Java Program to Convert Infix Expression to Postfix expression

Last Updated : 24 Oct, 2023

In this article let us discuss how to convert an infix expression to a postfix expression using Java.

Pre-Requisites:

1. Infix expression: Infix expressions are expressions where an operator is in between two operators. It is the generic way to represent an expression or relationship between the operators and operands mathematically. Example: 3 * 5, a + b

2. Postfix expression: Postfix expressions are expressions where an operator is placed after all of its operands. Example: 3 5 *, a b +

3. Required Data structures:

Stack: Stack is a linear data structure that follows the Last-In-First-Out principle. we are going to use a Stack data structure for the conversion of infix expression to postfix expression. To know more about the Stack data structure refer to this article - Stack Data Structure.

Rules to Convert Infix Expression to Postfix Expression

There are certain rules used for converting infix expressions to postfix expressions as mentioned below:

Initialize an empty stack to push and pop the operators based on the following rules.
You are given an expression string to traverse from left to right and while traversing when you encounter an
- operator: you can directly add it to the output (Initialize a data structure like a list or an array to print the output which stores and represents the required postfix expression).
- operand: pop the operands from the stack and add them to the output until the top of the stack has lower precedence and associativity than the current operand.
- open-parenthesis ( ' ( ' ): push it into the stack.
- closed-parenthesis ( ' ) ' ): Pop the stack and add it to the output until open-parenthesis is encountered and discard both open and closed parenthesis from the output.
Once you traverse the entire string, pop the stack and add it to the output, until the stack is empty.

Operators	Precedence	Associativity
^	Highest	Right to Left
*, /	High	Left to Right
+, -	Low	Left to Right

To know more about Precedence and Associativity, refer to this article - Precedence - Associativity

Example Explaining the Conversion

Let's consider an example to demonstrate the conversion of infix expression to postfix expression using stack.

Infix expression: 3 * 5 + ( 7 - 3 )

Procedure:

Step	Character Element	Stack	Output (Postfix Expression)	The Operation Performed on the Stack
1.	3		3	-
2.	*	*	3	push '*'
3.	5	*	3 5	-
4.	+	* +	3 5 *	pop '*' push '+'
5.	(	+ (	3 5 *	push '('
6.	7	+ (	3 5 * 7	-
7.	-	+ ( -	3 5 * 7	push '-'
8.	)		3 5 * 7 - +	pop '-' pop '+'

The output of the Infix expression 3 * 5 + ( 7 - 3 ) is 3 5 * 7 - +

Implementation:

Input: 3 * 5 + ( 7 - 3 )

Output: 3 5 * 7 - +

Let's implement the above procedure using Java:

Java

// Java Program to Convert Infix // expression to Postfix expression import java.util.*;  // Driver Class public class InfixPostfixConversion {     // lets define a method for conversion of infix     // expression to postfix expression     public static String infixToPostfix(String infix)     {          // The output will be represented as postfix         StringBuilder postfix = new StringBuilder();          // Initialize the stack to         // store the operators         Stack<Character> stk = new Stack<>();          for (char c : infix.toCharArray()) {              // if the encountered character is an operand             // add it to the output i.e postfix             if (Character.isLetterOrDigit(c)) {                 postfix.append(c);                  // if the encountered character is '(' push                 // it to the stack(stk)             }             else if (c == '(') {                 stk.push(c);                  // if the encountered character is ')' pop                 // the stack(stk) until '(' is encountered             }             else if (c == ')') {                 while (!stk.isEmpty()                        && stk.peek() != '(') {                     postfix.append(stk.pop());                 }                 stk.pop(); // discard '(' by popping it from                            // the stack             }             else {                  // if the encountered character is not                 // parenthesis or operand, then check the                 // precendence of the operator and pop the                 // stack and add it to the output                 // until the top of the stack has lower                 // precedence than the current character                 while (!stk.isEmpty()                        && precedence(stk.peek())                               >= precedence(c)) {                     postfix.append(stk.pop());                 }                 stk.push(c); // push the current operator to                              // the stack             }         }          // After traversing the entire string, check whether         // the stack is empty or not, if the stack is not         // empty, pop the stack and add it to the output*/         while (!stk.isEmpty()) {             postfix.append(stk.pop());         }          return postfix.toString();     }      // define a method to check the precedence of the     // operator     public static int precedence(char operator)     {         switch (operator) {         case '+':         case '-':             return 1;         case '*':         case '/':             return 2;         default:             return 0;         }     }      // main function     public static void main(String[] args)     {         System.out.println("Enter a Infix expression:");         Scanner sc = new Scanner(System.in);         String infix = sc.next();          sc.close();         String postfix = infixToPostfix(infix);          System.out.println("Postfix Expression: \n"                            + postfix);     } }

Output:

Enter a Infix expression: 3*5+(7-3)
Postfix Expression: 35*73-+

Complexity of the Above Method:

Time complexity: O(n) to traverse the entire string at least once.
Space complexity: O(n) for using stack space.

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Java

Java Program to Convert Infix Expression to Postfix expression

Pre-Requisites:

Rules to Convert Infix Expression to Postfix Expression

Example Explaining the Conversion

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