Recursive and Doubly Linked Lists
Lecture 9

Steven S. Skiena

Recursive List Implementation

The basic insertion and deletion routines for linked lists are more elegantly written using recursion.

  PROCEDURE Insert(VAR list: T; value:INTEGER) =
  (* inserts new element in list and maintains order *)
  VAR new: T;                     (*new node*)
  BEGIN
    IF list = NIL THEN            
      list:= NEW(T, key := value) (*list is empty*)
    ELSIF value < list.key THEN   (*proper place found: insert*)
      new := NEW(T, key := value);
      new.next := list;
      list := new;
    ELSE                          (*seek position for insertion*)
      Insert(list.next, value);
    END; (*IF list = NIL*)
  END Insert;

  PROCEDURE Remove(VAR list:T; value:INTEGER; VAR found:BOOLEAN) =
  (* deletes  (first) element with value from sorted list,
     or returns false in found if the element was not found *) 
  BEGIN
    IF list = NIL THEN            (*empty list*)
      found := FALSE
    ELSIF value = list.key THEN   (*elemnt found*)
      found := TRUE; 
      list := list.next 
    ELSE                          (*seek for the element to delete*)
      Remove(list.next, value, found);
    END;
  END Remove;

Doubly Linked Lists

Often it is necessary to move both forward and backwards along a linked list. Thus we need another pointer from each node, to make it doubly linked.

List types are analogous to dance structures:

• Conga line - singly linked list.
• Chorus line - doubly linked list.
• Hora circle - double linked circular list.

Extra pointers allow the flexibility to have both forward and backwards linked lists:

type
       pointer = REF node;
       node = record
              info : item;
              front : pointer;
              back : pointer;
       end;

Insertion

How do we insert p between nodes q and r in a doubly linked list?

p^.front = r;
p^.back = q;
r^.back = p;
q^.front = p;

It is not absolutely necessary to have pointer r, since r = q .front, but it makes it cleaner.

The boundary conditions are inserting before the first and after the last element.

How do we insert before the first element in a doubly linked list (head)?

p^.back = NIL;
p^.front = head;
head^.back = p;
head = p;       (* must point to entire structure *)

Inserting at the end is similar, except head doesn't change, and a back pointer is set to NIL.

Linked Lists: Pro or Con?

The advantages of linked lists include:

• Overflow can never occur unless the memory is actually full.
• Insertions and deletions are easier than for contiguous (array) lists.
• With large records, moving pointers is easier and faster than moving the items themselves.

The disadvantages of linked lists include:

• The pointers require extra space.
• Linked lists do not allow random access.
• Time must be spent traversing and changing the pointers.
• Programming is typically trickier with pointers.

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