tree definitions and properties tree is an abstract data type that stores elements hierarchically with the exception of the top elementeach element in tree has parent element and zero or more children elements tree is usually visualized by placing elements inside ovals or rectanglesand by drawing the connections between parents and children with straight lines (see figure we typically call the top element the root of the treebut it is drawn as the highest elementwith the other elements being connected below (just the opposite of botanical treeelectronics 'us & sales purchasing domestic international canada america africa manufacturing tv cd tuner overseas europe asia australia figure tree with nodes representing the organization of fictitious corporation the root stores electronics 'us the children of the root store &dsalespurchasingand manufacturing the internal nodes store salesinternationaloverseaselectronics 'usand manufacturing formal tree definition formallywe define tree as set of nodes storing elements such that the nodes have parent-child relationship that satisfies the following propertiesif is nonemptyit has special nodecalled the root of that has no parent each node of different from the root has unique parent node wevery node with parent is child of note that according to our definitiona tree can be emptymeaning that it does not have any nodes this convention also allows us to define tree recursively such that tree is either empty or consists of node rcalled the root of and (possibly emptyset of subtrees whose roots are the children of