# 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.

![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)

## Pseudocode for Basic Operations

### Insert

```text
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
```

```text
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

```text
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

```text
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

```text
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

```text
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

- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)