compute some property for each node in treebut computing that property for requires that we have already computed that same property for ' children such an application is illustrated in the following example example consider file system tree twhere external nodes represent files and internal nodes represent directories (example suppose we want to compute the disk space used by directorywhich is recursively given by the sum ofthe size of the directory itself the sizes of the files in the directory the space used by the children directories (see figure this computation can be done with apostorder traversal of tree after the subtrees of an internal node have been traversedwe compute the space used by by adding the sizes of the directory itself and of the files contained in to the space used by each internal child of vwhich was computed by the recursive postorder traversals of the children of recursive java method for computing disk space motivated by example java method diskspaceshown in code fragment performs postorder traversal of file-system tree tprinting the name and disk space used by the directory associated with each internal node of when called on the root of tree tdiskspace runs in time ( )where is the number of nodes of tprovided the auxiliary methods name and size take ( time figure the tree of figure representing file systemshowing the name and size of the associated file/directory inside each nodeand the disk space used by the associated directory above each internal node