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377. Convert Postfix to Infix Expression

Objective: Given a Postfix expression, write an algorithm to convert it into Infix expression.


Input: Postfix expression:  A B + 
Output: Infix expression- (A + B)

Input: Postfix expression:  ABC/-AK/L-*
Output: Infix expression: ((A-(B/C))*((A/K)-L))

Approach: Use Stack


Iterate the given expression from left to right, one character at a time

  1. If a character is operand, push it to stack.
  2. If a character is an operator, 
    1. pop operand from the stack, say it's s1.
    2. pop operand from the stack, say it's s2.
    3. perform (s2 operator s1) and push it to stack.
  3. Once the expression iteration is completed, initialize the result string and pop out from the stack and add it to the result.
  4. Return the result.

Please walk through the example below for more understanding.


Postfix Expression: ABC/-AK/L-*
Infix Expression: ((A-(B/C))*((A/K)-L))