In left-right rotation, first, you perform left rotation followed by right rotation In right-left rotation, first, you perform right rotation followed by a left rotation. Assign ‘a’ as the left child of ‘n’, if ‘b’ is the right child of ‘n’.Assign ‘a’ as the right child of ‘n’, if ‘b’ is the right child of ‘n’. Assign ‘a’ as the root of the tree if the parent of ‘b’ is NULL.Assign ‘b’ as the parent node of the right subtree of ‘a’, if ‘a’ has a right subtree.Consider the below given red-black tree.Look at the below algorithm for understanding. The nodes on the left of the tree are transformed on the right node is called the left rotation. Assign ‘b’ as the right child of ‘n’, if ‘a’ is right child of ‘n’.Assign ‘b’ as the left child of ‘n’, if ‘a’ is the left child of ‘n’.Assign ‘b’ as the root of the tree if the parent node of ‘a’ is NULL.Assign ‘a’ as a parent node of the left subtree of ‘b’, if ‘b’ has a left subtree.The nodes on the right of the tree are transformed on the left node is called the left rotation. Basically, there are two types of rotation in Red-Black Tree: 1) Left Rotation It helps to maintain the red-black tree properties which are sometimes violated while insertion and deletion operations. The rotation is the process of adjusting or interchange the nodes of the subtrees inside the tree in such a way that the height of the tree is restored. Hence, the red-black tree is potentially faster during insertion and deletion operations in comparison to AVL trees. But it is noted, that the red-black tree makes fewer structural changes to balance the height of the tree in comparison to AVL trees. Instead of a red-black tree, you can also use an AVL tree to balance the height of the tree. Therefore, the time complexity for search operation is reduced to O(log n) where n is the number of nodes in the tree. As the red-black tree maintains its height of the tree after every insertion and deletion operation, the tree can be avoided from skewing. This problem can be solved by using a red-black tree. Hence, as the height of the tree grows linearly, the search operation in the tree becomes the worst-case scenario and takes O(n) time where n is the total number of nodes inserted. Here, the height of the tree is 5 as the tree grows linearly when the new node is inserted. Consider the below image where the nodes inserted in the binary search tree are 10,20,30,40,50. Why Use Red-Black Tree?Īs you know that binary search tree maintains the natural order of the data inserted, but it does not restrict the size, length, or height of the tree. Remember that every node of the red-black tree consumes only 1 bit of memory storage to store the color information, hence the tree is identical to the classic binary search tree. Depth Property: Every path from the root node to any leaf node should have the same number of black-colored nodes.Therefore, there should not be two consecutive red nodes. Red Property: The child node is always black if the parent node is red in color.Leaf Property: Every leaf of the tree is black.Root Property: The color attribute of the root node is always black.Red/Black Property: Every node of the tree is colored either red or black.Tree Property: Red-Black tree should be a binary search tree.Therefore, the red-black tree follows the below properties: The importance of these colors in the nodes of the tree ensures that the tree is balanced while insertion and deletion operations of the node. Every node of the red-black tree contains an extra attribute denoting the color of the node, specifically, either red or black. A red-black tree is also called symmetric binary B-Tree. What is a Red-Black Tree?Ī red-black tree is the variation of the binary search tree with the property of self-balancing. Later we will also go through various advantages, disadvantages, and applications of the red-black tree. We will understand various operations of the red-black tree along with their algorithm, example, and python code. In this article, we will study what is a red-black tree is and why it is useful.
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