1. Advanced Data Structure using C++

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B + TREES LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) A simple B+ tree example linking the keys 1–7 to data values d1‐d7. Note the linked list (red) allowing rapid in‐order traversal. In computer science, a B+ tree (BplusTree) is a type of tree which represents sorted data in a way that allows for efficient insertion, retrieval and removal of records, each of which is identified by a key. It is a dynamic, multilevel index, with maximum and minimum bounds on the number of keys in each index segment (usually called a "block" or "node"). In a B+ tree, in contrast to a B‐ tree, all records are stored at the leaf level of the tree; only keys are stored in interior nodes. The order (branching factor) of a B+ tree measures the capacity of nodes (i.e. the number of children nodes) in the tree. It is defined as a number d such that , where m is the number of children in each node. For example, if the order of a B+ tree is 7, each internal node (except for the root) may have between 4 and 7 children; the root may have between 2 and 7 Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 220 ‐
Search LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) The algorithm to perform a search for a record r follows pointers to the correct child of each node until a leaf is reached. Then, the leaf is scanned until the correct record is found (or until failure). Function search (record r) u := root While (u is not a leaf) do Choose the correct pointer in the node move to the first node following the pointer u := current node scan u for r This pseudocode assumes that no repetition is allowed. Insertion • do a search to determine what bucket the new record should go in • if the bucket is not full, add the record. • otherwise, split the bucket. • allocate new leaf and move half the bucket's elements to the new bucket • insert the new leaf's smallest key and address into the parent. • if the parent is full, split it also • now add the middle key to the parent node • repeat until a parent is found that need not split • if the root splits, create a new root which has one key and two pointers. Characteristics For a b‐order B+ tree with h levels of index: • The maximum number of records stored is n = b h • The minimum number of keys is 2(b / 2) Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 221 ‐ h − 1
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ADVANCED DATA STRUCTURE NOTES (MT
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COLLISION LECTURE NOTES OF ADVANCED
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queue LECTURE NOTES OF ADVANCED DAT
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Step 2: Step 3 LECTURE NOTES OF ADV
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1. Advanced Data Structure using C++

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