Linked List

In computer science, a linked list is a linear collection of data elements, in which linear order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a group of nodes which together represent a sequence. Under the simplest form, each node is composed of data and a reference (in other words, a link) to the next node in the sequence. This structure allows for efficient insertion or removal of elements from any position in the sequence during iteration. More complex variants add additional links, allowing efficient insertion or removal from arbitrary element references. A drawback of linked lists is that access time is linear (and difficult to pipeline). Faster access, such as random access, is not feasible. Arrays have better cache locality as compared to linked lists.

Pseudocode for Basic Operations

Insert

Add(value)
  Pre: value is the value to add to the list
  Post: value has been placed at the tail of the list
  n ← node(value)
  if head = ø
    head ← n
    tail ← n
  else
    tail.next ← n
    tail ← n
  end if
end Add

Prepend(value)
 Pre: value is the value to add to the list
 Post: value has been placed at the head of the list
 n ← node(value)
 n.next ← head
 head ← n
 if tail = ø
   tail ← n
 end
end Prepend

Search

Contains(head, value)
  Pre: head is the head node in the list
       value is the value to search for
  Post: the item is either in the linked list, true; otherwise false
  n ← head
  while n != ø and n.value != value
    n ← n.next
  end while
  if n = ø
    return false
  end if
  return true
end Contains

Delete

Remove(head, value)
  Pre: head is the head node in the list
       value is the value to remove from the list
  Post: value is removed from the list, true, otherwise false
  if head = ø
    return false
  end if
  n ← head
  if n.value = value
    if head = tail
      head ← ø
      tail ← ø
    else
      head ← head.next
    end if
    return true
  end if
  while n.next != ø and n.next.value != value
    n ← n.next
  end while
  if n.next != ø
    if n.next = tail
      tail ← n
    end if
    n.next ← n.next.next
    return true
  end if
  return false
end Remove

Traverse

Traverse(head)
  Pre: head is the head node in the list
  Post: the items in the list have been traversed
  n ← head
  while n != ø
    yield n.value
    n ← n.next
  end while
end Traverse

Traverse in Reverse

ReverseTraversal(head, tail)
  Pre: head and tail belong to the same list
  Post: the items in the list have been traversed in reverse order
  if tail != ø
    curr ← tail
    while curr != head
      prev ← head
      while prev.next != curr
        prev ← prev.next
      end while
      yield curr.value
      curr ← prev
    end while
   yeild curr.value
  end if
end ReverseTraversal

Complexities

Time Complexity

Access	Search	Insertion	Deletion
O(n)	O(n)	O(1)	O(1)

Space Complexity

O(n)

References