The following is a grammar that allows you to omit parentheses in infix algebraic expressi...

The following is a grammar that allows you to omit parentheses in infix algebraic expressions when the precedence rules remove ambiguity. For example,a + b * c meansa + (b * c). However, the grammar requires parentheses when ambiguity would otherwise result. That is, the grammar does not permit left-to-right association when several operators have the same precedence. For example,a/b * c is illegal. Notice diat the definitions introduce factors and terms.

= |+| -

=| *|/

=|()

= a |b| ... | z

The recognition algorithm is based on a recursive chain of subtasks:find an expression—>find a term —>find a factor. What makes this a recursive chain is thatfind an expression usesfind a term, which in turn usesfind a factor. Find a factor either detects a base case or usesfind an expression,thus forming the recursive chain.

The pseudocode for the recognition algorithm follows:

FIND AN EXPRESSION

// The grammar specifies that an expression is either II a single term or a term followed by a + or a -,

// which then must be followed by a second term.

Find a term

if (the next symbol is a + or a -) {

Find a term }

//end if

FIND A TERM

// The grammar specifies that a term is either a II single factor or a factor followed by a * or a I,

// which must then be followed by a second factor.

Find a factor

if (the next symbol is a * or a I) {

Find a factor

} //end if

FIND A FACTOR

// The grammar specifies that a factor is either a

// single letter (the base case) or an

// expression enclosed in parentheses.

if (the first symbol is a letter){

Done

}

else if (the first symbol is a '('){

Find an expression starting at character after'('('

Check for‘)’

}

else{

No factor exists

}// end if

Design and implement a class of infix expressions, as described by the given grammar. Include a method to recognize a legal infix expression.

the algorithm must be able to backtrack when it hits a dead end, and you must eliminate the possibility that the algoridim will cycle.