sec - trees ( ( (cfigure example of inserting record that causes the - tree root to split (athe value is added to the - tree of figure this causes the node containing and to splitpromoting (bthis in turn causes the internal node containing and to splitpromoting (cfinallythe root node splitspromoting to become the left record in the new root the result is that the tree becomes one level higher postponed until the next sectionwhere it can be generalized for particular variant of the -tree the - tree insert and delete routines do not add new nodes at the bottom of the tree instead they cause leaf nodes to split or mergepossibly causing ripple effect moving up the tree to the root if necessary the root will splitcausing new root node to be created and making the tree one level deeper on deletionif the last two children of the root mergethen the root node is removed and the tree will lose level in either caseall leaf nodes are always at the same level when all leaf nodes are at the same levelwe say that tree is height balanced because the - tree is height balancedand every internal node has at least two childrenwe know that the maximum depth of the tree is log thusall - tree insertfindand delete operations require th(log ntime