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Trees

Tree represents the nodes connected by edges. We will discuss binary tree or binary search tree specifically.

Binary Tree is a special datastructure used for data storage purposes. A binary tree has a special condition that each node can have a maximum of two children. A binary tree has the benefits of both an ordered array and a linked list as search is as quick as in a sorted array and insertion or deletion operation are as fast as in linked list.

Binary Tree

Important Terms

Following are the important terms with respect to tree.

  • Path − Path refers to the sequence of nodes along the edges of a tree.

  • Root − The node at the top of the tree is called root. There is only one root per tree and one path from the root node to any node.

  • Parent − Any node except the root node has one edge upward to a node called parent.

  • Child − The node below a given node connected by its edge downward is called its child node.

  • Leaf − The node which does not have any child node is called the leaf node.

  • Subtree − Subtree represents the descendants of a node.

  • Visiting − Visiting refers to checking the value of a node when control is on the node.

  • Traversing − Traversing means passing through nodes in a specific order.

  • Levels − Level of a node represents the generation of a node. If the root node is at level 0, then its next child node is at level 1, its grandchild is at level 2, and so on.

  • keys − Key represents a value of a node based on which a search operation is to be carried out for a node.

Binary Search Tree Representation

Binary Search tree exhibits a special behavior. A node's left child must have a value less than its parent's value and the node's right child must have a value greater than its parent value.

Binary Search Tree