Stacks

1
Stacks Queues

• CSC 172
• SPRING 2002
• LECTURE 4

2
Agenda

• Stack
• Definition
• Implementation
• Analysis
• Queue
• Definition
• Implementation
• Analysis

3
Workshop sign-up

• Still time
• Dave Feil-Seifer df001i_at_mail.rochester.edu
• Ross Carmara rc001i_at_mail.rochester.edu
• Read Culotta article on team work in science

4
HOMEWORK 2

• AU
• 6.6.1,6.6.2(Java),6.6.4,6.6.6
• 6.7.1
• 6.8.1,6.8.2,6.8.3

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Stacks

• LIFO (last in, first out) data structure
• Restricts access to the most recently inserted
  item
• Stacks are an ADT with operations push pop
• void push(Object o)
• void pop()
• Object top()

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STACK
pop, top
push
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STACK INTERFACE

• public interface Stack
• void push(Object x) //insert
• void pop() // remove
• Object top() // find
• Object topAndPop() // find remove
• boolean isEmpty()
• void makeEmpty()

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Example Balance checking

• Compilers check for syntax errors
• One syntax error is mismatched delimiters
• must match
• ( must match )
• must match
• () is legal, but () is not
• Could you write a balance checker?

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A useful stack algorithm

• Balance checking
• Make an empty stack
• Read symbols until the end of file
• If the token is an opening symbol, push it onto
  the stack
• If the token is a closing symbol
• If the stack is empty, report an error
• Otherwise, pop the stack, if the symbol is not
  the corresponding opening symbol report an error
• At EOF if stack is not empty, report an error

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Trace by hand

• (())
• ()

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A useful stack algorithm

• Postfix evaluation
• We can rewrite the infix expression 12
• As the postfix expression 1 2
• Think like a computer
• load value 1 into accumulator
• load value 2 into register A
• Add value in register A to value in accumulator
• How about 1234 ?
• How about 234?
• How about 234?

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How to implement?

• Can you write method that evaluates postfix
  expressions?
• double postfixeval(Object items)
• Where objects in items are either
• Double
• Character

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Postfix evaluation using a stack

• Make an empty stack
• Read tokens until EOF
• If operand push onto stack
• If operator
• Pop two stack values
• Perform binary operation
• Push result
• At EOF, pop final result

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Trace by hand

• 1 2 3 4
• 2 3 4
• 2 3 4

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Stacks to manage function calls

• Especially for recursion
• Fibonacci numbers
• fib(1) fib(2) 1
• fib(n) fib(n-1) fib(n-2)
• int fib (int n)
• if (n lt 3) return 1
• else return fib (n-1) fib(n-2)

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Rewrite fib

• int fib (int n)
• int temp1, temp2
• if (n lt 3) return 1
• else
• temp1 fib (n-1)
• temp2 fib(n-2)
• return temp1 temp2

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fib(5)
fib(2)
1
fib(3)
fib(4)
fib(5)
18
fib(5)
fib(1)
1
fib(3) 1
fib(4)
fib(5)
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fib(5)
fib(3) 1 1
2
fib(4)
fib(5)
20
fib(5)
fib(2)
1
fib(4) 2
fib(5)
21
fib(5)
fib(4) 2 1
3
fib(5)
22
fib(5)
fib(2)
1
fib(3)
fib(5) 3
23
fib(5)
fib(1)
1
fib(3) 1
fib(5) 3
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fib(5)
fib(3) 1 1
2
fib(5) 3
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fib(5)

• fib(5) returns fib(4) fib(3) 3 2 5

fib(5) 3 2
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fib(5)
fib(1)
fib(2)
1
1
fib(3)
fib(3)
fib(3)
2
fib(5)
fib(5)
fib(5)
27
fib(5)
fib(2)
fib(1)
1
1
fib(3)
fib(3)
fib(3)
fib(2)
2
1
fib(4)
fib(4)
fib(4)
fib(4)
fib(4)
3
fib(5)
fib(5)
fib(5)
fib(5)
fib(5)
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Queues

• FIFO (first in, first out) data structure
• Restricts access to the least recently inserted
  item
• Queues ADT operations enqueue dequeue
• void enqueue(Object o)
• Object dequeue()
• Object getfront()

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QUEUES
enqueue
dequeue
getFront
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QUEUE INTERFACE

• public interface Queue
• void enqueue(Object x) //insert
• Object getFront() // find
• Object dequeue() // find remove
• boolean isEmpty()
• void makeEmpty()