DFA that begins with 'a' but does not contain substring 'aab'

Prerequisite: Introduction to Deterministic Finite Automata 
Construct a DFA that accepts string str starting with input alphabet 'a' but does not contain 'aab' as a substring over input {a, b}.

Examples: 

Input: str = "babba" 
Output: Not Accepted 
Explanation: 
The given string doesn't start with 'a'.

Input: str = "abbaaaaa" 
Output: Accepted 
Explanation: 
The given string start with 'a'and doesn't contains "aab" as a substring. 
 

Approach: 
The transition table helps to understand how the transition of each state takes place on the input alphabets. In the transition table initial state is represented by ---> and the final state is represented by *. There are 3 final states, one initial and one dead state. 

State Transition table of the given DFA: 
 

Below is the DFA diagram: 

Below is the implementation of the above DFA: 

Not Accepted

Time Complexity: O(N)  
Auxiliary Space: O(N)