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6-1 6 Stack ADTs Stack concepts. Stack applications. A stack ADT: requirements, contract. Implementations of stacks: using arrays, linked lists. Stacks in the Java class library. © 2001, D.A. Watt and D.F. Brown

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6-2 Stack concepts (1) A stack is a last-in-first-out sequence of elements. Elements can added and removed only at one end (the top of the stack). The depth of stack is the number of elements it contains. An empty stack has depth zero.

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6-3 Stack concepts (2) Illustration (stack of books): Moby Dick War & Peace Rob Roy Initially: Moby Dick War & Peace After remov- ing a book: Moby Dick War & Peace Misérables After adding “Misérables”: Moby Dick War & Peace Misérables 2001 After adding “2001”:

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6-4 Stack applications Interpreter (e.g., the Java Virtual Machine) maintains a stack containing intermediate results during evaluation of complicated expressions also containing arguments and return addresses for method calls and returns. Parser (e.g., a component of the Java compiler) maintains a stack containing symbols encountered during parsing.

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6-5 Example 1: text-file reversal A text file is a sequence of (zero or more) lines. To reverse the order of these lines, we must store them in a first-in-last-out sequence. Text-file reversal algorithm: To output the lines of file in reverse order: 1.Make line-stack empty. 2.For each line read from file, repeat: 2.1.Add line to the top of line-stack. 3.While line-stack is not empty, repeat: 3.1.Remove a line from the top of line-stack into line. 3.2.Output line. 4.Terminate.

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6-6 Example 2: bracketing (1) A phrase is well-bracketed if: for every left bracket, there is a later matching right bracket for every right bracket, there is an earlier matching left bracket the subphrase between a pair of matching brackets is itself well- bracketed. Examples (mathematical expressions): s (s – a) (s – b) (s – c) (– b + [b 2 – 4ac]) / 2a s (s – a) (s – b (s – c) s (s – a) s – b) (s – c) (– b + [b 2 – 4ac)] / 2a well-bracketed ill-bracketed

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6-7 Example 2 (2) Bracket matching algorithm: To test whether phrase is well-bracketed: 1.Make bracket-stack empty. 2.For each symbol sym in phrase (scanning from left to right), repeat: 2.1.If sym is a left bracket: 2.1.1.Add sym to the top of bracket-stack. 2.2.If sym is a right bracket: 2.2.1.If bracket-stack is empty, terminate with false. 2.2.2.Remove a bracket from the top of bracket-stack into left. 2.2.3.If left and sym are not matched brackets, terminate with false. 3.Terminate with true if bracket-stack is empty, or false otherwise.

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6-8 Stack ADT: requirements Requirements: 1)It must be possible to make a stack empty. 2)It must be possible to add (‘push’) an element to the top of a stack. 3)It must be possible to remove (‘pop’) the topmost element from a stack. 4)It must be possible to test whether a stack is empty. 5)It should be possible to access the topmost element in a stack without removing it.

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6-9 Stack ADT: contract (1) Possible contract, expressed as a Java interface: public interface Stack { // Each Stack object is a stack whose elements are objects. /////////////// Accessors /////////////// public boolean isEmpty (); // Return true if and only if this stack is empty. public Object getLast (); // Return the element at the top of this stack.

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6-10 Stack ADT: contract (2) Possible contract (continued): /////////////// Transformers /////////////// public void clear (); // Make this stack empty. public void addLast (Object elem); // Add elem as the top element of this stack. public Object removeLast (); // Remove and return the element at the top of this stack. }

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6-11 Implementation of stacks using arrays (1) Represent a bounded stack (depth maxdepth) by: variable depth, containing the current depth array elems of length maxdepth, containing the stacked elements in elems[0… depth–1]. Invariant: element 01 depth–1depthmaxdepth–1 Empty stack: 1 length=0 maxdepth–1 Illustration (maxdepth = 6): Moby Dick War & Peace Rob Roy 1 0 2 depth=3 4 5 topmost elementunoccupied

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6-12 Implementation using arrays (2) Java implementation: public class ArrayStack implements Stack { private Object[] elems; private int depth; /////////////// Constructor /////////////// public ArrayStack (int maxDepth) { elems = new Object[maxDepth]; depth = 0; }

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6-13 Implementation using arrays (3) Java implementation (continued): /////////////// Accessors /////////////// public boolean isEmpty () { return (depth == 0); } public Object getLast () { if (depth == 0) throw … ; return elems[depth-1]; }

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6-14 Implementation using arrays (4) Java implementation (continued): /////////////// Transformers /////////////// public void clear () { for (int i = 0; i < depth; i++) elems[i] = null; depth = 0; } public void addLast (Object elem) { if (depth == elems.length) throw … ; elems[depth++] = elem; }

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6-15 Implementation using arrays (5) Java implementation (continued): public Object removeLast () { if (depth == 0) throw … ; Object topElem = elems[--depth]; elems[depth] = null; return topElem; } } Analysis: Operations isEmpty, getLast, addLast, removeLast have time complexity O(1). Operation clear has time complexity O(n).

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6-16 Implementation of stacks using SLLs (1) Represent an (unbounded) stack by an SLL, such that the first node contains the topmost element. Invariant: element Empty stack: Illustration: Rob Roy War & Peace Moby Dick topmost element

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6-17 Implementation using SLLs (2) Java implementation: public class LinkedStack implements Stack { private SLLNode top; /////////////// Constructor /////////////// public LinkedStack () { top = null; }

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6-18 Implementation using SLLs (3) Java implementation (continued): /////////////// Accessors /////////////// public boolean isEmpty () { return (top == null); } public Object getLast () { if (top == null) throw … ; return top.element; }

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6-19 Implementation using SLLs (4) Java implementation (continued): /////////////// Transformers /////////////// public void clear () { top = null; } public void addLast (Object elem) { top = new SLLNode(elem, top); }

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6-20 Implementation using SLLs (5) Java implementation (continued): public Object removeLast () { if (top == null) throw … ; Object topElem = top.element; top = top.succ; return topElem; } } Analysis: All operations have time complexity O(1).

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6-21 Stacks in the Java class library Java provides no Stack interface or class as such. However, the java.util.LinkedList class provides all the above Stack operations. Illustration: import java.util.LinkedList; LinkedList bookStack = new LinkedList(); bookStack.addLast("Moby Dick"); bookStack.addLast("War & Peace"); bookStack.addLast("Rob Roy"); System.out.println(bookStack.removeLast());

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6-22 Example 3: text-file reversal revisited (1) Recall the text-file reversal algorithm of Example 1. Implementation: public static void reverse ( BufferedReader input, BufferedWriter output) throws IOException { LinkedList lineStack = new LinkedList(); for (;;) { String line = input.readLine(); if (line == null) break; // end of input lineStack.addLast(line); } input.close();

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6-23 Example 3 (2) Implementation (continued): while (! lineStack.isEmpty()) { String line = lineStack.removeLast(); output.write(line + "\n"); } output.close(); }

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