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Insertion and deletion are more complicated than lookup, since it may be necessary to split a node that becomes too large as the result of an insertion, or to coalesce nodes (that is, combine nodes) if a node becomes too small (fewer than n/2 pointers) Furthermore, when a node is split or a pair of nodes is combined, we must ensure that balance is preserved To introduce the idea behind insertion and deletion in a B+ -tree, we shall assume temporarily that nodes never become too large or too small Under this assumption, insertion and deletion are performed as de ned next Insertion Using the same technique as for lookup, we nd the leaf node in which the search-key value would appear If the search-key value already appears in the leaf node, we add the new record to the le and, if necessary, add to the bucket a pointer to the record If the search-key value does not appear, we insert the value in the leaf node, and position it such that the search keys are still in order We then insert the new record in the le and, if necessary, create a new bucket with the appropriate pointer Deletion Using the same technique as for lookup, we nd the record to be deleted, and remove it from the le We remove the search-key value from the leaf node if there is no bucket associated with that search-key value or if the bucket becomes empty as a result of the deletion We now consider an example in which a node must be split Assume that we wish to insert a record with a branch-name value of Clearview into the B+ -tree of Figure 128 Using the algorithm for lookup, we nd that Clearview should appear in the node containing Brighton and Downtown There is no room to insert the search-key value Clearview Therefore, the node is split into two nodes Figure 1211 shows the two leaf nodes that result from inserting Clearview and splitting the node containing Brighton and Downtown In general, we take the n search-key. asp.net upc-a UPC-A . NET Control - UPC-A barcode generator with free . NET ...
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NET UPC-A Generator Controls to generate GS1 UPC-A barcodes in VB. NET , C# applications. Download Free Trial Package | Developer Guide included ... values (the n 1 values in the leaf node plus the value being inserted), and put the rst n/2 in the existing node and the remaining values in a new node Having split a leaf node, we must insert the new leaf node into the B+ -tree structure In our example, the new node has Downtown as its smallest search-key value We need to insert this search-key value into the parent of the leaf node that was split The B+ -tree of Figure 1212 shows the result of the insertion The search-key value Downtown was inserted into the parent It was possible to perform this insertion because there was room for an added search-key value If there were no room, the parent would have had to be split In the worst case, all nodes along the path to the root must be split If the root itself is split, the entire tree becomes deeper The general technique for insertion into a B+ -tree is to determine the leaf node l into which insertion must occur If a split results, insert the new node into the parent of node l If this insertion causes a split, proceed recursively up the tree until either an insertion does not cause a split or a new root is created Figure 1213 outlines the insertion algorithm in pseudocode In the pseudocode, LKi and LPi denote the ith value and the ith pointer in node L, respectively The pseudocode also makes use of the function parent(L) to nd the parent of a node L We can compute a list of nodes in the path from the root to the leaf while initially nding the leaf node, and can use it later to nd the parent of any node in the path ef ciently The pseudocode refers to inserting an entry (V, P ) into a node In the case of leaf nodes, the pointer to an entry actually precedes the key value, so the leaf node actually stores P before V For internal nodes, P is stored just after V We now consider deletions that cause tree nodes to contain too few pointers First, let us delete Downtown from the B+ -tree of Figure 1212 We locate the entry for Downtown by using our lookup algorithm When we delete the entry for Downtown from its leaf node, the leaf becomes empty Since, in our example, n = 3 and 0 < (n 1)/2 , this node must be eliminated from the B+ -tree To delete a leaf node,. asp.net upc-a UPC-A Barcode Generator for ASP . NET Web Application
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The UPC-A Code and the assignment of manufacturer ID numbers is controlled in the ... ASP . NET /Windows Forms/Reporting Services/Compact Framework ... The goal is to write all unknown quantities in terms of the current source Io , which is why we solved for i 2 in this case Now let s apply KCL again, this time at node 2 as shown in Fig 3-35 This time we have 8 i 2 + 02 i 2 + i 6 = 0 i 6 = 8 + 08 i 2 Using (37), we can rewrite this as i 6 = 8 + 08 (Io 8) = 8 + 08Io 64 (39) As I ve mentioned, the video scenes album holds the video clips that you have captured or imported Only one video file can be open in the video scenes album at a time, but you can simply open and close the video files as needed The video scenes album shows an individual thumbnail for each scene That thumbnail is the first frame of the video clip As you add a scene to the movie, The McGraw Hill Companies, 2001 2
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