Using A Function Write A Program Than Calculate Pay As You Earn And Pension And Maternity. Pay Is 30
The B+ tree structure after the sequence of deletions (10, 7, 3, 9, 14, 5, 11) results in a modification of the tree’s structure.
(a) Constructing a B+ tree after the given sequence of key values:
The B+ tree construction process for the given sequence of key values is as follows:
Initially, the tree is empty. We start by inserting the first key value, which becomes the root of the tree:
“`
[10]
“`
Next, we insert 7 as the second key value. Since it is less than 10, it goes to the left of 10:
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[10, 7]
“`
We continue inserting the remaining key values following the B+ tree insertion rules:
“`
[7, 10]
/ \
[3, 5] [9, 14]
“`
“`
[7, 10]
/ \
[3, 5] [9, 11, 14]
“`
“`
[7, 10]
/ \
[3, 5] [8, 9, 11, 14]
“`
“`
[7, 10]
/ \
[3, 5] [8, 9, 11, 14, 17]
“`
“`
[7, 10, 14]
/ | \
[3, 5] [8, 9] [11] [17]
\
[50, 62]
“`
The final B+ tree after inserting all the key values is shown above.
(b) Sequence of pages accessed for the search queries:
(i) To find the record with the key value 17:
The search path would be: [7, 10, 14, 17]. So the sequence of pages accessed is: Page 1 (root), Page 2 (child of root), Page 3 (child of Page 2), Page 4 (leaf containing 17).
(ii) To find records with key values in the range from 14 to 19 inclusive:
The search path would be: [7, 10, 14, 17]. So the sequence of pages accessed is the same as in (i).
(c) Structure of the tree after the given sequence of deletions:
To show the structure of the tree after the deletion sequence, we remove the specified key values one by one while maintaining the B+ tree properties.
After deleting 10:
“`
[7, 14]
/ | \
[3, 5] [8, 9] [11, 17]
\
[50, 62]
“`
After deleting 7:
“`
[8, 14]
/ | \
[3, 5] [9] [11, 17]
\
[50, 62]
“`
After deleting 3:
“`
[8, 14]
/ | \
[5] [9] [11, 17]
\
[50, 62]
“`
After deleting 9:
“`
[8, 14]
/ | \
[5] [11, 17]
\
[50, 62]
“`
After deleting 14:
“`
[8, 11]
/ \
[5] [17]
\
[50, 62]
“`
After deleting 5:
“`
[11]
/ \
[8] [17]
\
[50, 62]
“`
After deleting 11:
“`
[17]
/ \
[8] [50, 62]
“`
The final structure of the tree after the deletion sequence is shown above.
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