figure shows tree and the corresponding red-black tree obtained by applying these transformations dotted lines surround the subtrees that were made from -nodes and -nodes the red-black rules are automatically satisfied by the transformation check that this is sotwo red nodes are never connectedand there is the same number of black nodes on every path from root to leaf (or null childfigure tree and its red-black equivalent you can say that -node in tree is equivalent to parent with red child in red-black treeand -node is equivalent to parent with two red children it follows that black parent with black child in red-black tree does not represent -node in - treeit simply represents -node with another -node child similarlya black parent with two black children does not represent -node operational equivalence not only does the structure of red-black tree correspond to treebut the operations applied to these two kinds of trees are also equivalent in tree the tree is kept balanced using node splits in red-black tree the two balancing methods are color flips and rotations -node splits and color flips