How much will your tree removal cost?

There are at least 2 keys in the sibling node, so move the right-most key to the parent, and move the right-most parent down. Now There are 2 keys in the leaf node, which is case #1.

Just delete N, resulting in this tree: Deleting His case # His in a leaf node, and there are no siblings with at least2 keys. Tree Deletion: Upward Phase Thegoaloftheupwardphaseoftreedeletionistopropagatetheholeupthetreeuntilit canbeeliminated. Itiseliminatedeither(1)bybeing\absorbed"intothetree(asinthecases 2,3,and4below)or(2)bybeingpropagatedallthewaytotherootofthetreebyrepeated.

You might learn about the first two in an algorithms class, and the third in a database class. Here we will look at yet another kind of balanced tree called a Tree. The important idea behind all of these trees is that the insert and delete operations may restructure the tree to keep it balanced. So lookup, insert, and delete will always be logarithmic in the number of nodes, but insert and delete may be more complicated than for binary-search trees.

In other cases, the parent of the node to be deleted is found, then the tree is fixed up (if necessary) so that it is still a tree. Once the parent of the node n to be deleted is found, there are two cases depending on how many children n has: If n has 3 childrenEstimated Reading Time: 5 mins. Jan 16, This is a redo of my earlier video on B-trees. It's now unlisted, but if you felt like seeing how much of a mess it was, the link is here: bushleaning.bar Feb 28, Proper way to Re-Balance a Tree after deleting the root node.

The goal is to remove 22 from the root node and re-balance the tree. First I remove 22, and replace it by its in-order successor Secondly I rebalance the resulting tree, by moving the empty node to the left.

The resulting tree. Oct 16, Trees is a data structure where all the data is stored at leaves. It provides basic functionality like insert, search, and delete.

Since all the data is stored in leaf nodes, all the operations has worst case time complexity of O (log N).