The tree data structure can be created by creating the nodes dynamically with the help of the pointers. The tree in the memory can be represented as shown below:. The above figure shows the representation of the tree data structure in the memory. In the above structure, the node contains three fields.
The second field stores the data; the first field stores the address of the left child, and the third field stores the address of the right child. The above structure can only be defined for the binary trees because the binary tree can have utmost two children, and generic trees can have more than two children. The structure of the node for generic trees would be different as compared to the binary tree. A node can be created with the help of a user-defined data type known as struct, as shown below:.
The above is the node structure with three fields: data field, the second field is the left pointer of the node type, and the third field is the right pointer of the node type. It is one of the types of the binary tree, or we can say that it is a variant of the binary search tree. AVL tree satisfies the property of the binary tree as well as of the binary search tree. It is a self-balancing binary search tree that was invented by Adelson Velsky Lindas.
Here, self-balancing means that balancing the heights of left subtree and right subtree. This balancing is measured in terms of the balancing factor.
We can consider a tree as an AVL tree if the tree obeys the binary search tree as well as a balancing factor. The balancing factor can be defined as the difference between the height of the left subtree and the height of the right subtree.
The balancing factor's value must be either 0, -1, or 1; therefore, each node in the AVL tree should have the value of the balancing factor either as 0, -1, or 1.
The red-Black tree is the binary search tree. The prerequisite of the Red-Black tree is that we should know about the binary search tree. In a binary search tree, the value of the left-subtree should be less than the value of that node, and the value of the right-subtree should be greater than the value of that node.
As we know that the time complexity of binary search in the average case is log 2 n, the best case is O 1 , and the worst case is O n.
When any operation is performed on the tree, we want our tree to be balanced so that all the operations like searching, insertion, deletion, etc. The red-black tree is a self-balancing binary search tree.
AVL tree is also a height balancing binary search tree then why do we require a Red-Black tree. In the AVL tree, we do not know how many rotations would be required to balance the tree, but in the Red-black tree, a maximum of 2 rotations are required to balance the tree.
It contains one extra bit that represents either the red or black color of a node to ensure the balancing of the tree. The splay tree data structure is also binary search tree in which recently accessed element is placed at the root position of tree by performing some rotation operations. Here, splaying means the recently accessed node. It is a self-balancing binary search tree having no explicit balance condition like AVL tree.
It might be a possibility that height of the splay tree is not balanced, i. Splay tree is a balanced tree but it cannot be considered as a height balanced tree because after each operation, rotation is performed which leads to a balanced tree.
Treap data structure came from the Tree and Heap data structure. So, it comprises the properties of both Tree and Heap data structures. In Binary search tree, each node on the left subtree must be equal or less than the value of the root node and each node on the right subtree must be equal or greater than the value of the root node.
In heap data structure, both right and left subtrees contain larger keys than the root; therefore, we can say that the root node contains the lowest value. In treap data structure, each node has both key and priority where key is derived from the Binary search tree and priority is derived from the heap data structure.
B-tree is a balanced m-way tree where m defines the order of the tree. Till now, we read that the node contains only one key but b-tree can have more than one key, and more than 2 children. It always maintains the sorted data. In binary tree, it is possible that leaf nodes can be at different levels, but in b-tree, all the leaf nodes must be at the same level.
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Company Questions. Artificial Intelligence. Cloud Computing. Viewed 2k times. Improve this question. Oh, you mean that kind of trees. Add a comment. Active Oldest Votes. Improve this answer. David Richerby David Richerby In the 19th century mathematicians did not really care about algorithms some exceptions here. Trees were definitely not used as a data structure like a search tree in these works.
Iverson and L. Johnson, IBM Corp. Perils and C. Schulz A. Schulz Does the second reference have a title? A programming notation for trees. That's from here: dl. Michael Kay Michael Kay 2 2 silver badges 3 3 bronze badges. Windley: Trees, forests, and rearranging. Sage Mitchell Sage Mitchell 2 2 bronze badges. Each node can have arbitrary number of children.
Nodes with no children are called leaves , or external nodes. Nodes, which are not leaves, are called internal nodes. Internal nodes have at least one child. Nodes with the same parent are called siblings. In the picture, B, C, D are called siblings. The depth of a node is the number of edges from the root to the node.
The depth of K is 2. The height of a node is the number of edges from the node to the deepest leaf. The height of B is 2. The height of a tree is a height of a root. A General Tree. A general tree is a tree where each node may have zero or more children a binary tree is a specialized case of a general tree. General trees are used to model applications such as file systems. Figure courtesy of www.
Each node will have TWO pointers: one to the leftmost child, and one to the rightmost sibling.
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