Stacks and Queues in Java

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In this section we describe two containers: the stack and the queue Both have simple interfaces and very efficient implementations Even so, as you will see, they are very useful data structures
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A stackrestricts accesstothe most recently inserted item
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A stack is a data structure in which all access is restricted to the most recently inserted element It behaves much like a stack of bills, stack of plates, or stack of newspapers The last item added to the stack is placed on the top and is easily accessible, whereas items that have been in the stack for a while are more difficult to access Thus the stack is appropriate if we expect to access only the top item; all other items are inaccessible In a stack the three natural operations of insert,remove,and find are renamed push,pop,and topThese basic operations are illustrated in Figure 72
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The Standard Template Library
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Stack model: Input to a stack is by push,output is by top, and deletion is by pop
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1 / / Stack protocol
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3 template <class Object> 4 class Stack 5 { 6 public: 7 virtual -Stack( ) {
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/ / Destructor
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virtual void push( const Object & x virtual void pop ( ) = 0 ; virtual const Object & top( ) const virtual boo1 isEmpty( ) const = 0; virtual void makeEmpty( ) = 0;
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/ / Insert / / Remove / / Find
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Protocol for the abstract stack class
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Stack operations take Of aConstant time
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The C++ class template shown in Figure 73 illustrates the typical protocol, which is similar to the protocol in the STL By pushing items and then popping them, we can use the stack to reverse the order of things Each stack operation should take a constant amount of time, independent of the number of items in the stack By analogy, finding today's newspaper in a stack of newspapers is fast, no matter how deep the stack is However, arbitrary access in a stack is not efficiently supported, so we do not list it as an option in the protocol What makes the stack useful are the many applications for which we need to access only the most recently inserted itetn An itnportant use of stacks is in cornpiler design
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722 Stacks and Computer Languages
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Compilers check programs for syntax errors Often, however, a lack of one symbol (eg, a missing * / or 1) causes the compiler to spill out numerous lines of diagnostics without identifying the real error Other compilers are simply quiet: some will tell you that -main is undefined, even though the real problem is a missing closing brace A useful tool in this situation is a program that checks on whether everything is balanced, that is, every { corresponds to a } , every [ to a ] , and so on The sequence [ ( ) I is legal, but [ ( 1 ) is not-so simply counting the numbers of each symbol is insufficient (Assume for now that we are processing only a sequence of tokens and won't worry about problems such as the character constant { not needing a matching } ) A stack is useful for checking unbalanced symbols because we know that when a closing symbol such as ) is seen, it matches the most recently seen unclosed ( Therefore, by placing opening symbols on a stack, we can easily check that a closing symbol makes sense Specifically, we have the following algorithm
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A stack can be used check 'Or unbalanced symbols
1 Make an empty stack 2 Read symbols until the end of the file a If the token is an opening symbol, push it onto the stack b If it is a closing symbol and if the stack is empty, report an error c Otherwise, pop the stack If the symbol popped is not the corresponding opening symbol, report an error 3 At the end of the file, if the stack is not empty, report an error In Section 121 we will develop this algorithm to work for (almost) all C++ programs Details include error reporting, processing of comments, strings, and character constants, as well as escape sequences The algorithm used to check balanced symbols suggests a way to implement function calls The problem is that, when a call is made to a new function, all the variables local to the calling function need to be saved by the system; otherwise, the new function would overwrite the calling routine's variables Furthermore, the current location in the calling routine must be saved so that the new function knows where to go after it is done The variables have generally been assigned by the compiler to machine registers, and conflicts will certainly arise The reason that this problem is similar to balancing symbols is because a function call and a function return are essentially the same as an open parenthesis and a closed parenthesis, so the same ideas should apply This indeed is the case: As discussed in Section 83, the stack is used to implement function calls in most procedural languages