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Here is an infix expression: 1 + 2*(3*4-5). Suppose that we are using the usual stack algorithm to convert the expression from infix to postfix notation.The maximum number of symbols that will appear on the stack AT ONE TIME during the conversion of this expression?1234

Question

Here is an infix expression: 1 + 2*(3*4-5). Suppose that we are using the usual stack algorithm to convert the expression from infix to postfix notation.The maximum number of symbols that will appear on the stack AT ONE TIME during the conversion of this expression?1234

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Solution

To convert the infix expression to postfix using a stack algorithm, we follow these steps:

  1. Scan the infix expression from left to right.
  2. If the scanned character is an operand, output it.
  3. Else,
    • If the precedence of the scanned operator is greater than the precedence of the operator in the stack(or the stack is empty), push it.
    • Else, Pop the operator from the stack until the precedence of the scanned operator is less-equal to the precedence of the operator residing on the top of the stack. Push the scanned operator to the stack.
  4. If the scanned character is an '(', push it to the stack.
  5. If the scanned character is an ')', pop and output from the stack until an '(' is encountered.
  6. Repeat steps 2-6 until infix expression is scanned.
  7. Pop and output from the stack until it is not empty.

Now, let's apply these steps to the given expression: 1 + 2*(3*4-5)

  1. Scan the expression, the first character is '1', an operand, so output it. Stack is empty.
  2. The next character is '+', an operator. The stack is empty, so push it to the stack. Stack: [+]
  3. The next character is '2', an operand, so output it. Stack: [+]
  4. The next character is '', an operator. Its precedence is greater than '+', so push it to the stack. Stack: [+,]
  5. The next character is '(', push it to the stack. Stack: [+,*,(]
  6. The next character is '3', an operand, so output it. Stack: [+,*,(]
  7. The next character is '', an operator. The stack top has '(', so push '' to the stack. Stack: [+,,(,]
  8. The next character is '4', an operand, so output it. Stack: [+,,(,]
  9. The next character is '-', an operator. Its precedence is less than '', so pop '' from the stack and output it. Then push '-' to the stack. Stack: [+,*,(,-]
  10. The next character is '5', an operand, so output it. Stack: [+,*,(,-]
  11. The next character is ')', so pop and output from the stack until '(' is encountered. Stack: [+,*]
  12. The expression is fully scanned, so pop and output from the stack until it is empty.

So, the maximum number of symbols that will appear on the stack at one time during the conversion of this expression is 4.

This problem has been solved

Similar Questions

Let X be the result when the below postfix expressionis evaluated:X = 4 5 1 + * 2 / 3 1 2 + * +Let Y be the maximum size of the operand stack, thevalue of X-Y is ________

Problem StatementTisha wants to learn mathematical expressions and she wants to create a program to accept multiple infix expressions from the user and convert them into postfix expressions using a Stack-based algorithm. The program should prompt the user to enter the number of expressions they wish to convert, and then accept each expression one by one. After converting each infix expression to a postfix, the program should print the corresponding postfix expression to the console. Input format :The first line of input consists of an integer N, denoting the number of infix expressions to be converted.The following N lines of input consist of the infix expressions to be converted.Output format :The N lines of output print "Postfix expression T: " where T is the expression number followed by the corresponding postfix expression for N inputs, in separate lines.Refer to the sample output for the formatting specifications.Code constraints :The maximum length of an infix expression is 100 characters.The program should support multiple infix expressions.The program should use a stack-based algorithm to convert infix expressions to postfix expressions.Sample test cases :Input 1 :1A+B*C-D/E^FOutput 1 :Postfix expression 1: ABC*+DEF^/-Input 2 :2A+B-CD+E/F-GOutput 2 :Postfix expression 1: AB+C-Postfix expression 2: DEF/+G-Input 3 :1a*(b+c)/d-eOutput 3 :Postfix expression 1: abc+*d/e-Note :The program will be evaluated only after the “Submit Code” is clicked.Extra spaces and new line characters in the program output will result in the failure of the test case.

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