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Q. Draw the expression tree of the infix expression written below and then convert it intoPrefix and Postfix expressions.
((a + b) + c * (d + e) + f )* (g + h )
Ans:
The expression given is:
The postfix expression obtained is: ((a+b)+c*(d+e)+f)*(g+h) = ((ab+)+c*(de+)+f)*(gh+) = ((ab+)+(cde+*)+f)*(gh+) = ((ab+cde+*+)+f)*(gh+) = (ab+cde+*+f+)*(gh+) =(ab+cde+*+f+gh+*) The prefix expression obtained is: ((a+b)+c*(d+e)+f)*(g+h) = ((+ab)+c*(+de)+f)*(+gh) = ((+ab)+(*c+de)+f)*(+gh) = ((++ab*c+de)+f)*(+gh) = (+++ab*c+def)*(+gh) = (*+++ab*c+def+gh)
The postfix expression obtained is:
((a+b)+c*(d+e)+f)*(g+h)
= ((ab+)+c*(de+)+f)*(gh+)
= ((ab+)+(cde+*)+f)*(gh+)
= ((ab+cde+*+)+f)*(gh+)
= (ab+cde+*+f+)*(gh+)
=(ab+cde+*+f+gh+*)
The prefix expression obtained is:
= ((+ab)+c*(+de)+f)*(+gh)
= ((+ab)+(*c+de)+f)*(+gh)
= ((++ab*c+de)+f)*(+gh)
= (+++ab*c+def)*(+gh)
= (*+++ab*c+def+gh)
This notation bounds a function to in constant factors. We say f(n) = Θ(g(n)) if there presents positive constants n 0 , c 1 and c 2 such that to the right of n 0 the value of f
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