2.Lists, Stacks, Queues§

A list is a finite, ordered sequence of data items.

Important concept: List elements have a position.

Notation: $<a_0, a_1, …, a_{n-1}>$

What operations should we implement?

List Implementation Concepts

Our list implementation will support the concept of a current position.

Operations will act relative to the current position.

$<20, 23\ |\ 12, 15>$

List ADT (1)

// List class ADT. Generalize by using "Object" for the element type.
// An alternative would be to use Java Generics.
public interface List { // List class ADT
  // Remove all contents from the list, so it is once again empty
  public void clear();

  // Insert "it" at the current location
  // The client must ensure that the list's capacity is not exceeded
  public boolean insert(Object it);

  // Append "it" at the end of the list
  // The client must ensure that the list's capacity is not exceeded
  public boolean append(Object it);

  // Remove and return the current element
  public Object remove();

List ADT (2)

  // Set the current position to the start of the list
  public void moveToStart();

  // Set the current position to the end of the list
  public void moveToEnd();

  // Move the current position one step left, no change if already at beginning
  public void prev();

  // Move the current position one step right, no change if already at end
  public void next();

  // Return the number of elements in the list
  public int length();

List ADT (3)

  // Return the position of the current element
  public int currPos();

  // Set the current position to "pos"
  public boolean moveToPos(int pos);

  // Return true if current position is at end of the list
  public boolean isAtEnd();

  // Return the current element
  public Object getValue();
}

List ADT Examples

List: $<12\ |\ 32, 15>$

L.insert(99);

Result: $<12\ |\ 99, 32, 15>$

Iterate through the whole list:

for (L.moveToStart(); !L.isAtEnd(); L.next()) {
  it = L.getValue();
  doSomething(it);
}

List Find Function

// Return true if k is in list L, false otherwise
static boolean find(List L, int k) {
  for (L.moveToStart(); !L.isAtEnd(); L.next())
    if (k == (Integer)L.getValue()) return true; // Found k
  return false;                                  // k not found
}

Array-Based List Class (1)

class AList implements List {
  private Object listArray[];             // Array holding list elements
  private static final int defaultSize = 10; // Default size
  private int maxSize;                    // Maximum size of list
  private int listSize;                   // Current # of list items
  private int curr;                       // Position of current element

  // Constructors
  // Create a new list object with maximum size "size"
  AList(int size) { 
    maxSize = size;
    listSize = curr = 0;
    listArray = new Object[size];         // Create listArray
  }
  // Create a list with the default capacity
  AList() { this(defaultSize); }          // Just call the other constructor

Array-Based List Insert

1 / 6 Settings

<<<>>>

Inserting an element at the head of an array-based list requires shifting all existing elements in the array by one position toward the tail.

// Insert "it" at current position
public boolean insert(Object it) {
if (listSize >= maxSize) return false;
for (int i=listSize; i>curr; i--) // Shift elements up
listArray[i] = listArray[i-1]; // to make room
listArray[curr] = it;
listSize++; // Increment list size
return true;
}

Saving...

Server Error
Resubmit

Link Class

Dynamic allocation of new list elements.

class Link {         // Singly linked list node class
  private Object e;  // Value for this node
  private Link n;    // Point to next node in list

  // Constructors
  Link(Object it, Link inn) { e = it; n = inn; }
  Link(Link inn) { e = null; n = inn; }

  Object element() { return e; }                  // Return the value
  Object setElement(Object it) { return e = it; } // Set element value
  Link next() { return n; }                       // Return next link
  Link setNext(Link inn) { return n = inn; }      // Set next link
}

Linked List Position (1)

1 / 3 Settings

<<<>>>

Here is a graphical depiction for a linked list storing five integers. The value stored in a pointer variable is indicated by an arrow "pointing" to something. A NULL pointer is indicated graphically by a diagonal slash through a pointer variable's box. The vertical line between the nodes labeled 23 and 10 indicates the current position (immediately to the right of this line).

Saving...

Server Error
Resubmit

Linked List Position (2)

1 / 7 Settings

<<<>>>

Another problem is that we have no link to get us to the preceding node (shown in yellow). So we have no easy way to update the yellow node's next pointer.

head

curr

tail

curr

tail

Saving...

Server Error
Resubmit

Linked List Position (3)

null

head

curr

tail

null

head

curr

tail

Linked List Class (1)

1 / 7 Settings

<<<>>>

Let's look at the data members for class LList.

class LList implements List {
private Link head; // Pointer to list header
private Link tail; // Pointer to last element
private Link curr; // Access to current element
private int listSize; // Size of list

Saving...

Server Error
Resubmit

Linked List Class (2)

1 / 5 Settings

<<<>>>

Now we look at the constructors for class LList.

// Constructors
LList(int size) { this(); } // Constructor -- Ignore size
LList() { clear(); }
// Remove all elements
public void clear() {
curr = tail = new Link(null); // Create trailer
head = new Link(tail); // Create header
listSize = 0;
}

Saving...

Server Error
Resubmit

Insertion

1 / 9 Settings

<<<>>>

The linked list before insertion. 15 is the value to be inserted.

// Insert "it" at current position
public boolean insert(Object it) {
curr.setNext(new Link(curr.element(), curr.next()));
curr.setElement(it);
if (tail == curr) tail = curr.next(); // New tail
listSize++;
return true;
}

null

head

curr

tail

Saving...

Server Error
Resubmit

Removal

1 / 7 Settings

<<<>>>

Now we look at the remove method.

// Remove and return current element
public Object remove () throws NoSuchElementException {
if (curr == tail) // Nothing to remove
throw new NoSuchElementException("remove() in LList has current of " + curr + " and size of "
+ listSize + " that is not a a valid element");
Object it = curr.element(); // Remember value
curr.setElement(curr.next().element()); // Pull forward the next element
if (curr.next() == tail) tail = curr; // Removed last, move tail
curr.setNext(curr.next().next()); // Point around unneeded link
listSize--; // Decrement element count
return it; // Return value
}

null

head

curr

tail

Saving...

Server Error
Resubmit

1 / 10 Settings

<<<>>>

Finally, we will look at how a few other methods work.

null

head

curr

tail

temp

curr

Saving...

Server Error
Resubmit

Overhead

Container classes store elements. Those take space.
Container classes also store additional space to organize the elements.
- This is called overhead
The overhead fraction is: overhead/total space

Comparison of Implementations

Array-Based Lists:
- Insertion and deletion are $\Theta(n)$ .
- Prev and direct access are $\Theta(1)$ .
- Array must be allocated in advance.
- No overhead if all array positions are full.
Linked Lists:
- Insertion and deletion are $\Theta(1)$ .
- Prev and direct access are $\Theta(n)$ .
- Space grows with number of elements.
- Every element requires overhead.

Space Comparison

"Break-even" point:

$DE = n(P + E)$

$n = \frac{DE}{P + E}$

E: Space for data value.

P: Space for pointer.

D: Number of elements in array.

Space Example

Array-based list: Overhead is one pointer (8 bytes) per position in array – whether used or not.
Linked list: Overhead is two pointers per link node one to the element, one to the next link
Data is the same for both.
When is the space the same?
- When the array is half full

Freelist

System new and garbage collection are slow.

Add freelist support to the Link class.

1 / 7 Settings

<<<>>>

We will illustrate using a freelist by performing a series of list operations. Let's start from an empty singly linked list and a freelist variable pointing to null.

null

head

curr

tail

freelist

Saving...

Server Error
Resubmit

Doubly Linked Lists

null

head

curr

tail

Container Class Design Issues

Storing a record vs. Storing a reference to a record
Homogeneity: Allow different record types? Check and block?
Deletion: What happens to the record?

Doubly Linked Node (1)

class Link {            // Doubly linked list node
  private Object e;     // Value for this node
  private Link n;       // Pointer to next node in list
  private Link p;       // Pointer to previous node

  // Constructors
  Link(Object it, Link inp, Link inn) { e = it;  p = inp; n = inn; }
  Link(Link inp, Link inn) { p = inp; n = inn; }

  // Get and set methods for the data members
  public Object element() { return e; }                     // Return the value
  public Object setElement(Object it) { return e = it; }    // Set element value
  public Link next() { return n; }                          // Return next link
  public Link setNext(Link nextval) { return n = nextval; } // Set next link
  public Link prev() { return p; }                          // Return prev link
  public Link setPrev(Link prevval) { return p = prevval; } // Set prev link
}

Doubly Linked Insert

1 / 10 Settings

<<<>>>

The linked list before insertion. 15 is the value to be inserted.

public boolean insert(Object it) {
curr = new Link(it, curr.prev(), curr);
curr.prev().setNext(curr);
curr.next().setPrev(curr);
listSize++;
return true;
}

null

head

curr

tail

Saving...

Server Error
Resubmit

Doubly Linked Remove

1 / 9 Settings

<<<>>>

Now we will look at the remove method. Here is the linked list before we remove the node with value 8.

public Object remove() {
if (curr == tail) return null; // Nothing to remove
Object it = curr.element(); // Remember value
curr.prev().setNext(curr.next()); // Remove from list
curr.next().setPrev(curr.prev());
curr = curr.next();
listSize--; // Decrement node count
return it; // Return value removed
}

null

head

curr

tail

Saving...

Server Error
Resubmit

Stacks

LIFO: Last In, First Out.

Restricted form of list: Insert and remove only at front of list.

Notation:

Insert: PUSH
Remove: POP
The accessible element is called TOP.

Stack ADT

public interface Stack { // Stack class ADT
  // Reinitialize the stack.
  public void clear();

  // Push "it" onto the top of the stack
  public boolean push(Object it);

  // Remove and return the element at the top of the stack
  public Object pop();

  // Return a copy of the top element
  public Object topValue();

  // Return the number of elements in the stack
  public int length();
}

Array-Based Stack (1)

Issues:

Which end is the top?
Where does “top” point to?
What are the costs of the operations?

Array-Based Stack (2)

class AStack implements Stack {
  private Object stackArray[];    // Array holding stack
  private static final int defaultSize = 10;
  private int maxSize;            // Maximum size of stack
  private int top;                // First free position at top

  // Constructors
  AStack(int size) {
    maxSize = size;
    top = 0; 
    stackArray = new Object[size]; // Create stackArray
  }
  AStack() { this(defaultSize); }

Linked Stack

// Linked stack implementation
class LStack implements Stack {
  private Link top;               // Pointer to first element
  private int size;               // Number of elements

  // Constructors
  LStack() { top = null; size = 0; }
  LStack(int size) { top = null; size = 0; }

What are the costs of the operations?

How do space requirements compare to the array-based stack implementation?

Queues

FIFO: First in, First Out

Restricted form of list: Insert at one end, remove from the other.

Notation:

Insert: Enqueue
Delete: Dequeue
First element: Front
Last element: Rear

Queue Implementation (1)

1 / 5 Settings

<<<>>>

Assume that there are n elements in the queue. By analogy to the array-based list implementation, we could require that all elements of the queue be stored in the first $n$ positions of the array.

front

rear

listSize

Saving...

Server Error
Resubmit

Queue Implementation (2)

1 / 9 Settings

<<<>>>

A more efficient implementation can be obtained by relaxing the requirement that all elements of the queue must be in the first $n$ positions of the array. We still require that the queue be stored be in contiguous array positions, but the contents of the queue will be permitted to drift within the array.

Saving...

Server Error
Resubmit

Queue Implementation (3)

1 / 7 Settings

<<<>>>

This implementation raises a new problem. When elements are removed from the queue, the front index increases.

front

rear

listSize

Saving...

Server Error
Resubmit

Circular Queue (1)

1 / 5 Settings

<<<>>>

The "drifting queue" problem can be solved by pretending that the array is circular and so allow the queue to continue directly from the highest-numbered position in the array to the lowest-numbered position.

Saving...

Server Error
Resubmit

Circular Queue (2)

1 / 8 Settings

<<<>>>

There remains one more serious, though subtle, problem to the array-based queue implementation. How can we recognize when the queue is empty or full?

Saving...

Server Error
Resubmit