- note that the build expression tree function of the expressiontree class is written in such way that leaf token can be any stringfor exampleit parses the expression ( *( + )howeverwithin the evaluate methodan error would occur when attempting to convert leaf token to number modify the evaluate method to accept an optional python dictionary that can be used to map such string variables to numeric valueswith syntax such as evaluate( : : : }in this waythe same algebraic expression can be evaluated using different values - as mentioned in exercise - postfix notation is an unambiguous way of writing an arithmetic expression without parentheses it is defined so that if "(exp op (exp )is normal (infixfully parenthesized expression with operation opthen its postfix equivalent is "pexp pexp op"where pexp is the postfix version of exp and pexp is the postfix version of exp the postfix version of single number or variable is just that number or variable sofor examplethe postfix version of the infix expression "(( ( ))/ is " /implement postfix method of the expressiontree class of section that produces the postfix notation for the given expression projects - implement the binary tree adt using the array-based representation described in section - implement the tree adt using linked structure as described in section provide reasonable set of update methods for your tree - the memory usage for the linkedbinarytree class can be streamlined by removing the parent reference from each nodeand instead having each position instance keep memberpaththat is list of nodes representing the entire path from the root to that position (this generally saves memory because there are typically relatively few stored position instances reimplement the linkedbinarytree class using this strategy - slicing floor plan divides rectangle with horizontal and vertical sides using horizontal and vertical cuts (see figure slicing floor plan can be represented by proper binary treecalled slicing treewhose internal nodes represent the cutsand whose external nodes represent the basic rectangles into which the floor plan is decomposed by the cuts (see figure the compaction problem for slicing floor plan is defined as follows assume that each basic rectangle of slicing floor plan is assigned minimum width and minimum height the compaction problem is to find the smallest possible height and width for each rectangle of the slicing floor plan that is compatible with the minimum dimensions