1. Advanced Data Structure using C++

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LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) • do a single pass down the tree, but before entering (visiting) a node, restructure the tree so that once the key to be deleted is encountered, it can be deleted without triggering the need for any further restructuring The algorithm below uses the former strategy. There are two special cases to consider when deleting an element: <strong>1.</strong> the element in an internal node may be a separator for its child nodes 2. deleting an element may put its node under the minimum number of elements and children. Each of these cases will be dealt with in order. Deletion from a leaf node • Search for the value to delete. • If the value is in a leaf node, it can simply be deleted from the node, • If underflow happens, check siblings to either transfer a key or fuse the siblings together. Deletion from an internal node Each element in an internal node acts as a separation value for two subtrees, and when such an element is deleted, two cases arise. In the first case, both of the two child nodes to the left and right of the deleted element have the minimum number of elements, namely L‐<strong>1.</strong> They can then be joined into a single node with 2L‐2 elements, a number which does not exceed U‐1 and so is a legal node. Unless it is known that this particular B‐tree does not contain duplicate data, we must then also (recursively) delete the element in question from the new node. In the second case, one of the two child nodes contains more than the minimum number of elements. Then a new separator for those subtrees must be found. Note that the largest element in the left subtree is still less than the separator. Likewise, the smallest element in the right subtree is the smallest element Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 218 ‐
LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) which is still greater than the separator. Both of those elements are in leaf nodes, and either can be the new separator for the two subtrees. • If the value is in an internal node, choose a new separator (either the largest element in the left subtree or the smallest element in the right subtree), remove it from the leaf node it is in, and replace the element to be deleted with the new separator. • This has deleted an element from a leaf node, and so is now equivalent to the previous case. Inserting Key 33 into a B‐Tree (w/ Split) Sample B‐Tree Searching a B‐Tree for Key 21 Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 219 ‐
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1. Advanced Data Structure using C++

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