Parsing String of symbols to Expression

Given an expression as a string str consisting of numbers and basic arithmetic operators(+, -, *, /), the task is to solve the expression. Note that the numbers used in this program are single-digit numbers and parentheses are not allowed.
Examples:

Input: str = “3/3+4*6-9” 
Output: 16 
Since (3 / 3) = 1 and (4 * 6) = 24. 
So the overall expression becomes (1 + 24 – 9) = 16
Input: str = “9*5-4*5+9” 
Output: 16 

Approach: A Stack class is created to store both numbers and operators (both as characters). The stack is a useful storage mechanism because, when parsing expressions, the last item stored needs to be accessed frequently; and a stack is a last-in-first-out (LIFO) container.
Besides the Stack class, a class called express(short for expression) is also created, representing an entire arithmetic expression. Member functions for this class allow the user to initialize an object with an expression in the form of a string, parse the expression, and return the resulting arithmetic value.
Here’s how an arithmetic expression is parsed. 
A pointer is started at the left and is iterated to look at each character. It can be either a number(always a single-digit character between 0 and 9) or an operator (the characters +, -, *, and /).
If the character is a number, it is pushed onto the stack. The first operator encountered is also pushed into the stack. The trick is subsequent operators are handled. Note that the current operator can’t be executed because the number that follows it hasn’t been read yet. Finding an operator is merely the signal that we can execute the previous operator, which is stored on the stack. That is, if the sequence 2+3 is on the stack, we wait until we find another operator before carrying out the addition.
Thus, whenever the current character is an operator (except the first), the previous number (3 in the preceding example) and the previous operator (+) are popped off the stack, placing them in the variables lastval and lastop. Finally, the first number (2) is popped and the arithmetic operation is carried on the two numbers (obtaining 5). 
However, when * and / which have higher precedence than + and – are encountered, the expression can’t be executed. In the expression 3+4/2, the + cant be executed until the division is performed. So, the 2 and the + are put back on the stack until the division is carried out.
On the other hand, if the current operator is a + or -, the previous operator can be executed. That is when the + is encountered in the expression 4-5+6, it’s all right to execute the -, and when the – is encountered in 6/2-3, it’s okay to do the division. Table 10.1 shows the four possibilities.

Previous Operator	Current Operator	Example	Action
+ or –	* or /	3+4/	Push previous operator and previous number (+, 4)
* or /	* or /	9/3*	Execute previous operator, push result (3)
+ or –	+ or –	6+3+	Execute previous operator, push result (9)
* or /	+ or –	8/2-	Execute previous operator, push result (4)

Below is the implementation of the above approach:

CPP

// C++ implementation of the approach
#include <cstring>
#include <iostream>
using namespace std;

// Length of expressions in characters
const int LEN = 80;

// Size of the stack
const int MAX = 40;

class Stack {
private:
    // Stack: array of characters
    char st[MAX];

    // Number at top of the stack
    int top;

public:
    Stack()
    {
        top = 0;
    }

    // Function to put a character in stack
    void push(char var)
    {
        st[++top] = var;
    }

    // Function to return a character off stack
    char pop()
    {
        return st[top--];
    }

    // Function to get the top of the stack
    int gettop()
    {
        return top;
    }
};

// Expression class
class Express {
private:
    // Stack for analysis
    Stack s;

    // Pointer to input string
    char* pStr;

    // Length of the input string
    int len;

public:
    Express(char* ptr)
    {
        pStr = ptr;
        len = strlen(pStr);
    }

    // Parse the input string
    void parse();

    // Evaluate the stack
    int solve();
};

void Express::parse()
{

    // Character from the input string
    char ch;

    // Last value
    char lastval;

    // Last operator
    char lastop;

    // For each input character
    for (int j = 0; j < len; j++) {
        ch = pStr[j];

        // If it's a digit then save
        // the numerical value
        if (ch >= '0' && ch <= '9')
            s.push(ch - '0');

        // If it's an operator
        else if (ch == '+' || ch == '-'
                 || ch == '*' || ch == '/') {

            // If it is the first operator
            // then put it in the stack
            if (s.gettop() == 1)

                s.push(ch);

            // Not the first operator
            else {
                lastval = s.pop();
                lastop = s.pop();

                // If it is either '*' or '/' and the
                // last operator was either '+' or '-'
                if ((ch == '*' || ch == '/')
                    && (lastop == '+' || lastop == '-')) {

                    // Restore the last two pops
                    s.push(lastop);
                    s.push(lastval);
                }

                // In all the other cases
                else {

                    // Perform the last operation
                    switch (lastop) {

                    // Push the result in the stack
                    case '+':
                        s.push(s.pop() + lastval);
                        break;
                    case '-':
                        s.push(s.pop() - lastval);
                        break;
                    case '*':
                        s.push(s.pop() * lastval);
                        break;
                    case '/':
                        s.push(s.pop() / lastval);
                        break;
                    default:
                        cout << "\nUnknown oper";
                        exit(1);
                    }
                }
                s.push(ch);
            }
        }
        else {
            cout << "\nUnknown input character";
            exit(1);
        }
    }
}

int Express::solve()
{
    // Remove the items from stack
    char lastval;
    while (s.gettop() > 1) {
        lastval = s.pop();
        switch (s.pop()) {

        // Perform operation, push answer
        case '+':
            s.push(s.pop() + lastval);
            break;
        case '-':
            s.push(s.pop() - lastval);
            break;
        case '*':
            s.push(s.pop() * lastval);
            break;
        case '/':
            s.push(s.pop() / lastval);
            break;
        default:
            cout << "\nUnknown operator";
            exit(1);
        }
    }
    return int(s.pop());
}

// Driver code
int main()
{

    char string[LEN] = "2+3*4/3-2";

    // Make expression
    Express* eptr = new Express(string);

    // Parse it
    eptr->parse();

    // Solve the expression
    cout << eptr->solve();

    return 0;
}

Java

import java.util.Stack;

public class ExpressionEvaluation {

    public static int evaluate(String expression) {
        // Create a stack to hold operands
        Stack<Integer> operands = new Stack<Integer>();

        // Create a stack to hold operators
        Stack<Character> operators = new Stack<Character>();

        for (int i = 0; i < expression.length(); i++) {
            char ch = expression.charAt(i);

            // If the current character is a whitespace, skip it
            if (ch == ' ') {
                continue;
            }

            // If the current character is a digit, push it to the operand stack
            if (Character.isDigit(ch)) {
                int num = 0;
                while (i < expression.length() && Character.isDigit(expression.charAt(i))) {
                    num = num * 10 + Character.getNumericValue(expression.charAt(i));
                    i++;
                }
                i--;
                operands.push(num);
            }

            // If the current character is an operator, push it to the operator stack
            else if (ch == '+' || ch == '-' || ch == '*' || ch == '/') {
                while (!operators.empty() && hasPrecedence(ch, operators.peek())) {
                    operands.push(applyOperation(operators.pop(), operands.pop(), operands.pop()));
                }
                operators.push(ch);
            }
        }

        while (!operators.empty()) {
            operands.push(applyOperation(operators.pop(), operands.pop(), operands.pop()));
        }

        return operands.pop();
    }

    public static boolean hasPrecedence(char op1, char op2) {
        if ((op1 == '*' || op1 == '/') && (op2 == '+' || op2 == '-')) {
            return false;
        }
        else {
            return true;
        }
    }

    public static int applyOperation(char op, int b, int a) {
        switch (op) {
            case '+':
                return a + b;
            case '-':
                return a - b;
            case '*':
                return a * b;
            case '/':
                if (b == 0) {
                    throw new UnsupportedOperationException("Cannot divide by zero");
                }
                return a / b;
        }
        return 0;
    }

    public static void main(String[] args) {
        String expression = "2+3*4/3-2";
        System.out.println(evaluate(expression));
    }
}

Python3

# Python implementation of the approach
import sys

# Size of the stack
MAX = 40

class Stack:
    def __init__(self):
        # Stack: array of characters
        self.st = [0] * MAX

        # Number at top of the stack
        self.top = 0

    # Function to put a character in stack
    def push(self, var):
        self.top += 1
        self.st[self.top] = var

    # Function to return a character off stack
    def pop(self):
        topval = self.st[self.top]
        self.top -= 1
        return topval

    # Function to get the top of the stack
    def gettop(self):
        return self.top

# Expression class
class Express:
    def __init__(self, ptr):

        # Stack for analysis
        self.s = Stack()

        # Pointer to input string
        self.pStr = ptr

        # Length of the input string
        self.len = len(self.pStr)

    # Parse the input string
    def parse(self):
        # Last value
        lastval = 0
        # Last operator
        lastop = 0

        # For each input character
        for j in range(self.len):
            ch = self.pStr[j]

            # If it's a digit then save the numerical value
            if ch >= '0' and ch <= '9':
                self.s.push(int(ch) - int('0'))

            # If it's an operator
            elif ch == '+' or ch == '-' or ch == '*' or ch == '/':

                # If it is the first operator then put it in the stack
                if self.s.gettop() == 1:
                    self.s.push(ch)

                # Not the first operator
                else:
                    lastval = self.s.pop()
                    lastop = self.s.pop()

                    # If it is either '*' or '/' and the last operator was either '+' or '-'
                    if (ch == '*' or ch == '/') and (lastop == '+' or lastop == '-'):
                        # Restore the last two pops
                        self.s.push(lastop)
                        self.s.push(lastval)

                    # In all the other cases
                    else:

                        # Perform the last operation
                        if lastop == '+':
                            self.s.push(self.s.pop() + lastval)
                        elif lastop == '-':
                            self.s.push(self.s.pop() - lastval)
                        elif lastop == '*':
                            self.s.push(self.s.pop() * lastval)
                        elif lastop == '/':
                            self.s.push(self.s.pop() / lastval)
                        else:
                            print("\nUnknown operator")
                            sys.exit(1)

                    self.s.push(ch)

            else:
                print("\nUnknown input character")
                sys.exit(1)

    # Evaluate the stack
    def solve(self):

        # Remove the items from stack
        lastval = 0
        while self.s.gettop() > 1:
            lastval = self.s.pop()
            lastop = self.s.pop()

            # Perform operation, push answer
            if lastop == '+':
                self.s.push(self.s.pop() + lastval)
            elif lastop == '-':
                self.s.push(self.s.pop() - lastval)
            elif lastop == '*':
                self.s.push(self.s.pop() * lastval)
            elif lastop == '/':
                self.s.push(self.s.pop() / lastval)
            else:
                print("\nUnknown operator")
                sys.exit(1)

        return int(self.s.pop())

# Driver code
if __name__ == "__main__":

    # Make expression
    string = "2+3*4/3-2"
    eptr = Express(string)

    # Parse it
    eptr.parse()

    # Solve the expression
    print(eptr.solve())

# This code is contributed by sdeadityasharma

C#

// C# implementation of the approach
using System;
using System.Collections.Generic;

public class ExpressionEvaluation {

  public static int evaluate(string expression)
  {
    // Create a stack to hold operands
    Stack<int> operands = new Stack<int>();

    // Create a stack to hold operators
    Stack<char> operators = new Stack<char>();

    for (int i = 0; i < expression.Length; i++) {
      char ch = expression[i];

      // If the current character is a whitespace,
      // skip it
      if (ch == ' ') {
        continue;
      }

      // If the current character is a digit, push it
      // to the operand stack
      if (Char.IsDigit(ch)) {
        int num = 0;
        while (i < expression.Length
               && Char.IsDigit(expression[i])) {
          num = num * 10
            + (int)Char.GetNumericValue(
            expression[i]);
          i++;
        }
        i--;
        operands.Push(num);
      }

      // If the current character is an operator, push
      // it to the operator stack
      else if (ch == '+' || ch == '-' || ch == '*'
               || ch == '/') {
        while (operators.Count > 0
               && hasPrecedence(ch,
                                operators.Peek())) {
          operands.Push(applyOperation(
            operators.Pop(), operands.Pop(),
            operands.Pop()));
        }
        operators.Push(ch);
      }
    }

    while (operators.Count > 0) {
      operands.Push(applyOperation(operators.Pop(),
                                   operands.Pop(),
                                   operands.Pop()));
    }

    return operands.Pop();
  }

  public static bool hasPrecedence(char op1, char op2)
  {
    if ((op1 == '*' || op1 == '/')
        && (op2 == '+' || op2 == '-')) {
      return false;
    }
    else {
      return true;
    }
  }

  public static int applyOperation(char op, int b, int a)
  {
    switch (op) {
      case '+':
        return a + b;
      case '-':
        return a - b;
      case '*':
        return a * b;
      case '/':
        if (b == 0) {
          throw new InvalidOperationException(
            "Cannot divide by zero");
        }
        return a / b;
    }
    return 0;
  }

  public static void Main(string[] args)
  {
    string expression = "2+3*4/3-2";
    Console.WriteLine(evaluate(expression));
  }
}

// This code is contributed by Chetan Bargal

Javascript

// JavaScript implementation of the approach

// Size of the stack
const MAX = 40;

class Stack {
constructor() {
// Stack: array of characters
this.st = Array(MAX).fill(0);
// Number at top of the stack
this.top = 0;
}

// Function to put a character in stack
push(value) {
this.top += 1;
this.st[this.top] = value;
}

// Function to return a character off stack
pop() {
let topval = this.st[this.top];
this.top -= 1;
return topval;
}

// Function to get the top of the stack
gettop() {
return this.top;
}
}

// Expression class
class Express {
constructor(ptr) {
// Stack for analysis
this.s = new Stack();
// Pointer to input string
this.pStr = ptr;
// Length of the input string
this.len = this.pStr.length;
}

// Parse the input string
parse() {
// Last value
let lastval = 0;
// Last operator
let lastop = 0;
// For each input character
for (let j = 0; j < this.len; j++) {
  let ch = this.pStr[j];

  // If it's a digit then save the numerical value
  if (ch >= '0' && ch <= '9') {
    this.s.push(parseInt(ch) - parseInt('0'));
  }
  // If it's an operator
  else if (ch == '+' || ch == '-' || ch == '*' || ch == '/') {
    // If it is the first operator then put it in the stack
    if (this.s.gettop() == 1) {
      this.s.push(ch);
    }
    // Not the first operator
    else {
      lastval = this.s.pop();
      lastop = this.s.pop();
      // If it is either '*' or '/' and the last operator was either '+' or '-'
      if ((ch == '*' || ch == '/') && (lastop == '+' || lastop == '-')) {
        // Restore the last two pops
        this.s.push(lastop);
        this.s.push(lastval);
      }
      // In all the other cases
      else {
        // Perform the last operation
        if (lastop == '+') {
          this.s.push(this.s.pop() + lastval);
        }
        else if (lastop == '-') {
          this.s.push(this.s.pop() - lastval);
        }
        else if (lastop == '*') {
          this.s.push(this.s.pop() * lastval);
        }
        else if (lastop == '/') {
          this.s.push(this.s.pop() / lastval);
        }
        else {
          console.log("\nUnknown operator");
          process.exit(1);
        }
      }
      this.s.push(ch);
    }
  }
  else {
    console.log("\nUnknown input character");
    process.exit(1);
  }
}
}
// Evaluate the stack
solve() {
// Remove the items from stack
let lastval = 0;
while (this.s.gettop() > 1) {
lastval = this.s.pop();
let lastop = this.s.pop();
// Perform operation, push answer
if (lastop == '+') {
this.s.push(this.s.pop() + lastval);
}
else if (lastop == '-') {
this.s.push(this.s.pop() - lastval);
}
else if (lastop == '*') {
this.s.push(this.s.pop() * lastval);
} else if (lastop == '/') {
this.s.push(this.s.pop() / lastval);
} else {
console.log("\nUnknown operator");
process.exit(1);
}
}

return parseInt(this.s.pop());
}
}

// Driver code
let st;
st = "2+3*4/3-2";
let eptr = new Express(st);
eptr.parse();
console.log(eptr.solve());

// This code is contributed by japmeet01

Output:

4

Time Complexity: O(N).
Auxiliary Space: O(N).