called rotationbecause of the geometric way we can visualize the way it changes if ythe trinode restructuring method is called single rotationfor it can be visualized as "rotatingy over (see figure and otherwiseif xthe trinode restructuring operation is called double rotationfor it can be visualized as first "rotatingx over and then over (see figure and dand figure some computer researchers treat these two kinds of rotations as separate methodseach with two symmetric types we have chosenhoweverto unify these four types of rotations into single trinode restructuring operation no matter how we view itthoughthe trinode restructuring method modifies parentchild relationships of ( nodes in twhile preserving the inorder traversal ordering of all the nodes in in addition to its order-preserving propertya trinode restructuring changes the heights of several nodes in tso as to restore balance recall that we execute the method restructure(xbecause zthe grandparent of xis unbalanced moreoverthis unbalance is due to one of the children of now having too large height relative to the height of ' other child as result of rotationwe move up the "tallchild of while pushing down the "shortchild of thusafter performing restructure( )all the nodes in the subtree now rooted at the node we called are balanced (see figure thuswe restore the heightbalance property locally at the nodes xyand in additionsince after performing the new entry insertion the subtree rooted at replaces the one formerly rooted at zwhich was taller by one unitall the ancestors of that were formerly unbalanced become balanced (see figure (the justification of this fact is left as exercise - thereforethis one restructuring also restores the height-balance property globally