in an -way search treeit is not compulsory that every node has exactly - values and subtrees ratherthe node can have anywhere from to - valuesand the number of sub-trees can vary from (for leaf nodeto where is the number of key values in the node is thus fixed figure -way search tree of order upper limit that defines how many key values can be stored in the node consider the -way search tree shown in fig here so node can store maximum of two key values and can contain pointers to three sub-trees in our examplewe have taken very small value of so that the concept becomes easier for the readerbut in practicem is usually very large using -way search treelet us lay down some of the basic properties of an -way search tree note that the key values in the sub-tree pointed by are less than the key value similarlyall the key values in the sub-tree pointed by are less than so on and so forth thusthe generalized rule is that all the key values in the sub-tree pointed by pi are less than kiwhere ps ps - note that the key values in the sub-tree pointed by are greater than the key value similarlyall the key values in the sub-tree pointed by are greater than so on and so forth thusthe generalized rule is that all the key values in the sub-tree pointed by pi are greater than ki- where ps ps - in an -way search treeevery sub-tree is also an -way search tree and follows the same rules trees tree is specialized -way tree developed by rudolf bayer and ed mccreight in that is widely used for disk access tree of order can have maximum of - keys and pointers to its sub-trees tree may contain large number of key values and pointers to sub-trees storing large number of keys in single node keeps the height of the tree relatively small tree is designed to store sorted data and allows searchinsertionand deletion operations to be performed in logarithmic amortized time tree of order (the maximum number of children that each node can haveis tree with all the properties of an -way search tree in addition it has the following properties every node in the tree has at most (maximumm children every node in the tree except the root node and leaf nodes has at least (minimumm/ children this condition helps to keep the tree bushy so that the path from the root node to the leaf is very shorteven in tree that stores lot of data the root node has at least two children if it is not terminal (leafnode all leaf nodes are at the same level an internal node in the tree can have number of childrenwhere ps ps it is not necessary that every node has the same number of childrenbut the only restriction is that the node should have at least / children as tree of order is given in fig figure tree of order