Bài giảng Cấu trúc dữ liệu_Phần Stack

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Chapter 6

Stacks

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Chapter Objectives

• Define a stack abstract data type

solve problems

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Stacks

• A stack is a linear collection whose elements

are added and removed from one end

• A stack is LIFO – last in, first out

• The last element to be put on the stack is the first element to be removed

• A stack is usually depicted vertically, with

additions and deletions occurring at the top

of the stack

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FIGURE 6.1

A conceptual view of a stack

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FIGURE 6.2

The operations on a stack

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FIGURE 6.3

The StackADT interface in UML

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Listing 6.1

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Postfix Expressions

• Let's examine a program that uses a stack to

evaluate postfix expressions

• In a postfix expression, the operator comes after its two operands

• We generally use infix notation, with

parentheses to force precedence:

(3 + 4) * 2

• In postfix notation, this would be written

3 4 + 2 *

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Postfix Expressions

• To evaluate a postfix expression:

– scan from left to right, determining if the next

token is an operator or operand

– if it is an operand, push it on the stack

– if it is an operator, pop the stack twice to get the two operands, perform the operation, and push the result onto the stack

• At the end, there will be one value on the

stack, which is the value of the expression

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FIGURE 6.4 Using a stack to

evaluate a postfix expression

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Postfix Expressions

• To simplify the example, let's assume the

operands to the expressions are integer

literals

any implementation of a stack would suffice

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Listing 6.2

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Listing 6.2 (cont.)

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Listing 6.3

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FIGURE 6.5 A UML class diagram

for the postfix expression program

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Using Stacks - Traversing a

Maze

• A classic use of a stack is to keep track of

alternatives in maze traversal or other trial

and error algorithms

• Using a stack in this way simulates recursion

– Recursion is when a method calls itself

either directly or indirectly

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Maze

calls by placing an activation record for each called method on the run-time stack

• When a method completes execution, it is

popped from the stack and control returns to the method that called it

– Which is now the activation record on the top of the stack

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Maze

• In this manner, we can traverse a maze by

trial and error by using a stack to keep track

of moves that have not yet been tried

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Listing 6.4

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Listing 6.5

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The LinkedStack Class

• Now let's examine a linked implementation of

a stack

used in Chapter 3 to define the linked

implementation of a set collection

• 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

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FIGURE 6.6 A linked

implementation of a stack

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LinkedStack - the push

Operation

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FIGURE 6.7 The stack after

pushing element E

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LinkedStack - the pop Operation

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FIGURE 6.8

The stack after a pop operation

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The ArrayStack Class

• Now let's examine an array-based

• We'll make the following 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

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FIGURE 6.9 An array

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ArrayStack - the push Operation

// Adds the specified element to the top of the stack, expanding // the capacity of the stack array if necessary.

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FIGURE 6.10

The stack after pushing element E

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ArrayStack - the pop Operation

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FIGURE 6.11 The stack after

popping the top element

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The java.util.Stack Class

• The Java Collections framework defines a

Stack class with similar operations

• It is derived from the Vector class and

therefore has some characteristics that are not appropriate for a pure stack

around since the original version of Java,

and has been retrofitted to meld with the

Collections framework

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FIGURE 6.12 A UML description

of the java.util.Stack class

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Analysis of Stack Operations

of the collection, they are generally efficient

and array implementations, are O(1)

implementations are O(1)

have that characteristic) aren't as efficient for all operations

Tiêu đề	Bài giảng Cấu trúc dữ liệu_Phần Stack
Thể loại	Bài giảng
Năm xuất bản	2005

Định dạng
Số trang	45
Dung lượng	1,81 MB