CSc212AB Data Structures Lecture 17

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CSc212AB Data StructuresLecture 17

• M. P. Johnson
• mpjohnson_at_gmail.com
• http//www-cs.ccny.cuny.edu/mjohnson/212/
• City College of New York, Spring, 2005

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Agenda

• Stacks
• Queues
• Recursion
• Hw4 up soon

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New topic Stacks

• Df ordered seq whose access is limited to
• FILO LIFO
• Simpler than list / list w/ limitation
• But hugely important
• 2nd after array
• Pops up all the time
• Idea each item stands on prev
• Each item removed is the oldest

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Stacks and the STL stack

• Definition
• A stack is a data structure of ordered entries
  such that entries can be inserted and removed at
  only one end (call the top)
• LIFO
• A stack is a Last-In/First-Out data structure.
  Entries are taken out of the stack in the reverse
  order of their insertion

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Stack ops - LL

• Push onto, pop off
• Lunch room trays
• Maybe also top look, dont remove
• Can back with LL or array
• LL

void stackpush(const dtype val)
list_head_insert(val)
dtype stackpop() dtype val
head-gtdata() list_head_remove()
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Stack ops - array

• Barring overflow, very fast
• Have datacapacity

void stackpush(const dtype val)
datatop o
void stackpush(const dtype val) return
data--top
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Stack apps

• Implementation pretty simple
• Just a restricted sequence
• Lots of important apps
• Simple one balancing symbols
• Exprs in formal langs must be valid, i.e.,
  parseable
• Html W3C
• Alg expressions
• C code
• One simple rule s, () cant cross
• Okay (), (), not ()(, )()(, ()
• How to check?

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Stack app 1 Balancing symbols alg

• Start with empty stack
• For each char
• if opening sym, push
• if closing sym, pop
• error if empty
• Error if not matching
• If get through w/o errors, then ok
• Draw runs for egs
• Complx for n chars?

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Stack app 2 parsing infix

• 2345 ?
• Normally interp as (23) (45) 26
• Win calc Standard interps as ((23) 4) 5 50
• Win calc sci doesnt
• w/o parens, infix notation is ambig
• Either way, Hard to parse
• Might get op long before second operand
• Have to remember op, retrieve when right
• MR, MC?
• Give eg

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postfix

• How to compute 23 45 with wincalcstd,
  conserving vars?
• compute a1 2 3 2 3
• compute a2 4 5 4 5
• compute a1 a1a2 a1 a2
• Can write as
• 2 3 4 5
• Postfix notation or reverse Polish
• Polish is prefix 2 3
• Jan Lukasiewicz

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Parsing postfix

• Parsing postfix much easier
• No ambig
• Simple alg
• Walk through expr
• See num ? push
• See (bin) opp ? pop twice, apply op, push
• When done, pop for result
• Thats all!
• Eg 652383/ ? 8

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Stack v. Queue

• Sequence of items
• Queue FIFO enQ/deQ
• Stack LIFO push/pop
• List usually implemented as either
• array
• Linked list
• Depending on freq of searchs v mods

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Stack app 3 Infix ? Postfix

• No one writes in postfix, so wheres it come
  from?
• Must convert from postfix
• With a stack
• A bit more diff than parsing postfix, but not too
  bad

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Infix ? Postfix rules

• Read operand ? print operand
• Read ( ? just push
• Read ) ? pop, print all until first (
• Parens not printed
• Dont pop ( in any other case
• Read ? pop stack until op w/ lwr prior
• ( counts as lowest prior

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Infix ? Postfix eg

• A bc
• A b c
• A (bc)
• Abc(def)g
• ? A b c d e f g