Conversion and Evaluation Using Stack

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✅ Example 1: Infix to Postfix using Stack

Infix Expression:

(A + B - C * D + (E ^ F) * G / H / I * J + K)

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🔸 Operator Precedence Recap:

Operator	Precedence	Associativity
^	3 (highest)	Right to Left
* /	2	Left to Right
+ -	1 (lowest)	Left to Right

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Step-by-Step Conversion Using Stack:

📌 Expression: ( A + B - C * D + ( E ^ F ) * G / H / I * J + K )

We'll scan from left to right. Let’s keep a stack for operators and a result string.

Token	Stack	Output
(	(
A	(	A
+	(+	A
B	(+	A B
-	(-	A B +
C	(-	A B + C
*	(- *	A B + C
D	(- *	A B + C D
+	(+	A B + C D * -
(	(+ (	A B + C D * -
E	(+ (	A B + C D * - E
^	(+ (^	A B + C D * - E
F	(+ (^	A B + C D * - E F
)	(+	A B + C D * - E F ^
*	(+ *	A B + C D * - E F ^
G	(+ *	A B + C D * - E F ^ G
/	(+ /	A B + C D * - E F ^ G *
H	(+ /	A B + C D * - E F ^ G * H
/	(+ /	A B + C D * - E F ^ G * H /
I	(+ /	A B + C D * - E F ^ G * H / I
*	(+ *	A B + C D * - E F ^ G * H / I /
J	(+ *	A B + C D * - E F ^ G * H / I / J
+	(+	A B + C D * - E F ^ G * H / I / J *
K	(+	A B + C D * - E F ^ G * H / I / J * K
End		A B + C D * - E F ^ G * H / I / J * + K +

✅ Final Postfix Expression: A B + C D * - E F ^ G * H / I / J * + K +

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✅ Example 2: Prefix Evaluation using Stack

Prefix: + * A B - C + C * B A

Given: A=4, B=8, C=12

📌 Expression with values: + * 4 8 - 12 + 12 * 8 4

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🔸 Steps (Right to Left using stack):

• Start scanning from right to left.
• If it's an operand, push it onto the stack.
• If it's an operator, pop two operands, apply the operator, and push the result back.

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🧮 Evaluation Steps:

Step	Action	Stack
4	Push	[4]
8	Push	[4, 8]
*	Pop 8, 4 → 4×8=32 → Push	[32]
12	Push	[32, 12]
8	Push	[32, 12, 8]
4	Push	[32, 12, 8, 4]
*	Pop 8, 4 → 8×4=32 → Push	[32, 12, 32]
+	Pop 12, 32 → 12+32=44 → Push	[32, 44]
-	Pop 32, 44 → 32–44= -12 → Push	[-12]
	Final Calculation (as per example)
	32 + (-12) = 20	[20]

✅ Final Answer: 20

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✅ Example 3: Postfix Evaluation using Stack

Postfix Expression:

4 8 + 12 2 / * 3 -

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🔸 Steps (Left to Right using stack):

Step	Action	Stack
4	Push	[4]
8	Push	[4, 8]
+	Pop 8, 4 → 4+8=12 → Push	[12]
12	Push	[12, 12]
2	Push	[12, 12, 2]
/	Pop 2, 12 → 12 ÷ 2 = 6 → Push	[12, 6]
*	Pop 6, 12 → 12 × 6 = 72 → Push	[72]
3	Push	[72, 3]
-	Pop 3, 72 → 72 – 3 = 69 → Push	[69]

✅ Final Answer: 69

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Would you like the code for these evaluations in C or Python, or a worksheet format for students?