-colour reds -right -colour blackdel_case ( ) sr figure sr insertion in case case is blacks' right child is redand is the left child of its parent in this casea left rotation is done at to make the parent of and ' right child after the rotationthe colours of and are interchanged and ' right child is coloured black once these steps are followedyou will observe that property and property remain valid case is explained in fig the code to fix case can be given as followsvoid del_case (struct node *nstruct node *ss sibling( ) -colour -parent -colourn -parent -colour blackif ( = -parent -lefts -right -colour blackrotate_left( -parent)else -left -colour blackrotate_right( -parent)applications of red-black trees red-black trees are efficient binary search treesas they offer worst case time guarantee for insertiondeletionand search operations red-black trees are not only valuable in time-sensitive applications such as real-time applicationsbut are also preferred to be used as building block in other data structures which provide worst-case guarantee avl trees also support (log nsearchinsertionand deletion operationsbut they are more rigidly balanced than red-black treesthereby resulting in slower insertion and removal but faster retrieval of data splay trees splay trees were invented by daniel sleator and robert tarjan splay tree is self-balancing binary search tree with an additional property that recently accessed elements can be re-accessed fast it is said to be an efficient binary tree because it performs basic operations such as insertionsearchand deletion in (log( )amortized time for many non-uniform sequences of operationssplay trees perform better than other search treeseven when the specific pattern of the sequence is unknown splay tree consists of binary treewith no additional fields when node in splay tree is accessedit is rotated or 'splayedto the rootthereby changing the structure of the tree since the