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CSC 263H               Tutorial Outline for Week  5             Winter 2004
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Augmenting data structures
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Example 1:

  - How do we compute MIN (return the smallest key stored in the tree)
    for a 2-3-4 tree?

  - What's the running time for MIN?

  - What if we need to carry out this operations very often?
    Can we make it faster without affecting the other operations?

  - What additional information could we store to help?

  - Given this extra information, what's the running time of MIN?

  - Do we have to change SEARCH to maintain this new information?
    How would you change it, and what would be its new running time?

  - Do we have to change INSERT to maintain this new information?
    How would you change it, and what would be its new running time?

  - Do we have to change DELETE to maintain this new information?
    How would you change it, and what would be its new running time?

Example 2:

  - What if we want to answer queries MIN(x): return the smallest key in
    the subtree rooted at node x, for abitrary nodes x in a 2-3-4 tree
    (not just for the root)?

  - What additional information could we store to help?

  - Given this extra information, what's the running time of MIN(x)?

  - Do we have to change SEARCH to maintain this new information?
    How would you change it, and what would be its new running time?

  - Do we have to change INSERT to maintain this new information?
    How would you change it, and what would be its new running time?

  - Do we have to change DELETE to maintain this new information?
    How would you change it, and what would be its new running time?