midterm2-solution - Midterm#2 EECS 341 Introduction to...

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1 Midterm #2: EECS 341 Introduction to Database Systems Fall 2014 11/17/14 CLOSE book/notes, NO computer/PDA/phone allowed Name:_____________________________________________________ Signature:____________________________________________________
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2 1. Given the following B+ tree: a) Draw the B+ tree after inserting 38. (6 points)
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3 b) Draw the B+ tree after deleting 26 from the original tree. (6 points)
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4 c) What is the maximum number of insertions in the original tree without causing it to grow to 4 levels? Briefly explain your answer. (9 points) Solution: See following figure blue arrow For root level: there are three empty pointers, so we can insert: 3*5*4=60 elements For second level: Left node: there are two empty pointers: 2*4=8 elements Right node: 2*4=8 elements For leaf level: we can insert another 6 elements Sum up: we can insert 82 elements. d) What is the maximum number of deletions from the original tree without causing it to shrink to 2 levels? Briefly explain your answer. (9 points) Solution: See following figure red arrow In order to meet the requirement: for each node which is not the root, the number of elements n must 2 ≤n≤4 So we can only delete the elements on leaf level, because the number of elements in the nodes which is on the second level has met the lower bond of 2.
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