CS1102 Tut 8 AVL Trees and Hashing

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CS1102 Tut 8 AVL Trees and Hashing

• Max Tan
• tanhuiyi_at_comp.nus.edu.sg
• S15-03-07 Tel[phone]http//www.comp.nus.edu.sg
  /tanhuiyi

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Groups assignment

• Group 1 - Question 4Group 2 - Question 1Group 3
  - Question 2Group 4 - Question 3

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First 15 minutes

• Any questions?
• Mock PE exam treat it as a practice!
• Unix Tutorial
• Pico editor
• Compiling in Unix
• Executing in Unix

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First 15 minutes

• Hashtable
• Linear Probing
• Quadratic Probing
• Separate Chaining

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Question 1

• Write an AVL ADT
• What are the public and private methods you need
  ?
• Public operations Add, Delete, Get, Size
• What do you need to do after you add?
• Balance
• When balancing, you need to rotateLeft and
  rotateRight
• To balance, you need to know the height of the
  left and right subtrees

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Question 1

• Algorithm for Balance, consider the cases
• Case1 Left.height gt right.height

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Question 1

• Algorithm for Balance, consider the cases
• Case2 Right.height gt left.height

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Question 1

• So, break it up into two cases and consider them
  seperately
• Write a rotateLeft and a rotateRight method to
  further simplify the problem!

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Question 1

• In this case we simply rotate right about x
• rotateRight(x)

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Question 1

• In this case just rotating right wont solve the
  problem! (why? See next slide)
• rotateLeft(y)
• rotateRight(x)

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Question 1
12
Question 1

• Simply rotate about x
• rotateLeft(x)

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Question 1

• Again simply rotating about x wont solve this
• rotateRight(z)
• rotateLeft(x)

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Question 1

• After you break it up its easy!
• Balance(Treenode T)if(leftchild.height gt
  rightchild.height)
• if(leftchild.leftHeight gt leftChild.rightHeight)
  
• //Case 1a (insert outer)
• rotateRight(t)
• else
• //Case 1b (insert inner)
• rotateLeft(leftChild)
• rotateRight(t)

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Question 1

• else //if(rightchild.height gt
  leftchild.height)
• if(rightchild.rightHeight gt rightchild.leftHeigh
  t)
• //Case 1a (insert outer)
• rotateLeft(t)
• else
• //Case 2a
• rotateRight(rightChild)
• rotateLeft(t)

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Question 1

• What is the worst case?

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Question 1

• Have to balance for each level!
• Question What is the maximum number of balance
  operations for an ADD operation?

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Question 2

• Good Hash function easy to compute
• Evenly distribute data

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Question 2

• (a) The hash table has size 2048. The search keys
  are English words.The hash function is h(key)
  (sum of positions in alphabet of keys letters)
  mod 2048
• In your lecture notes, Imagine a word is of
  length 10 (average), this hash function will
  generate values between (x 0) (x 260)
  where x is the starting index of the letter a
• All words will be hashed to that 260 locations,
  and not make use of the remaining 1700 locations!
• Also words like not and ton hash to the same
  location
• To improve, add weights to each letter!

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Question 2

• (b) The hash table has size 2048. The keys are
  strings that begin with a letter.The function
  is h(key) (position in alphabet of the first
  letter of key) mod 2048
• Even worst, all keys get hashed to (x0)
  (x26)th location in the array!
• Lots of collisions!
• Imagine if we try to hash the IC number!
  (Singaporean IC number starts with S)

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Question 2

• (c) The hash table is 10000 entries long. The
  search keys are integers in the range 0 to 9999.
  The hash function is
• h(key) (key random) truncated to an
  integer, where random is a number generated
  randomly from 0 to 1
• This hash function wont even work at all. This is
  because the random function will generate a
  different number each time it is called!
• This means you wont be able to recover the items
  you have inserted into the hashtable!

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Question 2

• (d) The hash table is 10000 entries long. The
  search keys are integers in the range 0 through
  9999. The hash function is given by the following
  Java method
• This hash function needs 1million operations to
  compute!
• It may be even, but it is too slow!

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Question 3

• Inserting 10,22,31,4,15,28,17,88,59 into a table
  using linear probing

10
22
31
4
28
17
88
59
d
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Question 3

• Inserting 10,22,31,4,15,28,17,88,59 into a table
  using quadratic probing

10
22
31
4
28
17
88
59
d
15
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Question 4

• A perfect hash function is one that has a
  one-to-one mapping between keys and hash values.

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Question 4

• Suppose h3(key) (3key mod 11) 1 and the table
  size is 10. The keys are integers from 0 to 9
  inclusive. Is h3 a perfect hash function? Why?
• No! h(0) h(5)!

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Question 4

• Suppose h2(key) (2key mod 11) 1 and the table
  size is 10. The keys are integers from 0 to 9
  inclusive. Is h2 a perfect hash function? Why?
• Yes, because the hash function generates a unique
  number for each key. Try it out exhaustively

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Question 4

• 20 1 h(x) 0
• 21 2 h(x) 1
• 22 4 h(x) 3
• 23 8 h(x) 7
• 24 16 h(x) 4
• 25 32 h(x) 9
• 26 64 h(x) 8
• 27 128 h(x) 6
• 28 256 h(x) 2
• 29 512 h(x) 5