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Dynamic Huffman Trees

Sibling property: there is an ordering of nodes such that C(n i )<=C( ni+1 ) for all i and for each adjacent pair of nodes n 2k-1 , n 2k are siblings in the Tree. Dynamic Huffman Trees. Example. Ordering is. Overflow. Overflow Part 2. Alles unter Kontrolle. Keeping track of Ordering.

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Dynamic Huffman Trees

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  1. Sibling property: there is an ordering of nodes such that C(ni)<=C(ni+1) for all i and for each adjacent pair of nodes n2k-1, n2k are siblings in the Tree. Dynamic Huffman Trees

  2. Example • Ordering is

  3. Overflow

  4. Overflow Part 2

  5. Alles unter Kontrolle

  6. Keeping track of Ordering • (one idea) Use Array representation of tree. • Store child/parent offsets (can’t use implicit representation, since Huffman trees aren’t necessarily “complete”) • (more clever) See if you can use pointers to require only 1 lookup to find the swap-node

  7. Increment Letter • Procedure IncrementLetter (letter) • letterPos = position of letter in Array representation of tree • suspectPos = letterPos • While suspectPos is not Root • Increment Count(letterPos) • If Count(suspectPos) > Count(suspectPos - 1) Then • { it got out of order } • lastOfCount = lowest #’d array index whose count is • the same as Count(suspectPos) used to be • Swap sub-Trees at lastOfCount, suspectPos • Else • { everything’s fine now } • Exit While • End If • suspectPos = Parent(lastOfCount) • End While

  8. Put new letter into tree Procedure InsertNewLetter (newLetter) { the NULL character is the special signal for a new character } Replace NULL node with newParentNode Make newParentNode a Parent of (NULL, newLetter) Run IncrementLetter algorithm on newLetter

  9. Exercise • Process 11-character text using dynamic Huffman tree. Write the encoding. • Periodically check if static tree would be the same • Use Array (used for Heap) or draw by hand. Text: The rather rash hero rode a horse that dashed with a wet head and dared to rise. It hid with tethered teeth that saw a sorrow. Oh, are these withered arrows of teeth so arid in war? Or has the horse the ride of heroes ridden in its hidden dose of worth? Letters: adefh iorst w (11 letters)

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