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# 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.

Below is the implementation of the above approach:

## CPP

 // C++ implementation of the approach#include #include using namespace std; // Length of expressions in charactersconst int LEN = 80; // Size of the stackconst 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 classclass 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 codeint 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 operands = new Stack();                 // Create a stack to hold operators        Stack operators = new Stack();                 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 approachimport sys # Size of the stackMAX = 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 classclass 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 codeif __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 approachusing System;using System.Collections.Generic; public class ExpressionEvaluation {   public static int evaluate(string expression)  {    // Create a stack to hold operands    Stack operands = new Stack();     // Create a stack to hold operators    Stack operators = new Stack();     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 stackconst MAX = 40; class Stack {constructor() {// Stack: array of charactersthis.st = Array(MAX).fill(0);// Number at top of the stackthis.top = 0;} // Function to put a character in stackpush(value) {this.top += 1;this.st[this.top] = value;} // Function to return a character off stackpop() {let topval = this.st[this.top];this.top -= 1;return topval;} // Function to get the top of the stackgettop() {return this.top;}} // Expression classclass Express {constructor(ptr) {// Stack for analysisthis.s = new Stack();// Pointer to input stringthis.pStr = ptr;// Length of the input stringthis.len = this.pStr.length;} // Parse the input stringparse() {// Last valuelet lastval = 0;// Last operatorlet lastop = 0;// For each input characterfor (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 stacksolve() {// Remove the items from stacklet lastval = 0;while (this.s.gettop() > 1) {lastval = this.s.pop();let lastop = this.s.pop();// Perform operation, push answerif (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 codelet 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).