{"id":9281,"date":"2022-08-25T11:30:16","date_gmt":"2022-08-25T11:30:16","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=9281"},"modified":"2024-06-20T08:06:45","modified_gmt":"2024-06-20T08:06:45","slug":"evaluation-of-postfix-expression","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/evaluation-of-postfix-expression\/","title":{"rendered":"Evaluation of Postfix Expression"},"content":{"rendered":"

\"\"<\/p>\n

Evaluating postfix expressions, also known as Reverse Polish Notation (RPN), is a fundamental concept in computer science and mathematics. Unlike the more familiar infix notation, where operators are placed between operands, postfix notation places operators after their operands. This method eliminates the need for parentheses to define operator precedence, making it simpler and more efficient for computer algorithms to parse and evaluate expressions. Understanding how to evaluate postfix expressions is crucial for anyone studying data structures, algorithms, or compiler design, as it provides insights into stack operations and expression parsing.<\/p>\n

What is Arithmetic Expression?<\/h2>\n

An Arithmetic expression is a finite combination of arithmetic operands, operators and brackets. The common way of representing an arithmetic expression is by using infix notation<\/a>. In infix notation, the operands are separated by an operator. <\/p>\n

For example:<\/strong><\/p>\n

    \n
  1. X + Y. <\/li>\n
  2. (X + Y) – Z.<\/li>\n
  3. X \/ Y<\/li>\n<\/ol>\n

    The infix notation is solved using the operator precedence rule.<\/p>\n

    Operator precedence table:<\/h3>\n\n
    1)<\/td>Parentheses<\/td><\/tr>
    2)<\/td>Addition(+), Subtraction(-)<\/td><\/tr>
    3)<\/td>Multiply(*), Divide(\/)<\/td><\/tr>
    4)<\/td>Relational operators(= <> < > <= >=)<\/td><\/tr>
    5)<\/td>IS<\/td><\/tr>
    6)<\/td>NOT(~)<\/td><\/tr>
    7)<\/td>AND(&&)<\/td><\/tr>
    8)<\/td>OR(||)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n

    Example:<\/strong>\n(4 + 5) (8 \/ 4 – 2)\n9 <\/em> (1 – 2)\n9 * -1\n-9<\/p>\n

    We can also represent an arithmetic expression using prefix or postfix notation.<\/p>\n

    Whhat is Postfix Notation?<\/h3>\n

    As the name suggests, post means after, hence in postfix notation the operator comes after the operators in the expression. In the postfix expression, we don’t use brackets. The prefix notation is commonly known as Reverse Polish notation.<\/p>\n

    Example:<\/strong>\nPretfix: NM-XY+\nInfix: (X + Y) <\/em> (M – N)<\/p>\n

    Algorithm to evaluate prefix notation using stack:<\/h3>\n

    Below is the Algorithm to evaluate prefix notation using stack:<\/p>\n

      \n
    1. Read the expression from left to right.<\/li>\n
    2. If the current character is an operand, push it to the stack.<\/li>\n
    3. If the current character is an operator, remove the top two characters from the stack. Let\u2019s say the removed characters are operand1 and operand2. Now. evaluate (operand1 operator operand2) and push the solution back to the stack.<\/li>\n
    4. The last character in the stack after traversing the complete prefix notation will be the solution.<\/li>\n<\/ol>\n

      Dry run to evaluate prefix notation using stack:<\/h3>\n

      \"\"<\/p>\n

      Implementation:<\/h3>\n\t\t\t\t\t\t