Define an ordered rooted tree. Cite any two applications of the tree structure, also illustrate using an example each the purpose of the usage.  

Ans: A  tree is a graph like that it is connected, it has no loop or circuit of any length and number of edges in it is one less as compared to the number of vertices.

If the downward slop of an arc is taken as the direction of the arc after that the above graph can be considered as a directed graph. In degree of node + is zero and of all other nodes is one. There are nodes such as 3, 4, 5, 2 and 5 without degree zero and all other nodes comprise out degree > 0. A node with in degree zero in a tree is known as root of the tree. Each tree has one and just only one root and that is why a directed tree is as well known as a rooted tree. The position of each labeled node is fixed, any change in the position of node will modify the meaning of the expression denoted by the tree. Such kind of tree is called ordered tree.

A tree structure is utilized in evaluation of an arithmetic expression (parsing technique) The other common application is search tree. The tree presented is an instance of expression tree. An instance of binary search tree is shown below.