ID3 algorithm:

Further for the calculation for information gain is the most difficult part of this algorithm. Hence ID3 performs a search whereby the search states are decision trees and the operator involves adding a node to an existing tree. So there uses information gain to measure the attribute to put in each node but performs a greedy search using this measure of worth. However the algorithm goes like:  by given a set of examples, S, categorised in categories ci, then as: 

1. Moreover choose the root node to be the attribute, A that scores the highest for information gain relative to S. 

2. Just for each value v that A can possibly take and draw a branch from the node. 

3. And for each branch from A corresponding to value v but calculate S_v. like: 

• Whether S_v is empty and choose the category cdefault that contains the most examples from S then put this as the leaf node category that ends that branch.
• Whether S_v contains only examples from a category c and put c as the leaf node category that ends that branch.
• Or else remove A from the set of attributes that can be put into nodes. And then put a new node in the decision tree, when the new attribute being tested in the node is the one that scores highest for information gain relative to S_v as note there not relative to S. However this new node starts the cycle again from 2 as with S replaced by S_v in the calculations then the tree gets built iteratively like this.

If considered the algorithm terminates either when the decision tree perfectly classifies the examples or when all the attributes have been exhausted.