tree structure the height of the tree will be important in analyzing the time-complexities of various algorithms applied to binary trees the structural properties of binary trees can also play role in the efficiency of an algorithm in factsome algorithms require specific tree structures full binary tree is binary tree in which each interior node contains two children full trees come in many different shapesas illustrated in figure figure examples of full binary trees perfect binary tree is full binary tree in which all leaf nodes are at the same level the perfect tree has all possible node slots filled from top to bottom with no gapsas illustrated in figure figure perfect binary tree binary tree of height is complete binary tree if it is perfect binary tree down to height and the nodes on the lowest level fill the available slots from left to right leaving no gaps consider the two complete binary trees in figure if any of the three leaf nodes labeled abor in the left tree were missingthat tree would not be complete likewiseif either leaf node labeled or in the right tree were missingit would not be complete implementation binary trees are commonly implemented as dynamic structure in the same fashion as linked lists binary tree is data structure that can be used to implement many different abstract data types since the operations that binary tree supports