Stack Expression Conversion: 18 flashcards
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1. What is the standard data structure used for converting infix expressions to postfix or prefix?
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A stack, because it follows LIFO (Last In, First Out) order, which helps manage operator precedence and parentheses during conversion.
2. In the infix-to-postfix conversion algorithm, what happens when an operand (e.g., a variable or number) is read?
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It is immediately appended to the output (postfix expression).
3. When converting infix to postfix using a stack, what is done with an opening parenthesis '('?
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It is pushed onto the stack.
4. When converting infix to postfix, what happens when a closing parenthesis ')' is encountered?
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Operators are popped from the stack and appended to the output until an opening parenthesis '(' is encountered. The '(' is then popped and discarded.
5. What is the rule for popping operators from the stack when a new operator is read during infix-to-postfix conversion?
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Pop and output operators from the stack while they have higher or equal precedence to the new operator (for left-associative operators). Then push the new operator onto the stack.
6. Given the infix expression `A + B * C`, what is the postfix equivalent?
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`A B C * +`
7. Given the infix expression `(A + B) * C`, what is the postfix equivalent?
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`A B + C *`
8. What is the postfix form of the infix expression `A * (B + C) / D`?
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`A B C + * D /`
9. What is the postfix form of the infix expression `A + B * C - D`?
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`A B C * + D -`
10. What is the postfix form of the infix expression `A * B + C / D`?
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`A B * C D / +`
11. What is the postfix form of the infix expression `(A + B) * (C - D)`?
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`A B + C D - *`
12. What is the postfix form of the infix expression `A + B + C`?
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`A B + C +`
13. What is the postfix form of the infix expression `A ^ B ^ C` (assuming right-associative exponentiation)?
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`A B C ^ ^`
14. What is the prefix form of the infix expression `A + B * C`?
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`+ A * B C`
15. What is the prefix form of the infix expression `(A + B) * C`?
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`* + A B C`
16. What is the prefix form of the infix expression `A * (B + C) / D`?
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`/ * A + B C D`
17. What is the prefix form of the infix expression `A + B * C - D`?
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`- + A * B C D`
18. What is the prefix form of the infix expression `A * B + C / D`?
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`+ * A B / C D`
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