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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)
Q. The degree of a node is defined as the number of children it has. Shear show that in any binary tree, the total number of leaves is one more than the number of nodes of degree 2
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