Midterm Review

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Midterm Review

• CSC 172
• SPRING 2002
• LECTURE 15

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Diversity

• The Faculty of the College affirms that
  diversity, pluralism, and respect for difference
  are fundamental values in our community. Learning
  cannot advance in an atmosphere of prejudice or
  intimidation. All members of our community --
  regardless of culture, religion, gender, or
  sexual orientation -- are entitled to learn and
  work in an environment of civility, dignity,
  fairness, and mutual respect.
• As a faculty, we condemn recent events on campus
  that exhibit bigotry, insensitivity to life, and
  hostility toward people on the basis of their
  ethnicity, religion, or sexual orientation.
  These malevolent behaviors and attitudes
  undermine our collective work and have no place
  in our community of learning.
• As scholars, we encourage one another -- and as
  teachers we encourage our students -- to reject
  these expressions of intolerance and work
  together to build the kind of open community that
  makes authentic learning possible. We cannot
  afford to be indifferent. We must speak out
  against these deplorable expressions. We must
  expect better of ourselves and of one another.
  
• Thank you,
• Sanford L. Segal
• Chair of the Faculty Council
• Steering Committee

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Freedom of thought

• Do people have the right to hold wrong opinions?
• Do we tolerate intolerance?
• Treating people decently does not imply approval.

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Professionalism

• People have both public and private lives
• Sort of like public and private interfaces
• public life provides a context for social
  interaction
• public life is to some degree regulated (laws,
  cultures)
• We often deal with people with whom we disagree
  because we can share purposes with people
• Professionalism allows us to maintain a workable
  public interface with diverse people
• Tolerance (public) does not imply that you agree
  (private)
• So, it is possible to maintain both workable
  social relationships and individual freedom of
  thought

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Scholarship

• Being a member of the university community
  implies a shared objective a public society
• The tradition of scholarship is a tradition of
  openness
• This implies having the courage to take credit
  for your statements
• Having to take credit for your statements tends
  to raise the level of discussion

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General Recurrence Relations

• The solution to
• T(n) aT(n/b) O(nk)

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Proof

• Assume T(1) 1
• Assume n is a power of b
• n bm
• n/b bm-1
• nk (bm)k bmk bkm (bk)m
• So,
• T(bm) aT(bm-1) (bk)m

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Divide by am
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Telescoping
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agtbk

• The sum is a geometric series with ratio lt 1
• Since the sum of such an infinite series would
  converge to a constant, the finite sum is also
  bound by a constant

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abk

• Each term of the sum is 1
• The sum contains 1logbn terms
• abk implies logba k

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altbk

• The sum is a geometric series with ratio gt 1

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(Aside)

• Prove by induction on n

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(No Transcript)
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Chuck-a-Luck

• Show that in Chuck-a-Luck, the probability of any
  event in which all three dice have different
  values is twice the probability of any event
  where one number appears exactly twice and six
  times the probability of any event in which all
  three dice show the same number.

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Chuck-a-Luck

• Show that in Chuck-a-Luck, the probability of any
  event in which all three dice have different
  values is twice the probability of any event
  where one number appears exactly twice and six
  times the probability of any event in which all
  three dice show the same number.

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Chuck-a-Luck

• An event is a unique throw of the dice
• There are 6 different events of all the same
  number
• P(all 1s) 1/216
• P(all 2s) 1/216
• P(all 6s) 1/216

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Chuck-a-Luck

• There are 120 events where all the numbers are
  distinct 654
• But some are indistinguishable
• There are 6 ways to arrange 3 items
• P(any event where all numbers different) 6/216
• So,

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Chuck-a-Luck

• There are 30 different ways of getting the same
  number exactly twice 65
• For each event (say 2 1s, and one 2) there
  are 3 ways to get it ((1,1,2),(1,2,1),(2,1,1))
• P(any event where one number appears twice)
  3/216

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Error Correcting Codes

• If no two strings in a code differ in fewer than
  three positions, then we can actually correct a
  single error, by finding the unique string in the
  code that differes from the received string in
  only one position. It turns out that there is a
  code of 7 bit string that corrects single errors
  and contains 16 strings. Find such a code.

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Error Correcting Codes

• 0000 and 0001 differ by 1
• 0000 and 0011 differ by 2
• 0000 and 0111 differ by 3
• So, if I only allowed 0000 and 0111 and there was
  only one error, then I could always recover
• 0001,0010,0100,1000 -gt 0000
• 1111,0011,0101,0110 -gt 0111

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Error Correcting Codes
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
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Error Correcting codes d 1
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
0 0 0 1 1 0 0
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Error Correcting codes d 1
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
0 0 1 0 0 1 0
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Error Correcting codes d 1
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
0 1 0 0 0 0 0
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Error Correcting codes d 1
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
1 0 0 0 0 0 1
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Error Correcting codes d 2
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
1 1 0 0 1 1 0
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Error Correcting codes d 2
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
1 0 1 0 1 0 0
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Error Correcting codes d 2
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
1 0 0 1 0 1 0
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Error Correcting codes d 2
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
0 1 1 0 0 0 1
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Error Correcting codes d 2
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
0 1 0 1 0 1 1
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Error Correcting codes d 2
a b c d P(abc) P(abd) P(bcd)
0 0 0 0 1 1 1
0 0 1 1 0 0 1
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So, whats on the exam? (180 min)

• Linked Lists (code)
• Stacks (algs)
• Queues (algs)
• Proof by induction (section)
• Recurrence Relations (math)

• Big-Oh (section)
• Run time of code segments
• Combinatorics (section)
• Probability
• Recursion (QS,MS, etc)

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Homework Solutions

• http//www.cs.rochester.edu/pawlicki/lectures/CSC
  172

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When and where is the exam

• Friday March 8th
• 8AM-11AM, 632 CSB 4 students
• 2PM-5PM, 115 Harkness