20BCE1545 CSE2011 DSA D1 DA1.docx - Tree is a hierarchical...

Tree is a hierarchical data structure which are defined by a collection of nodes which
represent a value. Each node is connected to other nodes by edges. The tree
originates from a node known as root node which does not have a parent node.
Every node in the tree has only one parent node and are connected to its children by
edges.
RED-BLACK TREE:
Red-Black tree is a binary search tree in which each node contains an extra bit which
shows the colour of the node, either red or black. The red and black colour is meant
for balancing the tree at the time of insertion and deletion.
Properties of Red-Black Tree:
1) Every node in the Red-Black tree is coloured red or black
2) The root of the tree is black
3) Every leaf node in the tree is black
4) The children of every red node are always black
5) The path between a node to its descendent leaf has the same black-depth
Example of Red-Black Tree:
Operations of Red-Black Tree:
a) Insertion Operation:
In a Red-Black Tree every node being inserted should be of colour red. The insertion
operation in Red-Black Tree is similar to that of Binary Search Tree. The following
steps should be considered for performing insertion operation of Red-Black Tree:
 First check whether the tree is empty.

 If the tree is empty then insert new node as a black coloured root node and
exit from the operation.
 Insert a red coloured new node as leaf node if the tree is not empty
 If the parent of the new node is black then exit the operation.