GeeksForGeeks Question

Question

• If arity of operators is fixed, then which of the following notations can be used to parse expressions without parentheses? a) Infix Notation (Inorder traversal of a expression tree) b) Postfix Notation (Postorder traversal of a expression tree) c) Prefix Notation (Preorder traversal of a expression tree)

  A	b and c
  B	Only b
  C	a, b and c
  D	None of them

  What arity of operators?

Comments

which point you are not understanding?

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yes finally i understand the meaning.

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Option A is correct

Answer 1

Ans.-option a

Consider inorder traversal or infix as

a+b*c+d*e+f+g

its prefix is

++a*bc++*defg

And postfix expression is

abc*++de*f+g++

Here prefix and postfix can be calculated in right way by using algorithms. [Arity for each operator is given].But inorder can give different values.

Answer 2

arity means the number of operands that an operator works on e.g. arithmetic operators are binary i.e. they can be applied on two operands simultaneously 4+2,9*4 etc

here question is if arity is fixed how can we evaluate an expression correctly if it does not have parenthesis.

By the help of parenthesis we give evaluate expression by precedence by using precedence rules.

we don't have any algorithm which can evaluate infix expressions without parenthesis as it can give different results but for postfix and prefix we have algorithms which directly solve them.

So answer is A i.e. only Postfix and prefix notations can be used.