CS 280 Data Structures

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CS 280Data Structures

• Professor John Peterson

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Test 1

• Well do a test next week on Wednesday. It will
  take the entire period. You can have 1 page of
  notes.
• Think about all of the homework / projects /
  quizzes weve had. Ill be doing something
  similar.
• There will be a little programming.
• I have graded homework!
• Im slowly getting projects graded watch your
  email.

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Call Trees

• A call tree shows the different calls to
  methods and their arguments. For example, in
  sorting 2,4,3,7,1,8, if the pivot is 4, this
  will generate calls to qs 2,3,1 and qs 7, 8.
  Im not worried about the ordering of elements
  coming out of partition I could have said
  2,1,3 as well. Lets draw a full tree on the
  board.

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Complexity

• Whats the time complexity?
• partition takes O(s) time, where n size of
  subarray (this is bounded by O(n), why?)
• So how many recursive calls are there and how
  long does each take?
• That depends on the shape of the call tree.

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A Good Call Tree

• Suppose the partition always divides the array in
  half.
• What does the call tree look like in terms of
  size?
• What is the complexity in this case?

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A Bad Call Tree

• Suppose the pivot happens to divide the array
  into unequal parts the pivot is always the
  highest thing in the subarray. What does the
  call tree look like? What is the complexity?
  How might we get a bad tree?

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Preventing Bad Trees

• Choose the pivot in the middle. This is the
  right choice for sorted data and its unlikely
  that this would be bad for any common data
  ordering
• Choose the pivot randomly this defeats any
  pattern in the incoming data.
• Middle pivots are usually good enough. Note
  that a bad strategy has to be bad most of the
  time a few bad picks dont mess up the
  complexity.