Stacks and Queues

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Stacks and Queues

• Joe Komar

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Stacks and Queues Overview

• Dont represent real-world data but more
  programmer tools temporary for running of
  program
• Only one item can be read or removed at a given
  time (versus arrays)
• More abstract than arrays the underlying
  implementation is hidden and its interface is
  what is important

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Stacks

• Only the last item inserted in a stack is
  available
• Used to parse arithmetic expressions
• Used with other data structures
• Binary trees
• Graphs
• Concepts also used in hardware design
• First-in, Last-out
• Pushing placing an item on the top of the stack
• Popping removing an item from the top of the
  stack
• (see example applet) (see example code)

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Stack Examples

• Reversing a string
• Push each character
• Pop each character
• (see example code)
• Delimiter matching
• Left delimiter must have matching right delimiter
• Later opening delimiters need to be closed before
  previous opening delimiters
• (see example code)

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Efficiency of Stacks and Queues

• Time is not dependent on how many items there are
  in the stack or queue
• Therefore, O(1) time for both insertion and
  deletion (there is NO searching)

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Queues

• British for line
• First-in, first-out
• Programmers tool e.g., search a graph
• Real-world modeling waiting lines of people,
  planes, data packets, etc.
• Insert (put, add, enque) an item at the rear
  (back, tail, end) of the queue
• Remove (delete, get, deque) an item from the
  front (head) of the queue
• (see example applet and circular queue ring
  buffer) (see example code)

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Priority Queues

• Just like a queue (first-in, first-out)
• Ordered by some key value, usually from low to
  high
• Used as a programmers tool
• Used for other data structures such as Weighted
  Graphs
• Used in operating systems (preemtive,
  multitasking)
• Often use a heap as its underlying implementation
  (quick insertion)
• (see example applet) (see example code)

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Priority Queue Efficiency

• Deletion O(1)
• Insertion O(N)

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Parsing Arithmetic Expressions

• Uses stacks
• Transform the expression (infix format) into
  postfix format (complex)
• Evaluate the postfix expression (easy)
• ((AB)C)-D ? ABCD-
• AB(C-D/(EF)) ? ABCDEF/-

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Evaluating an expression

• 5
• 6
• 2
• End
• 562

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Evaluating an Expression

• (
• 5
• 6
• )
• 2
• End
• (56)2

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Translating Infix to Postfix

• AB-C ABC-
• ABC ABC
• A(BC) ABC
• AB(C-D) ABCD-
• (see translation rules in text)
• (see example code)

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Evaluating Postfix Expressions

• Creating postfix from infix is not trivial at
  all!
• Rules for postfix evaluation
• If operand, push it into the stack
• If operator, pop the two operands from the stack
  and apply the operator to them, then push the
  result
• (see example code)

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Summary

• Stacks, queues, and priority queues are typically
  programmer tools
• Only one data item is accessed
• Stack is first-in, last-out
• Queues are first-in, first-out
• Priority queues retain ordered data
• Can all be implemented with arrays or other
  mechanisms such as linked lists
• Stacks are indispensable for arithmetic
  expression evaluation