Stacks and Applications

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Stacks and Applications
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Stack

• A stack is a data structure of entries in order.
• Entries can be inserted and removed only at one
  end - the top.
• Insert an entry push operation.
• Remove an entry pop operation.
• A stack is a Last in/First out data structure
  -LIFO

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Most important

• A stack can only
• be accessed
• at the top.

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Another stack
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Application Matching parentheses

• pseudocode
• while the expression still has entries
• read a character c
• if c is (, put ( on the stack.
• if c is ), pop symbol from stack. If the stack
  is empty, parentheses are unbalanced.
• if c is anything else, do nothing.
• if stack is not empty, then parentheses are
• unbalanced.
• else parentheses are balanced.

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Apply the algorithm to

• (37(75)(9-10))
• 6((5-4)7(513)
• (7-6(59(4-2))))
• Show the stacks
• Can you improve the algorithm so it tells whether
  too many ( or too many )?

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Application Evaluating parenthesized expressions

• An expression is completely parenthesized,
  contains numbers, blanks, operations.
• Always evaluate the left-most subexpression that
  has no inner parentheses, and replace it with its
  value.
• ((6(12/4))(2(7-2)))
• Right parentheses tell us when to evaluate.
• Use stacks to keep track of numbers, operators.

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Application Evaluating parenthesized expressions

• pseudocode
• while there is still input
• read an item
• if it is a number, put it on the number stack
• if it is an operator, put it on the operator
  stack
• if it is a left parenthesis or blank, do
  nothing.
• if it is a right parenthesis, take the top two
• numbers from the number stack, and the top
• operation from the operator stack, combine the
  
• numbers with the operator, and put the result
  onto
• the number stack.
• The final result is the number on the number
  stack.

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Evaluate this expression

• Follow the pseudocode.
• Write out the stacks.
• (((129)/3)6)((6-4)/6))

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STL stack interface p.350

• Some members of the stackltItemgt Class from
  ltstackgt
• // TYPEDEFS
• // value_type the data type of the items in the
• //stack from the Item parameter
• // size_type the data type for a variable that
• //keeps track of how many items in a stack
• // CONSTRUCTOR Default constructor Creates an
  empty
• //stack
• // VOID FUNCTIONS TO INSERT AND REMOVE ITEMS
• // pop( ) pop is a void function that
  pops(removes)
• //the top item of the stack
• // push(const Item entry) Pushes the item onto
  the
• //top of the stack

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STL stack interface

• Some members of the stackltItemgt Class from
  ltstackgt
• // FUNCTIONS TO EXAMINE THE STACK AND ITS ITEMS
• // empty( ) const Returns true if the stack is
  empty
• //(otherwise returns false)
• // size( ) const Returns the number of items in
  the
• //stack
• // top( ) Returns a reference to the top item
  on
• //the stack (without removing it)
• // VALUE SEMANTICS
• // Assignments and the copy constructor may be
  used
• //with stackltItemgt objects.

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STL Programmers Guide

• http//www.sgi.com/tech/stl/stack.html

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Postfix or reverse Polish notation

• Write operator after the two numbers being
  combined 5 8
• Can write expressions without parentheses and
  without hierarchy of operations 5 8 3 6
• Invented by Jan Lukasiewicz, Polish logician

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Used on early HP calculators

• http//www.hpmuseum.org/rpn.htm
• Easy to program uses one stack
• Makes user do the work of converting expression
  to reverse Polish

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Application Evaluating postfix notation

• pseudocode
• while there is still input
• read an item
• if it is a number, put it on the stack
• if it is an operator, pop two numbers from
  the stack, combine them with the
  operator, and push the result back onto
  stack.
• The final result is the number on the stack.

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Evaluate

• Follow the pseudocode show the stack.
• 5 8 3 6
• 5 7 8 12 /