Assume that the operators +, −, × are left associative and ^ is right…
2009
Assume that the operators +, −, × are left associative and ^ is right associative. The order of precedence (from highest to lowest) is ^, ×, +, −. The postfix expression corresponding to the infix expression is
a + b × c − d ^ e ^ f- A.
abc x + def ^ ^ −
- B.
abc x + de ^ f ^ −
- C.
ab + c × d − e^f^
- D.
− + a × b c^^ def
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Correct answer: A
To convert the infix expression a + b × c − d ^ e ^ f to postfix, we follow operator precedence and associativity rules. First, handle the highest precedence operator ^ (right-associative): d ^ e ^ f becomes d e f ^^ . Next, handle ×: b × c becomes b c × . Then combine with + (left-associative): a + b c × becomes a b c × + . Finally, handle −: (a b c × +) - (d e f ^^) becomes a b c × + d e f ^^ - .
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