the positional list adt the abstract data types that we have considered thus farnamely stacksqueuesand double-ended queuesonly allow update operations that occur at one end of sequence or the other we wish to have more general abstraction for examplealthough we motivated the fifo semantics of queue as model for customers who are waiting to speak with customer service representativeor fans who are waiting in line to buy tickets to showthe queue adt is too limiting what if waiting customer decides to hang up before reaching the front of the customer service queueor what if someone who is waiting in line to buy tickets allows friend to "cutinto line at that positionwe would like to design an abstract data type that provides user way to refer to elements anywhere in sequenceand to perform arbitrary insertions and deletions when working with array-based sequences (such as python list)integer indices provide an excellent means for describing the location of an elementor the location at which an insertion or deletion should take place howevernumeric indices are not good choice for describing positions within linked list because we cannot efficiently access an entry knowing only its indexfinding an element at given index within linked list requires traversing the list incrementally from its beginning or endcounting elements as we go furthermoreindices are not good abstraction for describing local position in some applicationsbecause the index of an entry changes over time due to insertions or deletions that happen earlier in the sequence for exampleit may not be convenient to describe the location of person waiting in line by knowing precisely how far away that person is from the front of the line we prefer an abstractionas characterized in figure in which there is some other means for describing position we then wish to model situations such as when an identified person leaves the line before reaching the frontor in which new person is added to line immediately behind another identified person tickets me figure we wish to be able to identify the position of an element in sequence without the use of an integer index