====== RUN 2 ====== ==== Postfix Evaluation ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root Sample Postfix Equation: 45^14*232+$2-/12%24*/* Please enter a postfix expression: 35*76^+ The postfix expression = 35*76^+ Calculations: 3*5 = 15 7^6 = 117649 15+117649 = 117664 Final answer = 117664 ====== RUN 3 ====== ==== Postfix Evaluation ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root Sample Postfix Equation: 45^14*232+$2-/12%24*/* Please enter a postfix expression: 45^4*32+$2-/12%24*/* The postfix expression = 45^4*32+$2-/12%24*/*
Calculations: 4^5 = 1024 1024*4 = 4096 3+2 = 5 √5 = 2.23607 2.23607-2 = 0.236068 4096/0.236068 = 17350.9 1%2 = 1 2*4 = 8 1/8 = 0.125 17350.9*0.125 = 2168.87 Final answer = 2168.87

C++ || Stack Based Infix To Postfix Conversion (Single Digit)

March 23, 2012 admin 4 Comments

This page consists of another homework assignment which was presented in a C++ Data Structures course. No matter which institution you attend, it seems every instructor assigns a program similar to this at one time or another.

Want to evaluate a postfix expression? Click here.

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

REQUIRED KNOWLEDGE FOR THIS PROGRAM

What Is Infix? What Is Postfix? Stack Data Structure Cin.getline How To Convert To Postfix The Order Of Operations #include "ClassStackType.h"

The program demonstrated on this page has the ability to convert a normal infix equation to postfix equation, so for example, if the user enters the infix equation of (1*2)+3, the program will display the postfix result of 12*3+.

Before we get into things, here is a helpful algorithm for converting from infix to postfix in pseudo code:





		
		
			// An algorithm for infix to postfix expression conversion.
// For example,   a + b - c     translates to   a b + c -
//                a + b * c     translates to   a b c * +
//                (1 + 2) / (5 + 6)   goes to   1 2 + 5 6 + /
// Valid operands are single digits: 0-9, a-z, A-Z
// Valid operators are: +, -, *, /, (, ), ^, $
// Highest precedence:   ^, $
// Lowest precedence:    +,-
// ) never goes on stack.
// ( has lowest precedence on the stack and highest precedence outside of stack.
// Bottom of the stack has the lowest precedence than any operator.
// Use a prec() function to compare the precedence of the operators based on the above rules.
// Note there is little error checking in the algorithm!

void ConvertInfixToPostfix(string infix)
{
  while there is input
  {
    if input is a number or a letter
        place onto postfix string
    else
        if input is '('  // '(' has lowest precedence in the stack, highest outside
            push input on stack
        else if input is ')'
            while stack is not empty and top of stack is not '('
                place item from top of stack onto postfix string
                pop stack
            if stack is not empty // pops '(' off the stack
                pop stack
            else error  // no matching '('
        else if input is a math operator
            if stack is empty
                push input on stack
            else
                if prec(top of stack) >= prec(current math operator)
                    while stack is not empty and prec(top of stack) >= prec(current math operator)
                        place item from top of stack onto postfix string
                        pop stack
                push current math operator on stack
        else error
  }
  while stack is not empty
  {
    place item from top of stack onto postfix string
    pop stack
  }
}// http://programmingnotes.org/
			
				
					
				
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						// An algorithm for infix to postfix expression conversion.
// For example,   a + b - c     translates to   a b + c -
//                a + b * c     translates to   a b c * +
//                (1 + 2) / (5 + 6)   goes to   1 2 + 5 6 + /
// Valid operands are single digits: 0-9, a-z, A-Z
// Valid operators are: +, -, *, /, (, ), ^, $
// Highest precedence:   ^, $
// Lowest precedence:    +,-
// ) never goes on stack.
// ( has lowest precedence on the stack and highest precedence outside of stack.
// Bottom of the stack has the lowest precedence than any operator.
// Use a prec() function to compare the precedence of the operators based on the above rules.
// Note there is little error checking in the algorithm!
 
void ConvertInfixToPostfix(string infix)
{
  while there is input
  {
    if input is a number or a letter
        place onto postfix string
    else
        if input is '('  // '(' has lowest precedence in the stack, highest outside
            push input on stack
        else if input is ')'
            while stack is not empty and top of stack is not '('
                place item from top of stack onto postfix string
                pop stack
            if stack is not empty // pops '(' off the stack
                pop stack
            else error  // no matching '('
        else if input is a math operator
            if stack is empty
                push input on stack
            else
                if prec(top of stack) >= prec(current math operator)
                    while stack is not empty and prec(top of stack) >= prec(current math operator)
                        place item from top of stack onto postfix string
                        pop stack
                push current math operator on stack
        else error
  }
  while stack is not empty
  {
    place item from top of stack onto postfix string
    pop stack
  }
}// http://programmingnotes.org/

======= INFIX TO POSTFIX CONVERSION =======

This program uses a custom template.h class. To obtain the code for that class, click here.





		
		
			Infix To Postfix Conversion (Single Digit)
			
C++
			
			// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Mar 23, 2012
//    Taken From: http://programmingnotes.org/
//    File:  PostfixConversion.cpp
//    Description: Demonstrate the use of a stack based infix to 
//         postfix conversion.
// ============================================================================
#include <iostream>
#include <cctype>
#include <cstdlib>
#include <cstring>
#include "ClassStackType.h"
using namespace std;

// function prototypes
void DisplayDirections();
void ConvertInfixToPostfix(char* infix);
int OrderOfOperations(char token);
bool IsMathOperator(char token);

int main()
{
    // declare variables
    char expression[50]; // array holding the infix data
    
    // display directions to user
    DisplayDirections();
    
    // get data from user
    cout<<"\nPlease enter an infix expression: ";
    cin.getline(expression, sizeof(expression));
    
    cout <<"\nThe Infix expression = "<<expression<<endl;
    
    ConvertInfixToPostfix(expression);
    
    cout<<"The Postfix expression = "<<expression<<endl;
    
    return 0;
}// end of main

void DisplayDirections()
{
    cout << "\n==== Infix to Postfix Conversion ====\n"
        <<"\nMath Operators:\n"
        <<"+ || Addition\n"
        <<"- || Subtraction\n"
        <<"* || Multiplication\n"
        <<"/ || Division\n"
        <<"% || Modulus\n"
        <<"^ || Power\n"
        <<"$ || Square Root\n"
        <<"Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)\n";
}// end of DisplayDirections

void ConvertInfixToPostfix(char* infix)
{
    // declare function variables
    int infixCounter = 0;
    int postfixCounter = 0;
    char token = 'a';
    char postfix[50];
    StackType<char> charStack;
    
    // loop thru array until there is no more data
    while(infix[infixCounter] != '\0')
    {
        // push numbers/letters onto 'postfix' array
        if(isdigit(infix[infixCounter]) || isalpha(infix[infixCounter]))
        {
            postfix[postfixCounter] = infix[infixCounter];
            ++postfixCounter;
        }
        else if(isspace(infix[infixCounter]))
        {
            // DO NOTHING
        }
        else if(IsMathOperator(infix[infixCounter]))
        {
            // if stack is empty, place first math operator onto stack
            token = infix[infixCounter];
            if(charStack.IsEmpty())
            {
                charStack.Push(token);
            }
            else
            {
                // get the current math operator from the top of the stack
                token = charStack.Top();
                charStack.Pop(); 
                
                // use the 'OrderOfOperations' function to check equality
                // of the math operators
                while(OrderOfOperations(token) >= OrderOfOperations(infix[infixCounter]))
                {
                    // if stack is empty, do nothing
                    if(charStack.IsEmpty())
                    {
                        break;
                    }
                    // place the popped math operator from above ^
                    // onto the postfix array
                    else
                    {
                        postfix[postfixCounter] = token;
                        ++postfixCounter;
                        // pop the next operator from the stack and 
                        // continue the process until complete
                        token = charStack.Top();
                        charStack.Pop();
                    }
                }
                // push any remainding math operators onto the stack
                charStack.Push(token);
                charStack.Push(infix[infixCounter]);
            }
        }
        // push outer parentheses onto stack
        else if(infix[infixCounter] == '(')
        {
            charStack.Push(infix[infixCounter]);
        }
        else if(infix[infixCounter] == ')')
        {
            // pop the current math operator from the stack
            token = charStack.Top();
            charStack.Pop();
            while(token != '(' && !charStack.IsEmpty())
            {
                // place the math operator onto the postfix array
                postfix[postfixCounter] = token;
                ++postfixCounter; 
                // pop the next operator from the stack and
                // continue the process until complete
                token = charStack.Top();
                charStack.Pop();
            }
        }
        else
        {
            cout<<"\nINVALID INPUT\n";
            exit(1);
        }
        ++infixCounter;
    }
    
    // place any remaining math operators from the stack onto
    // the postfix array
    while(!charStack.IsEmpty())
    {
        postfix[postfixCounter] = charStack.Top();
        ++postfixCounter; 
        charStack.Pop();
    }
    
    postfix[postfixCounter] = '\0';
    // copy the data from the postfix array into the infix array
    // the data in the infix array gets sent back to main
    // since the array is passed by reference
    strcpy(infix,postfix);
}// end of ConvertInfixToPostfix

int OrderOfOperations(char token)
{// this function checks priority of each math operator
    int priority = 0;
    
    if(token == '^'|| token == '$')
    {
        priority = 4; 
    }
    else if(token == '*' || token == '/' || token == '%')
    {
        priority = 3;
    }
    else if(token == '-')
    {
        priority = 2;
    }
    else if(token == '+')
    {
        priority = 1;
    }
    return priority; 
}// end of OrderOfOperations

bool IsMathOperator(char token)
{// this function checks if operand is a math operator
     switch(token)
     {
        case '+': 
            return true;
            break;
        case '-': 
            return true;
            break;
        case '*':
            return true;
            break;
        case '/': 
            return true;
            break;
        case '%': 
            return true;
            break;
        case '^': 
            return true;
            break; 
        case '$': 
            return true;
            break;  
        default:
            return false;
            break;
     }
}// http://programmingnotes.org/
			
				
					
				
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						// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Mar 23, 2012
//    Taken From: http://programmingnotes.org/
//    File:  PostfixConversion.cpp
//    Description: Demonstrate the use of a stack based infix to 
//         postfix conversion.
// ============================================================================
#include <iostream>
#include <cctype>
#include <cstdlib>
#include <cstring>
#include "ClassStackType.h"
using namespace std;
 
// function prototypes
void DisplayDirections();
void ConvertInfixToPostfix(char* infix);
int OrderOfOperations(char token);
bool IsMathOperator(char token);
 
int main()
{
    // declare variables
    char expression[50]; // array holding the infix data
    
    // display directions to user
    DisplayDirections();
    
    // get data from user
    cout<<"\nPlease enter an infix expression: ";
    cin.getline(expression, sizeof(expression));
    
    cout <<"\nThe Infix expression = "<<expression<<endl;
    
    ConvertInfixToPostfix(expression);
    
    cout<<"The Postfix expression = "<<expression<<endl;
    
    return 0;
}// end of main
 
void DisplayDirections()
{
    cout << "\n==== Infix to Postfix Conversion ====\n"
        <<"\nMath Operators:\n"
        <<"+ || Addition\n"
        <<"- || Subtraction\n"
        <<"* || Multiplication\n"
        <<"/ || Division\n"
        <<"% || Modulus\n"
        <<"^ || Power\n"
        <<"$ || Square Root\n"
        <<"Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)\n";
}// end of DisplayDirections
 
void ConvertInfixToPostfix(char* infix)
{
    // declare function variables
    int infixCounter = 0;
    int postfixCounter = 0;
    char token = 'a';
    char postfix[50];
    StackType<char> charStack;
    
    // loop thru array until there is no more data
    while(infix[infixCounter] != '\0')
    {
        // push numbers/letters onto 'postfix' array
        if(isdigit(infix[infixCounter]) || isalpha(infix[infixCounter]))
        {
            postfix[postfixCounter] = infix[infixCounter];
            ++postfixCounter;
        }
        else if(isspace(infix[infixCounter]))
        {
            // DO NOTHING
        }
        else if(IsMathOperator(infix[infixCounter]))
        {
            // if stack is empty, place first math operator onto stack
            token = infix[infixCounter];
            if(charStack.IsEmpty())
            {
                charStack.Push(token);
            }
            else
            {
                // get the current math operator from the top of the stack
                token = charStack.Top();
                charStack.Pop(); 
                
                // use the 'OrderOfOperations' function to check equality
                // of the math operators
                while(OrderOfOperations(token) >= OrderOfOperations(infix[infixCounter]))
                {
                    // if stack is empty, do nothing
                    if(charStack.IsEmpty())
                    {
                        break;
                    }
                    // place the popped math operator from above ^
                    // onto the postfix array
                    else
                    {
                        postfix[postfixCounter] = token;
                        ++postfixCounter;
                        // pop the next operator from the stack and 
                        // continue the process until complete
                        token = charStack.Top();
                        charStack.Pop();
                    }
                }
                // push any remainding math operators onto the stack
                charStack.Push(token);
                charStack.Push(infix[infixCounter]);
            }
        }
        // push outer parentheses onto stack
        else if(infix[infixCounter] == '(')
        {
            charStack.Push(infix[infixCounter]);
        }
        else if(infix[infixCounter] == ')')
        {
            // pop the current math operator from the stack
            token = charStack.Top();
            charStack.Pop();
            while(token != '(' && !charStack.IsEmpty())
            {
                // place the math operator onto the postfix array
                postfix[postfixCounter] = token;
                ++postfixCounter; 
                // pop the next operator from the stack and
                // continue the process until complete
                token = charStack.Top();
                charStack.Pop();
            }
        }
        else
        {
            cout<<"\nINVALID INPUT\n";
            exit(1);
        }
        ++infixCounter;
    }
    
    // place any remaining math operators from the stack onto
    // the postfix array
    while(!charStack.IsEmpty())
    {
        postfix[postfixCounter] = charStack.Top();
        ++postfixCounter; 
        charStack.Pop();
    }
    
    postfix[postfixCounter] = '\0';
    // copy the data from the postfix array into the infix array
    // the data in the infix array gets sent back to main
    // since the array is passed by reference
    strcpy(infix,postfix);
}// end of ConvertInfixToPostfix
 
int OrderOfOperations(char token)
{// this function checks priority of each math operator
    int priority = 0;
    
    if(token == '^'|| token == '$')
    {
        priority = 4; 
    }
    else if(token == '*' || token == '/' || token == '%')
    {
        priority = 3;
    }
    else if(token == '-')
    {
        priority = 2;
    }
    else if(token == '+')
    {
        priority = 1;
    }
    return priority; 
}// end of OrderOfOperations
 
bool IsMathOperator(char token)
{// this function checks if operand is a math operator
     switch(token)
     {
        case '+': 
            return true;
            break;
        case '-': 
            return true;
            break;
        case '*':
            return true;
            break;
        case '/': 
            return true;
            break;
        case '%': 
            return true;
            break;
        case '^': 
            return true;
            break; 
        case '$': 
            return true;
            break;  
        default:
            return false;
            break;
     }
}// http://programmingnotes.org/

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

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

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

Want to evaluate a postfix expression? Click here for sample code.

Once compiled, you should get this as your output
(Note: the code was compile three separate times to display different output)

====== RUN 1 ======
==== Infix to Postfix Conversion ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4) Please enter an infix expression: ((a+b)+c)/(d^e) The Infix expression = ((a+b)+c)/(d^e) The Postfix expression = ab+c+de^/ ====== RUN 2 ====== ==== Infix to Postfix Conversion ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4) Please enter an infix expression: (3*5)+(7^6) The Infix expression = (3*5)+(7^6) The Postfix expression = 35*76^+ ====== RUN 3 ====== ==== Infix to Postfix Conversion ==== Math Operators: + || Addition - || Subtraction * || Multiplication / || Division % || Modulus ^ || Power $ || Square Root Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)
Please enter an infix expression: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4) The Infix expression = (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4) The Postfix expression = 45^14*232+$2-/12%24*/*

Tag Archives: infix

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

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

C++ || Stack Based Postfix Evaluation (Single Digit)

C++ || Stack Based Infix To Postfix Conversion (Single Digit)

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