Stacks, Queues and Linked Lists

Transcription

1 Stacks, Queues and Linked Lists Stacks Queues Linked Lists Singly Linked Lists Doubly Linked Lists Double-Ended Queues Inspectable Containers 4-1 Stack A stack is a data structure which has the following properties: It can hold objects which are pushed onto it. When an object is pushed onto a stack, it is put on the top of the stack. If another object is pushed onto the stack, the newly pushed object will now be on the top of the stack, and the old top object will be pushed beneath it. It will be on the top again if all the objects that are pushed after have been removed. The object on the top of the stack can be popped out from the stack. That is, the stack has a last-in-first-out (LIFO) structure. No object in the stack other than the one on the top can be accessed from outside. 4-2

2 Stack ADT push (o): Insert object o at the top of the stack. Input: Object Output: None pop (): Remove from the stack and return the top object on the stack; an error occurs if the stack is empty. Output: Object top (): Return the top object on the stack, without removing it; an error occurs if the stack is empty. Output: Object 4-3 Stack ADT isempty (): Return a boolean indicating if the stack is empty. Output: Boolean size (): Return the number of objects in the stack. Output: Integer 4-4

3 De-coupling of the ADT The 5 methods we saw in the previous slides can be divided into 2 groups: those belong only to Stack (push, pop, top) and those do not (isempty, size). isempty and size are methods that apply to all data containers. So we can divide the ADT into hierarchy: DataContainer Stack 4-5 Stack Interface public interface DataContainer { // return the # of s in stack public int size (); } // test if stack is empty public boolean isempty (); public interface Stack extends DataContainer { // insert onto stack public void push (Object ); // return and remove the top public Object pop () throws StackEmptyException; } // return the top public Object top () throws StackEmptyException; 4-6

4 Stack Example Operation Output S push (5) - (5) push (3) - (5,3) pop () 3 (5) push (7) - (5,7) pop () 7 (5) top () 5 (5) pop () 5 () pop () Error () isempty () true () push (9) - (9) push (7) - (9,7) push (3) - (9,7,3) push (5) - (9,7,3,5) size () 4 (9,7,3,5) pop () 5 (9,7,3) 4-7 Array-Based Implementation TOP S t N-1 4-8

5 Analysis Advantage: Simple Efficient Problem: Size Limitation Stack overflow Array size may not be utilized Method Time size O (1) isempty O (1) top O (1) push O (1) pop O (1) 4-9 Casting of Return Types The returned object are always instances of the class Object. For that object to be useful, type casting has to be performed. Example: To reverse an integer array a[] public static Integer[] reverse (Integer[] a) { ArrayStack S = new ArrayStack (a.length); Integer[] b = new Integer [a.length]; for (int i=0; i<a.length; i++) S.push(a[i]); for (int i=0; i<a.length; i++) b[i] = (Integer) (S.pop ()); return (b); } 4-10

6 Stack Application in Computer Science Java Method Stack is an example of stack. Especially useful in recursive call. public static long fact (long n) { if (n <= 1) return (1); else return (n * fact (n-1)); } fool: PC=320 m=7 cool: PC=216 j=5 k=7 main: PC=14 i=5 Java Stack 4-11 Main() { int i=5; cool (i);... } cool (int j) { int k=7; fool (k);... } 320 fool (int m) {... } Java Program Stack Application - History Tracking Internet browsers has two buttons: Back and Forward, that allow you to navigate among the pages that you have recently visited. Back Current Page Forward 4-12

7 Stack Application - History Tracking Use 2 stacks - namely back and forward. Whenever a new page is displayed, the address of the current page is pushed onto one of the stacks. When the user press the Back button, the top page on the back stack is popped out and displayed. At the same time, the address of the current page is pushed onto the forward stack. When the user press the Forward button, the top page on the forward stack is popped out and display. At the same time, the address of the current page is pushed onto the back stack. When the user click a link, the address of the current page is pushed onto the back stack, and the contents in the forward stack is cleared Stack Application - History Tracking Another example: word processors usually have undo and redo capability. Use 2 stacks - namely undo and redo. Whenever a new operation is done, the operation is pushed onto one of the stacks. When the user press the Undo button, the top operation on the undo stack is popped out and the operation is reversed. This operation is pushed back onto the redo stack. When the user press the Redo button, the top operation on the redo stack is popped out and the operation is executed. This operation is pushed back onto the undo stack. When the user perform a new operation, the operation is pushed onto the undo stack, and the contents in the redo stack is cleared. 4-14

8 Queues A queue is a data structure which has the following properties: It can hold objects which are inserted (enqueued) into it. The enqueued object can be removed (dequeued) if and only if all the objects enqueued before it have been dequeued. That is, the queue has a first-in-first-out (FIFO) structure. When an object inside a queue is ready for dequeued, it is said at the front position. No object in the queue other than the one at the front can be accessed from outside Queue ADT enqueue (o): Insert object o at the rear of the stack. Input: Object Output: None dequeue (): Remove and return from the queue the object at the front; an error occurs if the queue is empty. Output: Object front (): Return, but do not remove, the front object in the queue; an error occurs if the queue is empty. Output: Object isempty (): Return a boolean indicating whether the queue is empty. Output: Boolean size (): Return the number of objects in the queue. Output: Integer 4-16

9 Queue Example Fast Food Drive Through Operation Output Q enqueue (5) - (5) enqueue (3) - (5,3) dequeue () 5 (3) enqueue (7) - (3,7) dequeue () 3 (7) front () 7 (5) dequeue () 7 () dequeue () Error () isempty () true () qnqueue (9) - (9) enqueue (7) - (9,7) enqueue (3) - (9,7,3) enqueue (5) - (9,7,3,5) size () 4 (9,7,3,5) dequeue () 9 (7,3,5) 4-17 Array Implementation Similar to the array implementation of stack. front = rear if queue is empty. One problem, cell are not reusable after dequeued. Solution: Move cells so front is always at Q[0] - slow. Circular array - does front = rear mean queue empty or queue full? Use a separate variable to keep size. Only allow N-1 s in the array. 4-18

10 Array-Based Implementation Q f r N-1 Q r f N-1 Note 1:f is an index to the cell of Q storing the first of the queue (which is the candidate to be remove by a dequeue operation), unless the queue is empty (in which case f=r). Note 2:r is an index to the available array cell in Q Analysis Advantage: Simple Efficient Problem: Size Limitation Queue overflow Array size may not be utilized Method Time size O (1) isempty O (1) front O (1) enqueue O (1) dequeue O (1) 4-20

11 Queue Application in Computer Science Memory allocation in Java is an example of queue. Vector items = new Vector (12); Queue of free blocks Program Code Java Stack Free Memory Memory Heap Fixed size - doesn t grow Grows into higher memory Grows into lower memory 4-21 Array-Based Stacks and Queues Revisit The Array-based stack and queue implementations are simple and efficient. But the problem is its size limitation. We have to estimate a maximum size of the stack and queue. If we underestimate, we will run into the (stack/queue) overflow situation. If we overestimate, we are wasting memory. To allow the stacks and queues to grow without worrying about its capacity, we can copy s into a new and larger array. The insertion operations (push, enqueue) is O(n) when the stacks and/or queues are full. In chapter, we will see that this is actually not a big problem on average. 4-22

12 Linked Lists What we want is a way to implement the stacks and queues, but without the size limitation. It will also be good if we can preserve the simplicity and efficiency of the array-based implementations. Linked-lists can be used for this purpose. As the name implies, a linked-list is a list of objects linked together by pointers Singly Linked Lists Ottawa Montreal Kingston Toronto 4-24

13 Node Insertion/Deletion At Head Inserting an at the of a list: Create a node containing the new. Link the new node to the of the original list. Point the to the new node. Deleting an at the of a list: Point the to its. Delete the first. Both operation take O(1) time Node Insertion At Head Montreal Kingston Toronto Ottawa Montreal Kingston Toronto Ottawa Montreal Kingston Toronto 4-26

14 Node Deletion At Head Ottawa Montreal Kingston Toronto Ottawa Montreal Kingston Toronto Montreal Kingston Toronto 4-27 Node Insertion/Deletion At End Inserting an at the end of a list: Create a node containing the new. Link the last in the original list to the new node. Point the tail to the new node. Deleting an at the end of a list: Point the tail to its previous. Delete the first. Insertion: O(1) time, deletion: more difficult, why? Fortunately, we don t need deletion at end to use singly linked list to implement the stacks and queues. 4-28

15 Node Insertion At End tail Ottawa Montreal Kingston Toronto tail tail Ottawa Montreal Kingston Toronto Ottawa Montreal Kingston Toronto 4-29 Node Deletion At End (?) tail Ottawa Montreal Kingston Toronto tail Ottawa Montreal Kingston Toronto tail Ottawa Montreal Kingston 4-30

16 Double-Ended Queues A double-ended queue (deque) is a data structure that combines the operations of a stack and a queue. Elements can only be inserted into a deque at either the front end or the rear end. Only s at either the front end or the rear end can be removed from the deque Deque ADT insertfirst (o): Insert object o at the beginning of deque. Input: Object Output: None insertlast (o): Insert object o at the end of deque. Input: Object Output: None removefirst (): Remove and return the first. Output: Object removelast (): Remove and return the last. Output: Object 4-32

17 Deque ADT first (): Return the first object in the deque. Output: Object last (): Return the last object in the deque. Output: Object size (): Return the number of s in the deque. Output: Integer isempty (): Return true if deque is empty. Output: Boolean 4-33 Deque Example Operation Output D insertfirst (3) - (5) insertfirst(5) - (5,3) removefirst () 5 (3) insertlast (7) - (3,7) removefirst() 3 (7) removelast() 7 () removefirst () Error () isempty () true () insertfirst (9) - (9) insertlast (7) - (9,7) size () 2 (9,7) insertfirst (3) - (3,9,7) insertlast (5) - (3,9,7,5) isempty () false (3,9,7,5) removelast () 5 (3,9,7) 4-34

18 Adapter Pattern The Adapter Pattern is a design pattern that we adapt another class s method in our class. Each method involves usually very simple one to two lines implementation. Example, we can use the Deque as the adapter to implement Stack and/or Queue Implementing Stacks and Queues with Deques A deque can be used to implement a stack and/or a queue. The following tables map the stack/queue methods to the corresponding deque methods. Stack Method Implementation size () size () isempty () isempty () top () last () push (o) insertlast (o) pop () removelast () Queue Method Implementation size () size () isempty () isempty () front () frist () enqueue (o) insertlast (o) dequeue () removefirst () 4-36

19 Inserting Node at Front er trailer A B C er trailer A B C D er trailer D A B C 4-37 Deleting Node at End er trailer D A B C er trailer D A B C er trailer D A B 4-38

20 Analysis Method Time size O (1) isempty O (1) first O (1) last O (1) insertfirst O (1) insertlast O (1) removefirst O (1) removelast O (1) 4-39 Summary Stacks, Queues and Deques are all uninspectable data structures. That means not all s in the data structures are accessible at all time. For example, only the top in a stack is accessible. In chapter, we will study more inspectable data structures, namely vector, lists and sequences. These data structures allow the users to alter any data at any time. 4-40