Write an algorithm for converting infix expression into postfix expression.
Question
Write an algorithm for converting infix expression into postfix expression.
Solution
Sure, here is a step-by-step algorithm for converting an infix expression into a postfix expression:
- Initialize an empty stack and a postfix string.
- Read the infix expression from left to right.
- If the scanned character is an operand, add it to the postfix string.
- If the scanned character is an operator and if the stack is empty, push the operator into the stack.
- If the scanned operator has higher precedence than the operator in the stack (or the stack is empty), push it into the stack. If the scanned operator has lower or equal precedence than the operator in the stack, pop the operator from the stack and add it to the postfix string. Repeat this step until the stack is not empty and top of the stack has greater precedence.
- If the scanned character is an '(', push it to the stack.
- If the scanned character is an ')', pop and output from the stack until an '(' is encountered. Remove both '(' and ')'.
- Repeat steps 3-7 until all characters are scanned.
- After all characters are scanned, we have to pop any remaining elements from the stack and add them to the postfix string.
- Now, the postfix string contains the postfix expression of the given infix expression.
This algorithm uses the stack data structure to hold the operators and has a time complexity of O(n), where n is the number of characters in the infix expression.
Similar Questions
Convert infix expression to postfix 4*8/2+(9+8-7^2)-5*9
Meenu is studying computer science and is currently learning about expressions in infix notation. She needs a program to convert infix expressions to postfix notation to help her with her studies. Can you help her by providing a program that performs this conversion?The program should support the following operations:Check if a character is an operator (+, -, *, or /).Determine the precedence of an operator.Convert an infix expression to postfix notation.ExampleInput:(3+4)5Output:34+5Note: This is a sample question asked in TCS recruitment.Input format :The input consists of the infix expression to be converted to postfix notation.Output format :The output displays the postfix expression equivalent of the input infix expression.Refer to the sample output for formatting specifications.Code constraints :The input line will not exceed a length of 100 characters.The infix expression may contain operators (+, -, *, /) and parentheses (,).Sample test cases :Input 1 :A+B*C-D/EOutput 1 :Postfix expression: ABC*+DE/-Input 2 :3+4*5/(6-2)Output 2 :Postfix expression: 345*62-/+Input 3 :(3+4)5Output 3 :Postfix expression: 34+5
Convert the infix expression to postfix expression, input: A/B+C^ * (D + (- E) / F) . The output is?Select one:O a. +/AB^ * C + (- D) / E * FOb. AB/CDEF/-*+OC. AB/CDEF/-+*Od. AB/CDEF/*+-
The postfix expression of the infix expression 4 * ( 3 + 2 - 6 ) / 8A4 3 2 + 6 - * 8 /B4 * 3 2 + 6 - 8 /C4 3 2 + * 6 8 / -D4 * 3 2 6 - + 8 /
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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