Queues - Data Structures - Lecture Slides, Slides of Data Structures and Algorithms

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Queues,Stacks and

Topological sort

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STACK QUEUES

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Stacks

• All access is restricted to the most recently inserted elements
• Basic operations are push, pop, top.

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Stack

push (^) pop, top

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Non-Computer Examples

• Stack of papers
• Stack of bills
• Stack of plates
• Expect O ( 1 ) time per stack operation. (In other words, constant time per operation, no matter how many items are actually in the stack).

Balanced Symbol Algorithm

• Make an empty stack.
• Repeatedly read tokens; if the token is
  • an opening symbol, push it onto the stack
  • a closing symbol
    • and the stack is empty, then report an error;
    • otherwise pop the stack and verify that the popped symbol is a match (if not report an error)
• At the end of the file, if the stack is not empty, report an error.

Example

• Input: {()}
• Push {
• Push (; stack has {(
• Pop; popped item is ( which matches ). Stack now has {.
• Pop; popped item is { which matches }.
• End of file; stack is empty, so all is good.

Procedure Stack

• Matching symbols is similar to procedure call and procedure return, because when a procedure returns, it returns to the most recently active procedure. Procedure stack can be used to keep track of this.
• Abstract idea: when procedure call is made, save current state on a stack. On return, restore the state by popping the stack.

Activation Records

• Actual implementation is slightly different (note that text describes the abstract implementation).
• The top of stack can store the current procedure environment.
• When procedure is called, the new enviromment is pushed onto stack.
• On return, old enviroment is restored by pop

Queues

• All access is restricted to the least recently inserted elements
• Basic operations are enqueue, dequeue, getFront.

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enqueue^ Queue dequeue getFront

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Examples

• Line for Panther tickets
• Line printer queue
• Queue is a British word for line.
• Expect O ( 1 ) time per queue operation because it is similar to stack. The word "queueing" and its derivatives are the only English words with five consecutive vowels.

Array Implementations

• Stack can be implemented with an array and an integer top that stores the array index of the top of the stack.
• Empty stack has top equal to -1.
• To push, increment the top counter, and

write in the array position.

• To pop, decrement the top counter.

Stages

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top(-1)

A top(0) (^) A

B top(1)

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Running Time

• Without array doubling, all operations are constant time, and do not depend on number of items in the stack.
• With array, doubling, a push could occasionally be O ( N ). However, it is essentially O ( 1 ) because each array doubling that costs N assignments is preceded by N / non-doubling pushes.

Queues: Simple Idea

• Store items in an array with front item at index zero and back item at index Back.
• Enqueue is easy: increment Back.
• Dequeue is inefficient: all elements have to be shifted.
• Result: Dequeue will be O ( N ).