We try recoloring first, if recoloring doesn’t work, then we go for rotation. Following is detailed algorithm. The algorithms has mainly two cases depending upon the color of uncle. If uncle is red, we do recoloring. If uncle is black, we do rotations and/or recoloring.
Color of a NULL node is considered as BLACK.
Let x be the newly inserted node.
1) Perform standard BST insertion and make the color of newly inserted nodes as RED.
2) If x is root, change color of x as BLACK (Black height of complete tree increases by 1).
3) Do following if color of x’s parent is not BLACK or x is not root.
….a) If x’s uncle is RED (Grand parent must have been black from property 4)
……..(i) Change color of parent and uncle as BLACK.
……..(ii) color of grand parent as RED.
……..(iii) Change x = x’s grandparent, repeat steps 2 and 3 for new x.