Notes

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Notes

• Office hours for jfh Tu/Th 230-4, but will
  extend to 430 by request (send email).

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Seam Carving Demo
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Seam Carving Algorithm

• Find cost/path of best seam from bottom row to
  bottom (easy)?
• Foreach higher row
• foreach pixel
• Find least cost of three pixels beneath
• Mark it as next step in path
• add its cost to importance of this pixel record
  this cost
• At top row
• Find lowest-cost pixel
• Follow its path

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Dynamic Programming

• Start from the end and work back
• Cache previously computed results
• Instance of inductive thinking

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ltInductiongt
6
Mapping the internet

• You can use a tool called ping to find out the
  round-trip time to any point in the internet
• Can you figure out the topology of the internet
  that way (whos connected to whom directly)?
• In practice, no
• Topology keeps changing
• Network has cycles multiple ways to get from
  here to there

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Reduced problem

• In an acyclic (no cycles) network, if you know
  all pairwise distances, can you find the
  topology?
• Example
• Note symmetry AB BA

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Harder problem
9
Harder problem
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Generic Solution

• If we could just reduce the size by one, wed be
  in good shape, because that 2x2 problem was
  really easy!

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Stacks

• Saw them last semester Java stack-traces.
• The stack trace shows how you got here when you
  have an error
• The stack tells the program how to continue when
  its done with this procedure invocation!
• Stacks are great as breadcrumbs (Hansel and
  Gretel)?
• Good for looking back for recent extreme events
• Great for checking clean code (matching parens,
  matching tags in HTML, etc.)?

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StacksThe Stack Interface
public int size()? public boolean
isEmpty()? public E top()? public void push(E
element)? public E pop()?
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Array Based StacksFinite Size Implementation
Constructor public ArrayStack(int capacity)
S ? (E) new Objectcapacity // array t
? -1 // top of stack
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Style Notes

• Note missing from both definitions are the
  class-definitions. For Java, it might look like
  this
• public class ArrayStack
• public ArrayStack(int capacity)
• S ? (E) new
• For Python, its this
• class ArrayStack()
• """Array-based implementation of finite
  stack"""
• def __init__(self, capacity)
• self.S None for x in range(0,
• Note doc string just after class name, and
  indentation.

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Array Based Stacks
public int size() return t 1 public
boolean isEmpty() return (t lt 0) public E
top() if (isEmpty())? throw
EmptyStackException return St public E
pop() if (isEmpty())? throw
EmptyStackException --t return St 1
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Array Based StacksFinite Size Implementation
public void push(E obj) if (t S.length -
1)? throw FullStackException t St ?
obj
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Array Based StacksGrowable Implementation
Constructor public ArrayStack(int capacity)
S ? (E) new Object1 // array t ? -1 //
top of stack
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Array Based Stacks Grow-by-One Implementation
public void push(E obj) if (t S.length() -
1) A ? (E) new
Object S.length 1 for i ? 0 to
S.length - 1 Ai ? Si S ?
A t St ? obj
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Array Based Stacks Array-Doubling Implementation
public void push(E obj) if (t S.length() -
1) A ? (E) new
Object S.length 2 for i ? 0 to
S.length - 1 Ai ? Si S ?
A t St ? obj
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Array Based Stacks
public static void testStack() ArrayStackltInteg
ergt s ? new ArrayStackltIntegergt()? s.push(3)?
s.push(4)? s.push(5)? print(s.pop()) //
'5' print(s.top()) // '4' s.push(8)? s.push(9)
? print(s.size()) // '4' // push a lot of elts
to test // array doubling s.push(0)? print(s.po
p()) // '0' s.push(1)? s.push(6)? s.push(7)?
s.push(9)? s.push(10)? print(s.size()) //
'9' while (!s.isEmpty()) print(s.pop() '
')? // '10 9 7 6 1 9 8 4 3' print(newline)? s
.top() // EmptyStackEx testStack() invoke
test code!
def test_stack() s ArrayStack()? s.push(3)?
s.push(4)? s.push(5)? print s.pop()
'5' print s.top() '4' s.push(8)? s.push(9)?
print len(s) '4' push a lot of elts to
test array doubling s.push(0)? print s.pop()
'0' s.push(1)? s.push(6)? s.push(7)? s.pus
h(9)? s.push(10)? print len(s) '9' while
not s.is_empty() print s.pop(), '10 9 7 6
1 9 8 4 3' print print newline s.top()
EmptyStackEx test_stack() invoke test code!
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Python Exceptions
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Printing in Python
To tell Python what to print when the user tries
to print your stack, you need to implement the
__str__ method. This method constructs a string
and then returns it to be printed by Python.
This is like overriding toString() in Java)?
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Notes on Python Style
def __init__(self, capacity) self.S None
for x in range(0, capacity) self.t -1 top
of stack

• Good practice indicate private variables with
  underscore (or even two see python doc)
• Problem harder to read, uses more space on
  slides.
• Solution YOU should do this I wont.

def __init__(self, capacity) self._S None
for x in range(0, capacity) self._t -1 top
of stack