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Week 11 - Monday What did we talk about last time? Euler paths - - PowerPoint PPT Presentation
Week 11 - Monday What did we talk about last time? Euler paths - - PowerPoint PPT Presentation
Week 11 - Monday What did we talk about last time? Euler paths Network flow Started B-trees Lab hours Wednesdays at 5 p.m. in The Point 113 Saturdays at noon in The Point 113 CS Club Tuesdays at 5 p.m. in The
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Lab hours
- Wednesdays at 5 p.m. in The Point 113
- Saturdays at noon in The Point 113
CS Club
- Tuesdays at 5 p.m. in The Point 113 (or next door in The Point 112)
- Halloween party tomorrow!
Women in STEM panel
- Tonight at 6 p.m. in The Point 113
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s t a b c d 12 16 10 9 20 7 4 4 14 13
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Binary trees are great However, only two splits means that you have a height of log2
n when you want to store n things
- If n = 1,000,000, log2 n = 20
What if depth was expensive? Could we have say, 10 splits?
- If n = 1,000,000, log10 n = 6
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Answer: When the tree is in secondary storage Each read of a block from disk storage is slow
- We want to get a whole node at once
- Each node will give us information about lots of child nodes
- We don’t have to make many decisions to get to the node we want
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A B-tree of order m has the following properties: 1.
The root has at least two subtrees unless it is a leaf
- 2. Each nonroot and each nonleaf node holds k keys and k + 1 pointers
to subtrees where m/2 ≤ k ≤ m
3.
Each leaf node holds k keys where m/2 ≤ k ≤ m
- 4. All leaves are on the same level
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50 10 15 20 70 80 6 8 11 12 16 18 21 25 27 29 54 56 71 76 81 89
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12 5 8 13 15
Insert 7
12 5 7 8 13 15
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12 2 5 7 8 13 15
Insert 6
6 12 2 5 13 15 7 8
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Insert the following numbers:
- 86 69 81 15 100 94 8 27 56 68 92 89 38 53 88
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When the list of keys drops below half m, we have to
redistribute keys
In the worst case, we have to delete a level
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Instead of requiring every non-root node to be half full, every
non-root node must be at least 2/3 full
Key redistribution becomes more complex However, the tree is fuller
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Essentially, make a B-tree such that all the leaves are tied
together in a linked list
It is also necessary that all keys in a B-tree appear as leaves Some other variations are possible, but we’ll end the list here
6 12 2 5 12 13 15 6 7 8
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Hard graph problems Intractability and NP-completeness
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Work on Project 3 Study for Exam 2
- Next Monday