To delete a key in a B-tree: Step 1. If the key k is in node x and x is a leaf, delete the key k from x. Step 2. If the key k is in node x and x is an internal node, do the following: 2a) If the child y that precedes k in node x has at least t keys, then find the predecessor k’ of k in the sub-tree rooted at y. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2b) If y has fewer than t keys, then, symmetrically, examine the child z that follows k in node x. If z has at least t keys, then find the successor k’ of k in the subtree rooted at z. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2c) Otherwise, if both y and z have only t-1 keys, merge k and all of z into y, so that x loses both k and the pointer to z, and y now contains 2t-1 keys. Then free z and recursively delete k from y. 1) Write pseudo code for Step (1) for function B-Tree-Delete-Key(x, k). Make sure your pseudo code is detailed with respect to the actual deletion that takes place in the leaf node. (don't just state"delete k from x") 2) Write pseudo code for Step (2a) for function B-Tree-Delete-Key(x, k). Make sure your pseudo code is detailed with respect to the actual deletion that takes place in the internal node. Here, specify details with what takes place in the algorithm with regards to finding the predecessor, recursively deleting k', and replacing k by k' in x, don't just say what this step states in the problem statement)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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To delete a key in a B-tree:

Step 1. If the key k is in node x and x is a leaf, delete the key k from x.

Step 2. If the key k is in node x and x is an internal node, do the following:

2a) If the child y that precedes k in node x has at least t keys, then find the predecessor k’ of k in the sub-tree rooted at y. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.)

2b) If y has fewer than t keys, then, symmetrically, examine the child z that follows k in node x. If z has at least t keys, then find the successor k’ of k in the subtree rooted at z. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.)

2c) Otherwise, if both y and z have only t-1 keys, merge k and all of z into y, so that x loses both k and the pointer to z, and y now contains 2t-1 keys. Then free z and recursively delete k from y.

1) Write pseudo code for Step (1) for function B-Tree-Delete-Key(x, k). Make sure your pseudo code is detailed with respect to the actual deletion that takes place in the leaf node. (don't just state"delete k from x")

2) Write pseudo code for Step (2a) for function B-Tree-Delete-Key(x, k). Make sure your pseudo code is detailed with respect to the actual deletion that takes place in the internal node. Here, specify details with what takes place in the algorithm with regards to finding the predecessor, recursively deleting k', and replacing k by k' in x, don't just say what this step states in the problem statement)

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