POTD 8: Indexing

Purpose:

• Understand the concepts of indexing
• Use B+ tree to find records, insert keys, and delete keys
• Get ready to work on homework assignment
• Prepare for exam 2

You may make a copy of a worksheet and complete this activity or type your answers in any text editor.

You may work alone or with 3-4 other students in this course.

1. Construct a B+ tree for the following set of key values:

   (10, 15, 20, 30, 60, 65, 80, 95, 100, 112, 124, 140, 148)

   Assume that the tree is initially empty and values are added in ascending order. Construct B+ tree for the cases where the number of pointers (n) that will fit in one node is five.
   [sample solution]
   Insert 10
   Insert 15
   Insert 20
   Insert 30
   
   Insert 60, node (root) full, split
   
   Add parent (new root), copy 20 to root
   
   
   Insert 65
   
   
   Insert 80, leaf full, split
   
   Copy 60 to root (update parent)
   
   
   Insert 95
   
   
   Insert 100, leaf full, split
   
   Copy 80 to root (update parent)
   
   
   Insert 112
   
   
   Insert 124, leaf full, split
   
   Copy 100 to root (update parent)
   
   
   Insert 140
   
   
   Insert 148, leaf full, split
   
   Copy 124 to root
   
   
   Root full, split, push middle value up (becomes new root node)
   
   
   Update pointers
   
   
   
2. Use the B+ tree constructed in question 1, what is the minimum number of pointers to be followed to satisfy the query: Get all records of data associated with key(s) between 40 and 85?
   [sample solution]
   
   Need at least 4 pointers to answer this question
   
   
   
   
3. Use the B+ tree from question 1, apply each of the following operations in order, and show the tree after each operation.
   1. Insert 18
      [sample solution]
      
      
      
   2. Insert 40
      [sample solution]
      
      
      
   3. Insert 85
      [sample solution]
      
      
      
   4. Delete 124
      [sample solution]
      
      
      Shift left
      
      
      
   5. Insert 138
      [sample solution]
      
      
      
   6. Insert 135
      [sample solution]
      
      
      
   7. Insert 120
      [sample solution]
      Node full, split
      
      Copy 120 up to parent, update pointers
      
      

Grading rubric

• (5 points) — Providing evidence of your attempt, minimal effort

(-2.5 points) for 24 hours late (submitted after 11-Apr-2024 12pm/noon EST, by 12-Apr-2024 12pm/noon EST)
(-5 points) for 48 hours late (submitted after 12-Apr-2024 12pm/noon EST, by 13-Apr-2024 12pm/noon EST)

Submission

• [optional] Take a selfie (or picture) of your team and submit it with your POTD
• Include all team member names and computingIDs in the report.
• You may do one of the following:
  • Write on the paper and take picture(s) of your POTD, or
  • Type and save your POTD as a .pdf file — No Word document.
• Each team submits only one copy.
• Upload your report as a PDF to POTD 8 on Gradescope. Make sure you connect your partner to your group on Gradescope so that everyone receives credit.
• Please verify that your POTD is accessible. Making your submission available to instructors and course staff is your responsibility; if we cannot access or open your file(s), we have to assign a zero grade. Be sure to test access to your file(s) before the due date.

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