by means of proper binary tree with (nnodes - what are the minimum and maximum number of internal and external nodes in an improper binary tree with nodesr- show tree achieving the worst-case running time for algorithm depth - give justification of proposition - what is the running time of algorithm height (tv(code fragment when called on node distinct from the root of tr- let be the tree of figure and refer to code fragments and give the output of tostringpostorder(tt root() give the output of parentheticrepresentation(tt root() - describe modification to parentheticrepresentationfrom code fragment so that it uses the length(method for string objects to output the parenthetic representation of tree with line breaks and spaces added to display the tree in text window that is characters wide - draw an arithmetic expression tree that has four external nodesstoring the numbers and (with each number stored in distinct external nodebut not necessarily in this order)and has three internal nodeseach storing an operator from the set /}so that the value of the root is the operators may return and act on fractionsand an operator may be used more than once