COT 5405

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COT 5405

• Spring 2009
• Discussion Session 3

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Introduction

• Our weekly discussion class are like organized TA
  office hours.
• Here we encourage students to come with their
  problems and questions about class and book.
• Rather than doing One-to-one discussion like
  regular TA office hours, we do group discussion
  to solve problems.
• We mostly discuss about proofs and problems
  presented in regular lecture classes, but in more
  details. To help better understanding of them.
• Again, we encourage students to come to Tuesdays
  discussion class more frequently.
• Unfortunately no video is available for EDGE
  students. As this is not lecture, just like TA
  office hour.

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Problem 1

• In the algorithm SELECT, the input elements are
  divided into groups of 5.
• Will the algorithm work in linear time if they
  are divided into groups of 7?
• Argue that SELECT does not run in linear time if
  groups of 3 are used.

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Problem 2

• Let X1 .. n and Y 1 .. n be two arrays, each
  containing n numbers already in sorted order.
  Give an O (lg n)-time algorithm to find the
  median of all 2n elements in arrays X and Y.

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Problem 3

• Show that the second smallest of n elements can
  be found with n ?lg n? - 2 comparisons in the
  worst case.
• (Hint Also find the smallest element.)

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Problem 4
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Problem 5

• You are the TA for a class with an enrollment of
  n students. You have their final scores
  (unsorted), and you must assign them one of the k
  available grades (A, B, C etc.). The constraints
  are (assuming n is a multiple of k)
• Exactly (n/k) students get each grade (for
  example, if n 30, and k 3, i.e. the available
  grades are A,B,C, then exactly 10 students get
  A, 10 get B, and 10 get C)
• A student with lower score doesnt get a higher
  grade than a student with a higher score
  (however, they may get the same grade)
• Assuming that each student received a different
  score, derive an efficient algorithm and give its
  complexity in terms of n and k.

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Problem 6
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Problem 7
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Problem 8

• Consider a list of size n, which has at most log
  n distinct numbers, the rest being repetitions of
  those numbers.
• Design an algorithm to sort this list in
• O(n log log n) time.
• (Hint First partition the list into n / log n
  lists of size log n and use a merge sort-like
  strategy).

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Problem 9
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Comments

• Problems 1,2,3,4,5,6(a) and 8 were discussed in
  discussion session 3.
• We do not plan to provide any written solution to
  these problems.
• Students are welcome to send us email with
  solutions of these problems. We can verify your
  solutions.