Assume that the operators +, -, × are left associative and ^ is right…
2004
Assume that the operators +, -, × are left associative and ^ is right associative. The order of precedence (from highest to lowest) is ^, x , +, -. The postfix expression corresponding to the infix expression a + b × c - d ^ e ^ f is
- A.
abc × + def ^ ^ -
- B.
abc × + de ^ f ^ -
- C.
ab + c × d - e ^ f ^
- D.
- + a × bc ^ ^ def
Attempted by 637 students.
Show answer & explanation
Correct answer: A
Correct postfix expression: a b c × + d e f ^ ^ -
Steps to convert the infix expression a + b × c - d ^ e ^ f to postfix using the given precedence and associativity:
Handle exponentiation first. Because ^ is right-associative, d ^ e ^ f is d ^ (e ^ f). Convert this to postfix as d e f ^ ^
Handle multiplication next. b × c becomes b c ×
Apply addition. With × higher precedence than +, form a + (b × c) and convert to postfix as a b c × +
Finally perform the subtraction of the exponent result from the addition result. Combine the two postfix parts: a b c × + d e f ^ ^ -