CHAPTER 6 Stacks

2 A stack is a linear collection whose elements are added and removed from one end The last element to be put on the stack is the first element to be removed A stack is LIFO – last in, first out

3 A conceptual view of a stack

4 Basic operations Push: store a data item at the top of the stack Pop: retrieve a data item from the top of the stack

5 Example Push Item 1 Push Item 2 Push Item 3 Pop Push Item 4 Pop Item 1 Item 2 Item 1 Item 3 Item 2 Item 1 Item 2 Item 1 Item 4 Item 2 Item 1

6 More operations on a stack

7 ADT definition of STACK Notation: Sstack eitem of same type as the elements of S bboolean value

8 Operations InitStack(S) Procedure to initialize S to an empty stack Preconditions: none Postconditions: S empty

9 Operations Push(S,e) Procedure to place an item e into S (if there is room, i.e. S is not full) Preconditions: S not full Postconditions: size of S increased by 1 Pop(S)  e Procedure to remove and return the last item stored in S (the top element) if S is not empty Preconditions: S not empty Postconditions: size of S decreased by 1

10 Operations Peek(S)  e Procedure to return (without removing) the last item stored in S (the top element) if S is not empty Preconditions: S not empty Postconditions: S not changed

11 Operations IsEmpty(S)  b Boolean function that returns TRUE if S is empty Preconditions: none Postconditions: S not changed

12 Stack AXIOMS s.InitStack().IsEmpty() = true s.MakeEmpty().IsEmpty() = true s.Push(g).IsEmpty() = false s.Push(g).Pop() = s s.Peek() = s

13 Example A procedure to replace the elements of a nonempty stack, assuming they are of type integers, with their sum Pre: A nonempty stack with elements of type integers. Post: s contains only one element - the sum of previously stored elements.

14 Algorithm 1. element1  pop(S) 2. while stack is not empty repeat 2.1. element2  pop(S) 2.2. push(S,element1+element2) 2.3. element1  pop(S) 3. push(S,element1)

15 Stack applications Undo operations in editors Evaluating an arithmetic expression using postfix notation Converting infix expression into postfix expression Depth-first search in a tree/graph

16 Stack implementation The interface class Linked implementation Array implementation

17 The interface class public interface StackADT { // Adds one element to the top of this stack public void push (T element); // Removes and returns the top element from this stack public T pop(); // Returns without removing the top element of this stack public T peek(); // Returns true if this stack contains no elements public boolean isEmpty(); // Returns the number of elements in this stack public int size(); // Returns a string representation of this stack public String toString(); }

18 Linked implementation Internally, a stack is represented as a linked list of nodes, with a reference to the top of the stack and an integer count of the number of nodes in the stack LinearNode class is reused to define the nodes

19 Linked implementation

20 Array implementation Design decisions: maintain an array of Object references the bottom of the stack is at index 0 the elements of the stack are in order and contiguous an integer variable top stores the index of the next available slot in the array This approach allows the stack to grow and shrink at the higher indexes

21 Array implementation