1. Advanced Data Structure using C++

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LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) The worst case height of a B‐Tree is: where M is the maximum number of children a node can have. The m‐way tree has the potential to greatly reduce the height of a tree. A B‐ Tree is an m‐way search tree with the following additional properties: The root is either a leaf or it has 2…..m subtrees. All internal nodes have at least [m/2] nonnull subtrees at most m nonnull subtrees. All leaf nodes are at the same level; that is , the tree is perfectly balanced. A leaf node has at least [m/2] – 1 and at the most m‐1 entries. When the leaf node is full, we have a condition known as overflow. Overflow requires that the leaf node be split into two nodes, each containing half of the data. For example: a. b. Original node new node c. 11 14 21 78 97 11 14 21 78 78 97 create new right subtree 21 11 Prepared By : 14 78 97 Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 214 ‐
LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) Given a B‐Tree structure with an order of 5, we begin inserting 11,21,14 and 78. The first insert creates a node that becomes the root. The next three inserts simply place the data in the node in ascending key sequence. (a) When we try to insert 97, we discover that the node if full. We therefore create a new right subtree and move the larger half of the data to it, leaving the rest of the data in the original node (b). After creating the new node, we insert the median value data (21) into the parent of the original node. Because the original node was a root, we create a new root and insert 21 into it. Algorithms Search Searching is similar to searching a binary search tree. Starting at the root, the tree is recursively traversed from top to bottom. At each level, the search chooses the child pointer (subtree) whose separation values are on either side of the search value.Binary search is typically (but not necessarily) used within nodes to find the separation values and child tree of interest. Insertion In order to insert a key into a B‐tree, first a B‐Tree search is performed to find the correct location for the key. Then the key is inserted. Note that a node usually may have a space available for another key and pointer. However, the node may be already full and cannot accommodate another key. In that case, Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 215 ‐
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ADVANCED DATA STRUCTURE NOTES (MT
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1. Advanced Data Structure using C++

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