{"id":9287,"date":"2022-08-25T11:24:11","date_gmt":"2022-08-25T11:24:11","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=9287"},"modified":"2023-04-27T05:31:01","modified_gmt":"2023-04-27T05:31:01","slug":"arithmetic-expression-evaluation","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/arithmetic-expression-evaluation\/","title":{"rendered":"Arithmetic Expression Evaluation"},"content":{"rendered":"

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Arithmetic expression evaluation is the process of computing the value of a mathematical expression containing arithmetic operators, such as addition, subtraction, multiplication, and division, along with parentheses and operands. Before delving deep into the topic, let us first study what do mean by arithmetic expression in data structure.<\/p>\n

Arithmetic Expression in Data Structure<\/h2>\n

An Arithmetic expression is a finite combination of arithmetic operands, operators(such as, +, -, \/, *), and brackets. The common way of representing an arithmetic expression is by using infix notation. In infix notation, the operands are separated by an operator as shown in the below example.<\/p>\n

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

 X + Y.\n(X + Y) - Z.\nX \/ Y<\/code><\/pre>\n
We can clearly see here that the two operands are always separated by an operator or a parenthesis.<\/p>\n
The infix notation is solved using the operator precedence rule.<\/p>\n
Operator Precedence Table<\/h3>\n
The below table shows the precedence of the operators in a sequential manner.<\/p>\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><\/p>\n
(4 + 5) * (8 \/ 4 - 2)\n9 * (1 - 2)\n9 * -1\n-9<\/code><\/pre>\n
We can also represent an arithmetic expression using prefix or postfix notation.<\/a><\/p>\n
Prefix Notation<\/h3>\n
In prefix notation, the operator comes first and the operands come after them. In the prefix expression, we don\u2019t use brackets. The other name for prefix notation is Polish notation.<\/p>\n
Example:<\/strong><\/p>\n
Prefix: +XY-MN \nInfix: (X + Y) (M \u2013 N)<\/code><\/pre>\n
Algorithm to Evaluate Prefix Notation Using Stack<\/h3>\n
Here is the step-wise algorithm for the arithmetic expression evaluation using stack in Java.<\/p>\n
    \n
  1. Read the given expression from right to left using a for loop.<\/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
    Code Implementation<\/h3>\n
    The code for the arithmetic expression evaluation using stack in Java fro prefix notation is given below.<\/p>\n\t\t\t\t\t\t