Implement a Program That Read in a Postfix Expression Java

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Infix to Postfix Java

The infix and postfix expressions can have the post-obit operators: '+', '-', '%','*', '/' and alphabets from a to z. The precedence of the operators (+, -) is lesser than the precedence of operators (*, /, %). Parenthesis has the highest precedence and the expression inside it must exist converted start. In this section, nosotros volition learn how to catechumen infix expression to postfix expression and postfix to infix expression through a Java program.

For performing the conversion, nosotros employ Stack data construction. The stack is used to store the operators and parenthesis to enforce the precedence Outset parsing the expression from left to right. Before moving ahead in this department, ensure that y'all are friendly with the stack and its operations. Let's have a look at infix and postfix expressions.

Infix Expression

Infix expressions are those expressions in which the operator is written in-between the two or more operands. Usually, we utilize infix expression. For case, consider the following expression.

Postfix Expression

Postfix expressions are those expressions in which the operator is written after their operands. For example, consider the post-obit expression.

Infix vs Postfix Expression

Infix Expression	Postfix Expression
A*B/C	AB*C/
(A/(B-C+D))*(E-A)*C	ABC-D+/EA-*C*
A/B-C+D*E-A*C	AB/C-DE*AC*-

Infix to Postfix Conversion Example

Convert the (X - Y / (Z + U) * 5) infix expression into postfix expression.

Southward.N.	Input	Operand Stack	Postfix Expression
1	(	(	-
2	10	(	Ten
3	-	( -	X
4	Y	( -	XY
5	/	( - /	XY
vi	(	( - / (	XY
7	Z	( - / (	XYZ
eight	+	( - / ( +	XYZ
9	U	( - / ( +	XYZU
10	)	( - /	XYZU+
11	*	( - *	XYZU+/
12	V	( - *	XYZU+/5
13	)	-	XYZU+/V*-

Algorithm

1. Scan the infix notation from left to right one character at a fourth dimension.
2. If the next symbol scanned as an operand, suspend it to the postfix cord.
3. If the next symbol scanned every bit an operator, the:
   1. Popular and append to the postfix string every operator on the stack that:
      1. Is above the nigh recently scanned left parenthesis, and
      2. Has precedence higher than or is a right-associative operator of equal precedence to that of the new operator symbol.
   2. Push the new operator onto the stack
4. If a left parenthesis is scanned, push it into the stack.
5. If a correct parenthesis is scanned, all operators downward to the most recently scanned left parenthesis must be popped and appended to the postfix string. Furthermore, the pair of parentheses must be discarded.
6. When the infix string is fully scanned, the stack may nonetheless incorporate some operators. All the remaining operators should exist popped and appended to the postfix string.

Let'due south implement the higher up algorithm in a Coffee plan.

Coffee Program to Convert Infix Expression into Postfix Expression

InfixToPostfixConversion.java

Output:

Postfix to Infix Conversion Case

Catechumen the AB + CD - / postfix expression into infix expression.

S.Northward.	Input	Operand Stack	Infix Expression
1	A	A	-
2	B	A, B	-
iii	+	A + B	A+ B
4	C	A + B, C	-
5	D	A + B, C, D	-
6	-	A + B, C - D	C - D
7	/	A + B / C - D	A + B / C - D

Algorithm

1. Read the postfix expression from left to right one character at a time.
2. If it is operand push into operand stack.
3. If it is an operator, then:
   1. Pop ii operand from the stack.
   2. From infix expression and button into the operand stack
4. If the expression is not ended go to the first footstep.
5. Popular operand stack and display.
6. Exit

Permit'south implement the higher up algorithm in a Java plan.

Coffee Program to Convert Postfix Expression into Infix Expression

PostfixToInfixConversion.java

Output:

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