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Consider the following B+ tree with order 4:
[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
What will be the B+ tree after deleting the value 50?
  • a)
    [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
  • b)
    [10, 20, 30, 40, 60, 70, 80, 90, 100]
  • c)
    [10, 20, 30, 40, 60, 70, 80, 90]
  • d)
    [10, 20, 30, 40, 60, 70, 90, 100]
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider the following B+ tree with order 4:[10, 20, 30, 40, 50, 60, 7...
The value 50 will be deleted from the B+ tree, and the tree will be adjusted accordingly by redistributing keys.
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Most Upvoted Answer
Consider the following B+ tree with order 4:[10, 20, 30, 40, 50, 60, 7...
Introduction:
In B-trees, deletion of a value requires adjusting the tree structure to maintain the properties of a B-tree. The order of a B-tree determines the maximum number of children a node can have. In this case, we have a B-tree of order 4 with the following elements: [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]. We need to delete the value 50 and determine the resulting B-tree.

Deletion Process:
To delete a value from a B-tree, we follow these steps:
1. Start from the root node and search for the value to be deleted.
2. If the value is found in a leaf node, simply remove it from the node.
3. If the value is found in an internal node, we replace it with the largest value from its left subtree (predecessor) or the smallest value from its right subtree (successor). Then we recursively delete the predecessor or successor from the appropriate subtree.
4. After deletion, we check if any node has fewer than the minimum number of values required. If so, we perform the following operations to maintain the B-tree properties:
- If a neighboring sibling has more than the minimum number of values, we borrow a value from the sibling.
- If no neighboring sibling has enough values, we merge the node with one of its siblings.

Deletion of 50:
In our case, we want to delete the value 50. Following the deletion process described above, we perform the following steps:

1. Start from the root node and search for 50.
2. 50 is found in the leaf node containing [40, 50, 60]. We remove 50 from the node, resulting in [40, 60].
3. No further adjustments are required as the resulting node still satisfies the B-tree properties.

Final B-tree:
After deleting 50, the resulting B-tree will be:
[10, 20, 30, 40, 60, 70, 80, 90]

Explanation:
The resulting B-tree ([10, 20, 30, 40, 60, 70, 80, 90]) is obtained by deleting the value 50 from the original B-tree. The deletion process involves removing the value from the leaf node and ensuring that the resulting tree still satisfies the B-tree properties. In this case, no further adjustments are required as the resulting node has the minimum number of values required and the B-tree properties are maintained.
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