An Introduction to Data Structures

Chapter 16: An Introduction to Data Structures I

Chapter Goals

To be able to write programs with standard lists and iterators
To understand the advantages and disadvantages of the list data structure
To be able to implement linked lists

Linked Lists

Suppose you are maintaining a vector of sorted objects (such as employees)
- Many elements will need to be shifted back if an new object is inserted in the middle.
- Many elements will need to be shifted forward if an object is deleted from the middle.
Moving a large number of records can involve a substantial amount of computer time - O(n) time.
Rather than store a sequence of values in one long block of memory (like a vector or an array) a linked list stores each value in its own memory block, together with the locations of the neighboring blocks in the sequence.

Inserting an element into a list now requires no shifting, merely reassigning new locations to adjacent objects - O(1) time.

Removing an element from the list doesn't require shifts either - O(1) time.

The standard C++ library has an implementation of the linked list structure.
- First we will learn how to use the standard list.
- Later we will find out how to implement lists.
Doubly linked lists (as shown in the illustrations) have links going in both directions.
Singly linked lists only link elements in one direction.

Just like the vector, the standard list is a template.

You can use push_back to add elements to the list.

list<string> staff;

staff.push_back("Cracker, Carl");
staff.push_back("Hacker, Harry");
staff.push_back("Lam, Larry");
staff.push_back("Sandman, Susan");

You cannot directly access elements using subscript access (e.g. staff[3]) - the values are not stored in one contiguous block in memory and there is no fast way to access them.
Instead you must start at the beginning of the list, and visit each element in turn using a list iterator. An iterator marks a position in the list.
```
list<string>::iterator pos;
pos = staff.begin();
```

To move an iterator forward in the list, use the ++ operator.
```
pos++;
```
To move an iterator backward in the list, use the -- operator.
```
pos--;
```
You can find the value that is stored in the position with the * operator.
```
string value = *pos;
```

The value *pos represent the value that is stored in the list.

*pos = "Van Dyck, Vicki"; // assign a value
 pos = staff.begin(); // assign a position

To insert another string before the iterator position, use the insert function.
```
staff.insert(pos, "Reindeer, Rudolph");
```

Each list has an end position that does not correspond to any value in the list but that points past the list's end.

pos = staff.end(); /* points past the end of the list */
staff.insert(pos, "Yaglov, Yvonne");
   /* insert past the end of list */

The end position does not point to any value, so you cannot look up the value at that position.
```
string value = *(staff.end()); /* ERROR */
```
Compare to accessing s[10] in a vector with 10 elements.

The end position is useful for stopping a traversal of the list.

pos = staff.begin();
while (pos != staff.end())
{  cout << *pos << "\n";
   pos++;
}

The traversal can be described more concisely with a for loop:

for (pos = staff.begin(); pos != staff.end(); pos++)
   cout << *pos << "\n";

Compare this to a traversal of a vector.

for (i = 0; i < s.size(); i++)
   cout << s[i] << "\n";

To remove an element from a list, you move an iterator to the position you want to remove, then call the erase
function.
```
pos = staff.begin();
pos++;
staff.erase(pos);
```

Linked Lists(`list1.cpp`)

Implementing Linked Lists (The Classes for Lists, Nodes, and Iterators)

We will start with a linked list of strings.

A linked list stores each value in a separate object called a node.

class Node {
public:
   Node(string s);
private:
   string data;
   Node* previous;
   Node* next;
friend class List;
friend class Iterator;
};

The friend declarations indicate the List and Iterator member functions are allowed to inspect and modify the private data members of the Node class.
A class should not grant friendship to another class lightly, because it breaks the privacy protection.

The list object holds the locations of the first and last nodes in the list.

class List {
public:
   List();
   void push_back(string s);
   void insert(Iterator pos, string s);
   Iterator erase(Iterator pos);
   Iterator begin();
   Iterator end();
private:
   Node* first;
   Node* last;
};

When the list is empty the first and last pointers are NULL.
A list object stores no data; it just knows where to find the node objects that store the list contents.

An iterator denotes a position in the list.

class Iterator {
public:
   Iterator();
   string get() const;     /* use instead of * */
   void next();            /* use instead of ++ */
   void previous();        /* use instead of -- */
   bool equals(Iterator b) const; /* use instead of == */
private:
   Node* position;
   Node* last;
friend class List;
};

We will enable the operators ++, --, * and == in the next chapter.
If the iterator points past the end of the list, then the position pointer is NULL.
The iterator stores a pointer to the last element of the list, so that the previous method can move the iterator back from the past-the-end position to the last element of the list.

Implementing Linked Lists (Implementing Iterators)

Iterators are created by the begin and end functions of the List class.

Iterator List::begin() {
   Iterator iter;
   iter.position = first;
   iter.last = last;
   return iter;
}

Iterator List::end() {
   Iterator iter;
   iter.position = NULL;
   iter.last = last;
   return iter;
}

The next function advances the iterator to the next position.

Note that it is illegal to advance the iterator once it is in the past-the-end position.
```
void Iterator::next()
{  assert(position != NULL)
   position = position->next;
}
```
The previous function is similar.

When the iterator points to the first element in the list, it is illegal to move it further backward.

void Iterator::previous()
{  if (position == NULL) position = last;
   else position = position->previous;
   assert(position != NULL);
}

The get function simply returns the data value of the node to which position points.

string Iterator::get() const
{  assert(position != NULL);
   return position->data;
}

The equals function compares two position pointers.

bool Iterator::equals(Iterator b) const
{  return position == b.position; }

Implementing Linked Lists (Implementing Insertion and Removal)

For the push_back function, we must first make a new node.
```
Node* newnode = new Node(s);
```

The node must point back to the old end node of the list, while the old end node must point to it.

newnode->previous = last; // (1)
last->next = newnode;     // (2)
last = newnode;           // (3) !

There is a special case when last is NULL (the list is empty).
```
if (last == NULL)
{  first = newnode;
   last = newnode;
}
```

The complete member-function:

void List::push_back(string s)
{  Node* newnode = new Node(s);
   if (last == NULL) /* list is empty */
   {  first = newnode;
      last = newnode;
   }
   else
   {  newnode->previous = last;
      last->next = newnode;
      last = newnode;
   }
}

To insert an element in the middle of the list requires manipulating both elements on either side of the new node.

There is a special case when the list is empty or the iterator is in the past-the-end position
.
```
if (iter.position == NULL)
{  push_back(s);
   return;
}
```
Otherwise we create temporary pointers to track the surrounding nodes.
```
Node* after = iter.position;
Node* before = after->previous;
```

We tell the new node where it belongs in the list.

newnode->previous = before; // (1)
newnode->next = after;      // (2)

Then update the surrounding nodes.

after->previous = newnode;  // (3)
if (before == NULL) /* insert at beginning */
   first = newnode;
else
   before->next = newnode;  // (4)

When know that after is not NULL, but before could be.

As with insertion, we will need to work with both the element before and after the one to be removed.

Of course we cannot remove a node that is not there.

assert(iter.position != NULL)

We create temporary pointers to track all three nodes we need to work with.

Node* remove = iter.position;
Node* before = remove->previous;
Node* after = remove->next;

We disconnect the node to be removed from the one before it; note the special case when we delete from the front of the list.

if (remove == first) first = after;
else   before->next = after;

We repeat the process with the node after the one to delete.

if (remove == last) last = before;
else   after->previous = before;

Finally we delete the node.

delete remove;