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===Insertion=== * Perform a search to determine which node the new record should go into. * If the node is not full (at most <math> b - 1 </math> entries after the insertion), add the record. * Otherwise, ''before'' inserting the new record ** Split the node. *** original node has <math>\lceil (K+1)/2 \rceil</math> items *** new node has <math>\lfloor (K+1)/2 \rfloor</math> items ** Copy <math>\lceil (K+1)/2 \rceil</math>-th key to the parent, and insert the new node to the parent. ** Repeat until a parent is found that need not split. ** Insert the new record into the new node. * If the root splits, treat it as if it has an empty parent and split as outlined above. B+ trees grow at the root and not at the leaves.<ref name=Navathe />
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