Is there anybody who knows how to do this? I really need help! Here\'s how it wo

Question

Is there anybody who knows how to do this? I really need help! Here's how it works:

Consider the problem of deletion. If we delete a key value, it is possible that a node drops below the size of M/2 keys, and some consolidation is possible. Write an algorithm for deletion of a specified key value from a B-tree, and give an example of deletion for two cases: deletion with consolidation, and deletion with consolidation and rebalance. To assist you, there is an Office diagram of a B-tree inserted for you to edit.

For this problem, include a list of the deletion algorithm in pseudocode form, and diagrams of the two cases listed above.

Explanation / Answer

There are two popular strategies for deletion from a B-tree.

The algorithm below uses the former strategy.

There are two special cases to consider when deleting an element:

The procedures for these cases are in order below.

Each element in an internal node acts as a separation value for two subtrees, therefore we need to find a replacement for separation. Note that the largest element in the left subtree is still less than the separator. Likewise, the smallest element in the right subtree is still greater than the separator. Both of those elements are in leaf nodes, and either one can be the new separator for the two subtrees. Algorithmically described below:

Rebalancing starts from a leaf and proceeds toward the root until the tree is balanced. If deleting an element from a node has brought it under the minimum size, then some elements must be redistributed to bring all nodes up to the minimum. Usually, the redistribution involves moving an element from a sibling node that has more than the minimum number of nodes. That redistribution operation is called a rotation. If no sibling can spare a node, then the deficient node must be merged with a sibling. The merge causes the parent to lose a separator element, so the parent may become deficient and need rebalancing. The merging and rebalancing may continue all the way to the root. Since the minimum element count doesn't apply to the root, making the root be the only deficient node is not a problem. The algorithm to rebalance the tree is as follows:

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