# DFA for strings not containing consecutive two a’s and starting with ‘a’

Prerequisite – Finite Automata Introduction
Problem: Construct deteministic finite automata (DFA) for strings not containing consecutive two a’s and starting with a.

Explanation:
Accept Strings that not contain consecutive two a’s. Check if a given string contain consecutive two a’s or not. The any occurrence of (b-z) should not affect the scenario. Strings should follow this pattern:

```a.(ww|(ww.a))*
where, ww = all possible character except a ```

All those strings that are not fall in the above mentioned pattern are not accepted.

Deterministic finite automata (DFA) of strings that not contain consecutive two a’s given as following below. The initial and starting state in this dfa is q0. Approach used:
In this program, consider the 6 states to be 0, 1, 2, 3, 4 and 5. Now let us take a variable named DFA which will be initially 0. Whenever any transition takes place, it will update the value of DFA with the number associated with new state.

Example:
If a transition occurs from state 0 to state 1 then the value of DFA will be updated to 1. If a transition occurs from state 2 to state 3 then the value of dfa will be updated to 3. In this way, apply this algorithm on entire string and if in the end, then reach state 1, 2, 4 or 5 then our string will be accepted otherwise not.

```Input : geeksaforaageeks
Output : NOT ACCEPTED

Input : aageeksforageeks
Output : NOT ACCEPTED

Input : ageeksaforageeks
Output : ACCEPTED ```

Implementation:

## C/C++

 `// C program to implement DFA for Strings ` `// not containing consecutive two a's ` `#include ` `#include ` ` `  `int` `dfa = 0; ` ` `  `// This function is for ` `// the starting state of DFA ` `void` `start(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) { ` `        ``dfa = 1; ` `    ``} ` `    ``else` `{ ` `        ``dfa = 3; ` `    ``} ` `} ` ` `  `// This function is for the first state of DFA ` `void` `state1(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) { ` `        ``dfa = 3; ` `    ``} ` `    ``else` `{ ` `        ``dfa = 4; ` `    ``} ` `} ` ` `  `// This function is for the second state  of DFA ` `void` `state2(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) { ` `        ``dfa = 5; ` `    ``} ` `    ``else` `{ ` `        ``dfa = 2; ` `    ``} ` `} ` ` `  `// This function is for the third state of DFA ` `void` `state3(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) { ` `        ``dfa = 3; ` `    ``} ` `    ``else` `{ ` `        ``dfa = 3; ` `    ``} ` `} ` ` `  `// This function is for the forth state of DFA ` `void` `state4(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) { ` `        ``dfa = 5; ` `    ``} ` `    ``else` `{ ` `        ``dfa = 2; ` `    ``} ` `} ` ` `  `void` `state5(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) { ` `        ``dfa = 3; ` `    ``} ` `    ``else` `{ ` `        ``dfa = 2; ` `    ``} ` `} ` ` `  `int` `isAccepted(``char` `str[]) ` `{ ` `    ``// store length of string ` `    ``int` `i, len = ``strlen``(str); ` ` `  `    ``for` `(i = 0; i < len; i++) { ` ` `  `        ``// printf("%d", dfa); ` `        ``if` `(dfa == 0) ` `            ``start(str[i]); ` ` `  `        ``else` `if` `(dfa == 1) ` `            ``state1(str[i]); ` ` `  `        ``else` `if` `(dfa == 2) ` `            ``state2(str[i]); ` ` `  `        ``else` `if` `(dfa == 3) ` `            ``state3(str[i]); ` ` `  `        ``else` `if` `(dfa == 4) ` `            ``state4(str[i]); ` ` `  `        ``else` `if` `(dfa == 5) ` `            ``state5(str[i]); ` ` `  `        ``else` `            ``return` `0; ` `    ``} ` `    ``if` `(dfa == 0) ` `        ``return` `0; ` `    ``else` `if` `(dfa == 3) ` `        ``return` `0; ` `    ``else` `        ``return` `1; ` `} ` ` `  `// driver code ` `int` `main() ` `{ ` `    ``char` `str[] = ``"ageeksaforageeks"``; ` `    ``if` `(isAccepted(str)) ` `        ``printf``(``"ACCEPTED"``); ` `    ``else` `        ``printf``(``"NOT ACCEPTED"``); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by SHUBHAMSINGH10. `

## Java

 `// Java program to implement DFA for Strings ` `// not containing consecutive two a's ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `static` `int` `dfa = ``0``; ` ` `  `// This function is for ` `// the starting state of DFA ` `static` `void` `start(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = ``1``; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = ``3``; ` `    ``} ` `} ` ` `  `// This function is for the first state of DFA ` `static` `void` `state1(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = ``3``; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = ``4``; ` `    ``} ` `} ` ` `  `// This function is for the second state of DFA ` `static` `void` `state2(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = ``5``; ` `    ``} ` `    ``else`  `    ``{ ` `        ``dfa = ``2``; ` `    ``} ` `} ` ` `  `// This function is for the third state of DFA ` `static` `void` `state3(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) ` `    ``{ ` `        ``dfa = ``3``; ` `    ``} ` `    ``else`  `    ``{ ` `        ``dfa = ``3``; ` `    ``} ` `} ` ` `  `// This function is for the forth state of DFA ` `static` `void` `state4(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = ``5``; ` `    ``} ` `    ``else`  `    ``{ ` `        ``dfa = ``2``; ` `    ``} ` `} ` ` `  `static` `void` `state5(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = ``3``; ` `    ``} ` `    ``else`  `    ``{ ` `        ``dfa = ``2``; ` `    ``} ` `} ` ` `  `static` `int` `isAccepted(``char` `str[]) ` `{ ` `    ``// store length of string ` `    ``int` `i, len = str.length; ` ` `  `    ``for` `(i = ``0``; i < len; i++)  ` `    ``{ ` ` `  `        ``// System.out.printf("%d", dfa); ` `        ``if` `(dfa == ``0``) ` `            ``start(str[i]); ` ` `  `        ``else` `if` `(dfa == ``1``) ` `            ``state1(str[i]); ` ` `  `        ``else` `if` `(dfa == ``2``) ` `            ``state2(str[i]); ` ` `  `        ``else` `if` `(dfa == ``3``) ` `            ``state3(str[i]); ` ` `  `        ``else` `if` `(dfa == ``4``) ` `            ``state4(str[i]); ` ` `  `        ``else` `if` `(dfa == ``5``) ` `            ``state5(str[i]); ` ` `  `        ``else` `            ``return` `0``; ` `    ``} ` `    ``if` `(dfa == ``0``) ` `        ``return` `0``; ` `    ``else` `if` `(dfa == ``3``) ` `        ``return` `0``; ` `    ``else` `        ``return` `1``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``char` `str[] = ``"ageeksaforageeks"``.toCharArray(); ` `    ``if` `(isAccepted(str) == ``1``) ` `        ``System.out.printf(``"ACCEPTED"``); ` `    ``else` `        ``System.out.printf(``"NOT ACCEPTED"``); ` ` `  `} ` `} ` ` `  `// This code is contributed by Arnab Kundu `

## Python 3

 `# Python3 program to implement DFA for Strings ` `# not containing consecutive two a's ` `     `  `# This function is for the dfa = starting   ` `# dfa = state (zeroth) of DFA    ` `def` `start(c):   ` `    ``if` `(c ``=``=` `'a'``):   ` `        ``dfa ``=` `1` `    ``else``:   ` `        ``dfa ``=` `3` `    ``return` `dfa   ` `     `  `# This function is for the first    ` `# dfa = state of DFA    ` `def` `state1(c):    ` `    ``if` `(c ``=``=` `'a'``):   ` `        ``dfa ``=` `3` `    ``else``:   ` `        ``dfa ``=` `4` `    ``return` `dfa   ` `     `  `# This function is for the second    ` `# dfa = state of DFA    ` `def` `state2(c):   ` `    ``if` `(c ``=``=` `'a'``):   ` `        ``dfa ``=` `5` `    ``else``:   ` `        ``dfa ``=` `2` `    ``return` `dfa   ` `     `  `# This function is for the third    ` `# dfa = state of DFA    ` `def` `state3(c):   ` `    ``if` `(c ``=``=` `'a'``):   ` `        ``dfa ``=` `3` `    ``else``:   ` `        ``dfa ``=` `3` `    ``return` `dfa   ` `     `  `# This function is for the fouth    ` `# dfa = state of DFA    ` `def` `state4(c):   ` `    ``if` `(c ``=``=` `'a'``):   ` `        ``dfa ``=` `5` `    ``else``:   ` `        ``dfa ``=` `2` `    ``return` `dfa  ` `     `  `     `  `# This function is for the fifth   ` `# dfa = state of DFA    ` `def` `state5(c):   ` `    ``if` `(c ``=``=` `'a'``):   ` `        ``dfa ``=` `3` `    ``else``:   ` `        ``dfa ``=` `2` `    ``return` `dfa    ` `     `  `def` `isAccepted(String):   ` `         `  `    ``# store length of Stringing    ` `    ``l ``=` `len``(String)   ` `         `  `    ``# dfa tells the number associated   ` `    ``# with the present dfa = state   ` `    ``dfa ``=` `0` `    ``for` `i ``in` `range``(l):    ` `        ``if` `(dfa ``=``=` `0``):    ` `            ``dfa ``=` `start(String[i])    ` `     `  `        ``elif` `(dfa ``=``=` `1``):    ` `            ``dfa ``=` `state1(String[i])    ` `     `  `        ``elif` `(dfa ``=``=` `2``) :   ` `            ``dfa ``=` `state2(String[i])    ` `     `  `        ``elif` `(dfa ``=``=` `3``) :   ` `            ``dfa ``=` `state3(String[i])    ` `     `  `        ``elif` `(dfa ``=``=` `4``) :   ` `            ``dfa ``=` `state4(String[i])  ` `         `  `        ``elif` `(dfa ``=``=` `5``) :   ` `            ``dfa ``=` `state5(String[i]) ` `        ``else``:   ` `            ``return` `0` `    ``if``(dfa ``=``=` `3` `or` `dfa ``=``=` `0``) :   ` `        ``return` `0` `    ``else``:   ` `        ``return` `1` `     `  `# Driver code    ` `if` `__name__ ``=``=` `"__main__"` `:   ` `    ``String ``=` `"ageeksaforageeks"` `    ``if` `(isAccepted(String)) :   ` `        ``print``(``"ACCEPTED"``)    ` `    ``else``:   ` `        ``print``(``"NOT ACCEPTED"``)    ` `    `  `# This code is contributed by SHUBHAMSINGH10. `

## C#

 `// C# program to implement DFA for Strings ` `// not containing consecutive two a's ` `using` `System; ` `     `  `public` `class` `GFG ` `{ ` `  `  `static` `int` `dfa = 0; ` `  `  `// This function is for ` `// the starting state of DFA ` `static` `void` `start(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = 1; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = 3; ` `    ``} ` `} ` `  `  `// This function is for the first state of DFA ` `static` `void` `state1(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = 3; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = 4; ` `    ``} ` `} ` `  `  `// This function is for the second state of DFA ` `static` `void` `state2(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = 5; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = 2; ` `    ``} ` `} ` `  `  `// This function is for the third state of DFA ` `static` `void` `state3(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``) ` `    ``{ ` `        ``dfa = 3; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = 3; ` `    ``} ` `} ` `  `  `// This function is for the forth state of DFA ` `static` `void` `state4(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = 5; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = 2; ` `    ``} ` `} ` `  `  `static` `void` `state5(``char` `c) ` `{ ` `    ``if` `(c == ``'a'``)  ` `    ``{ ` `        ``dfa = 3; ` `    ``} ` `    ``else` `    ``{ ` `        ``dfa = 2; ` `    ``} ` `} ` `  `  `static` `int` `isAccepted(``char``[] str) ` `{ ` `    ``// store length of string ` `    ``int` `i, len = str.Length; ` `  `  `    ``for` `(i = 0; i < len; i++)  ` `    ``{ ` `  `  `        ``// System.out.printf("%d", dfa); ` `        ``if` `(dfa == 0) ` `            ``start(str[i]); ` `  `  `        ``else` `if` `(dfa == 1) ` `            ``state1(str[i]); ` `  `  `        ``else` `if` `(dfa == 2) ` `            ``state2(str[i]); ` `  `  `        ``else` `if` `(dfa == 3) ` `            ``state3(str[i]); ` `  `  `        ``else` `if` `(dfa == 4) ` `            ``state4(str[i]); ` `  `  `        ``else` `if` `(dfa == 5) ` `            ``state5(str[i]); ` `  `  `        ``else` `            ``return` `0; ` `    ``} ` `    ``if` `(dfa == 0) ` `        ``return` `0; ` `    ``else` `if` `(dfa == 3) ` `        ``return` `0; ` `    ``else` `        ``return` `1; ` `} ` `  `  `// Driver code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``char` `[]str = ``"ageeksaforageeks"``.ToCharArray(); ` `    ``if` `(isAccepted(str) == 1) ` `        ``Console.WriteLine(``"ACCEPTED"``); ` `    ``else` `        ``Console.WriteLine(``"NOT ACCEPTED"``); ` `  `  `} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output:

`ACCEPTED `

The time complexity of this program is O(n)

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