tree separates the values held in its two sub-trees for exampleif node has child nodes (or sub-treesthen it must have separation values and all values in the leftmost subtree will be less than all values in the middle subtree will be between and and all values in the rightmost subtree will be greater than that allows insertion and searching to proceed from the root down in similar way to binary search trees the restriction on the number of children to lie between / and means that the best case height of an order -tree containing search keys is logm and the worst case height is logm/ clearly the costs of insertiondeletion and searching will all be proportional to the tree heightas in binary search treewhich makes them very efficient the requirement that all the leaf nodes are at the same level means that -trees are always balanced and thus have minimal heightthough rebalancing will often be required to restore that property after insertions and deletions the order of -tree is typically chosen to optimize particular application and implementation to maintain the conditions of the -tree definitionnon-leaf nodes often have to be split or joined when new items are inserted into or deleted from the tree (which is why there is factor of two between the minimum and maximum number of children)and rebalancing is often required this renders the insertion and deletion algorithms somewhat more complicated than for binary search trees an advantage of -trees over self balancing binary search treeshoweveris that the range of child nodes means that rebalancing is required less frequently disadvantage is that there may be more space wastage because nodes will rarely be completely full there is also the cost of keeping the items within each node orderedand having to search among thembut for reasonably small orders mthat cost is low exercisefind some suitable insertiondeletion and rebalancing algorithms for -trees