data structures using inserting new element in btree new element is simply added in the leaf node if there is space for it but if the data node in the tree where insertion has to be done is fullthen that node is split into two nodes this calls for adding new index value in the parent index node so that future queries can arbitrate between the two new nodes howeveradding the new index value in the parent node may cause itin turnto split in factall the nodes on the path from leaf to the root may split when new value is added to leaf node if the root node splitsa new leaf node is created and the tree grows by one level the steps to insert new node in btree are summarized in fig step insert the new node as the leaf node step if the leaf node overflowssplit the node and copy the middle element to next index node step if the index node overflowssplit that node and move the middle element to next index page figure algorithm for inserting new node in btree example consider the btree of order given and insert in it step insert step split the leaf node step split the index node figure inserting node in the given btree deleting an element from btree as in treesdeletion is always done from leaf node if deleting data element leaves that node emptythen the neighbouring nodes are examined and merged with the underfull node this process calls for the deletion of an index value from the parent index node whichin turnmay cause it to become empty similar to the insertion processdeletion may cause merge-delete wave to run from leaf node all the way up to the root this leads to shrinking of the tree by one level the steps to delete node from btree are summarized in fig step step step delete the key and data from the leaves if the leaf node underflowsmerge that node with the sibling and delete the key in between them if the index node underflowsmerge that node with the sibling and move down the key in between them figure algorithm for deleting node from btree