example an arithmetic expression can be represented by binary tree whose leaves are associated with variables or constantsand whose internal nodes are associated with one of the operators +-xand (see figure each node in such tree has value associated with it if node is leafthen its value is that of its variable or constant if node is internalthen its value is defined by applying its operation to the values of its children an arithmetic expression tree is proper binary treesince each operator +-xand takes exactly two operands of courseif we were to allow unary operatorslike negation (-)as in "- ,then we could have an improper binary tree figure binary tree representing an arithmetic expression this tree represents the expression (((( )/(( )(( ( ) )the value associated with the internal node labeled "/is recursive binary tree definition incidentallywe can also define binary tree in recursive way such that binary tree is either empty or consists ofa node rcalled the root of that stores an element binary tree (possibly empty)called the left subtree of binary tree (possibly empty)called the right subtree of