## Algorithm to insert a key in b-tree, Computer Engineering

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Algorithm to insert a key in B-tree is as follows:

1.  First search is completed for the place where the new record must be put. As the keys are inserted, they are sorted into the proper order.

2.  If the node can contain the new record, insert the new record at the appropriate pointer so that number of pointers remains one more than the number of records.

3.  If the node overflows due to there is an upper bound on the size of a node, splitting is needed. The node is divided into three parts; the middle record is passed upward and inserted into parent, leaving two children behind. If n is odd (n-1 keys in full node and the new target key), median key int(n/2)+1 is placed in parent node, the lower n/2 keys are put in the left leaf and the higher n/2 keys are put in the right leaf. If n is even, we might be have left biased or right biased means one key may be more in left child or right child correspondingly.

4.  Splitting may propagate up the tree because the parent, into which divided record is added, may overflow then it may be split.  If the root is needed to be split, a new record is formed with just two children.

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