DS – Expression Evaluation

Expression Evaluation

  • An algebraic expression is a legal combination of operands and operators.
  • Operand is a quantity (data) on which an operation is performed.
  • Operand may be a variable like a, b, c or constants like 1, 2, 3….
  • Operator is a symbol.
  • Example of an expression x+y*z

Notations: We can represent an expression in different notations.

Infix: Operator surrounded by operands.
Prefix: Operator proceeded by operands.
Postfix: Operator followed by operands.


  • Infix notation is seems to be simple but difficult to evaluate.
  • We need to consider the priority of operators and associativity of operators.
  • Expression 2+3*5 result depends on priority.
  • No need to consider these things in the evaluation of Prefix or Postfix expressions.

As there are 3 notations, we have total 6 conversions.

  1. Infix -> Postfix
  2. Infix -> Prefix
  3. Prefix -> Infix
  4. Prefix -> Postfix
  5. Postfix -> Infix
  6. Postfix -> Prefix
  • First 2 conversions can be performed using STACK. Hence we called these conversions are applications of STACK.
  • Remaining conversions use BST and STACK.

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