C++ || Simple Multi Digit, Decimal & Negative Number Infix To Postfix Conversion & Evaluation
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
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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 = 36Final 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 = -238.466Final 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 = 0.00855389Final 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 = -3978Final 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 = 277Final answer = 277
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