search trees case this case involves three nodesthe pivot ( )the left child of the pivot ( )and the right child (gof for this case to occurthe balance factor of the pivot is left high before the insertion and the new key is inserted into either the right subtree of this casewhich is illustrated in figure requires two rotations node has to be rotated left over node and the pivot node has to be rotated right over its left child the link modifications required to accomplish this rotation include setting the right child of as the new left child of the pivot nodechanging the left child of to become the right child of cand setting to be the new left child of > - or key key - or key key after before figure case double rotation with the pivot' left child rotated left over its right child and the pivot rotated right over its left child cases and the third case is mirror image of the first case and the fourth case is mirror image of the second case the difference is the new key is inserted in the right subtree of the pivot node or descendant of its right subtree the two cases are illustrated in figure new balance factors when new key is inserted into the treethe balance factors of the nodes along the path from the root to the insertion point may have to be modified to reflect the insertion the balance factor of node along the path changes if the subtree into which the new node was inserted grows taller the new balance factor of node depends on its current balance factor and the subtree into which the new node was inserted the resulting balance factors are provided herecurrent factor left subtree >right subtree <modifications to the balance factors are made in reverse order as the recursion unwinds when node has left high balance and the new node is inserted into