You are to write a Java program that allows the user to type in a mathematical f

Question

You are to write a Java program that allows the user to type in a mathematical formula at the keyboard and produces the answer on the screen WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).WITHOUT USING JAVA STACK***** ( HAVE TO MAKE OWN STACK).

The formula will be typed in INFIX notation and will include only positive integers for the numbers. The operators that are acceptable are the following: + (plus), - (minus), * (multiply), / (divide), and ^ (power). Parenthesis are also allowed.

You should allow the user to type in the equation of his choice and then display the answer on the screen. Display a real answer. (for example: 3 / 2 = 1.5, NOT 1)

ALSO DISPLAY THE POST-FIX EQUATION ON THE SCREEN.

The normal rules of mathematics apply (parenthesis have the highest precedence followed by the ^, followed by * and /, followed by - and +).

Do not allow the program to bomb and warn the user if the equation is wrong. For example: 2 + 43 / * 12 cannot be calculated because there are too many operators.

When I test the program, I will only type positive integers as input and you can assume the input equation is valid.

Hints: You should treat the equation as a queue of tokens and read the tokens from the queue one at a time. Convert the INFIX equation to a POSTFIX equation. Then resolve the POSTFIX equation.

Sample equations-> Postfix

12 +(2 – 4 ) /5 ->12 2 4 – 5 / +

43 + 3^4 * 2 / 34 – 9 ->43 3 4 ^ 2 * 34 / + 9 -

2 ^ 4+34 - 3 ->2 4 ^ 34 + 3 -

Here are 2 String methods that will come in handy: replaceAll and split. Example of program running:

Enter an equation: 12+ (6- 4 ) ^ (1+1) / 2

RPN: 12 6 4 – 1 1 + ^ 2 / +

Answer: 14

Explanation / Answer

import java.io.*;

   class Stack { char a[]=new char[100]; int top=-1;

   void push(char c)
   {
   try
   {
   a[++top]= c;
   }
   catch(StringIndexOutOfBoundsException e)
   {
   System.out.println("Stack full , no room to push , size=100");
   System.exit(0);
   }
   }

   char pop()
   {
   return a[top--];
   }

   boolean isEmpty()
   {
   return (top==-1)?true:false;
   }

   char peek()
   {
   return a[top];
   }

   }

   public class InfixToPostfix
   {

   static Stack operators = new Stack();

   public static void main(String argv[]) throws IOException
   {
       String infix;

       //create an input stream object
       BufferedReader keyboard = new BufferedReader (new InputStreamReader(System.in));

       //get input from user
       System.out.print(" Enter the algebraic expression in infix: ");
       infix = keyboard.readLine();

       //output as postfix
       System.out.println("The expression in postfix is:" + toPostfix(infix));

   }

   private static String toPostfix(String infix)
   //converts an infix expression to postfix
   {
       char symbol;
       String postfix = "";

                for(int i=0;i<infix.length();++i)
                   //while there is input to be read
       {
           symbol = infix.charAt(i);
           //if it's an operand, add it to the string
                        if (Character.isLetter(symbol))
               postfix = postfix + symbol;
           else if (symbol=='(')
           //push (
           {

               operators.push(symbol);
           }
           else if (symbol==')')
           //push everything back to (
           {
               while (operators.peek() != '(')
               {
                   postfix = postfix + operators.pop();
               }
               operators.pop();       //remove '('
           }
           else
           //print operators occurring before it that have greater precedence
           {
                                while (!operators.isEmpty() && !(operators.peek()=='(') && prec(symbol) <= prec(operators.peek()))
                   postfix = postfix + operators.pop();

               operators.push(symbol);
           }
       }
       while (!operators.isEmpty())
           postfix = postfix + operators.pop();
       return postfix;
   }

   static int prec(char x)
   {
       if (x == '+' || x == '-')
           return 1;
       if (x == '*' || x == '/' || x == '%')
           return 2;
       return 0;
   }
}

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