Program to build DFA that starts and end with ‘a’ from input (a, b)

DFA (Deterministic Finite Automaton or Acceptor) is a finite state machine that accepts or rejects strings of symbols. DFA accepts the string if it reaches the final state and rejects otherwise. 

Now the problem is, provided a string as input character by character and we have to check whether the string starts and ends with ‘a’. We can only store the current character, since there is no concept of memory and hence the DFA cannot store the string provided. Otherwise, we could have just checked the first and last character for this problem. The input set for this problem is (a, b).

We cannot store anything accept the current character, which make this program a little different and tough than other string related problems. 

Examples: 

Input :  a b a b a
Output : Yes
Explanation : (a b a b a) starts and 
end with 'a'

Input :  a b a b b
Output : No
Explanation : (a b a b b) starts with 
'a' but doesn't end with 'a'   

We first build a DFA for this problem. Making DFA is like making a flowchart for this program and then implement it in any language. You should have the knowledge of DFA and Finite Automata.

The DFA for given problem is: 

Implementation:

C++

// C++ Program to DFA that accept strings
// which starts and end with 'a' over input(a, b)
#include <iostream>
#include <time.h>
using namespace std;

int main()
{
    // for producing different random
    // numbers every time.
    srand(time(0));

    // random length of string from 1 - 16
    // we are taking input from input stream,
    // we can take delimiter to end the string
    int max = 1 + rand() % 15;

    // generating random string and processing it
    int i = 0;
    while (i < max) {

        // producing random character over
        // input alphabet (a, b)
        char c = 'a' + rand() % 2;
        cout << c << " ";
        i++;

        // first character is 'a'
        if (c == 'a') {

            // if there is only 1 character
            // i.e. 'a'
            if (i == max)
                cout << "YES\n";

            while (i < max) {
                c = 'a' + rand() % 2;
                cout << c << " ";
                i++;

                // if character is 'a' and it
                // is the last character
                if (c == 'a' && i == max) {
                    cout << "\nYES\n";
                }

                // if character is 'b' and it
                // is the last character
                else if (i == max) {
                    cout << "\nNO\n";
                }
            }
        }

        // first character is 'b' so no matter
        // what the string is, it is not going
        // to be accepted
        else {
            while (i < max) {
                c = 'a' + rand() % 2;
                cout << c << " ";
                i++;
            }
            cout << "\nNO\n";
        }
    }

    return 0;
}

Java

// JAVA Program to DFA that accept Strings
// which starts and end with 'a' over input(a, b)
import java.util.*;

class GFG
{

public static void main(String[] args)
{
    // for producing different random
    // numbers every time.
    Random r = new Random();

    // random length of String from 1 - 16
    // we are taking input from input stream,
    // we can take delimiter to end the String
    int max = 1 + r.nextInt()*10 % 15;

    // generating random String and processing it
    int i = 0;
    while (i < max)
    {

        // producing random character over
        // input alphabet (a, b)
        char c = (char) ('a' + r.nextInt()*10 % 2);
        System.out.print(c+ " ");
        i++;

        // first character is 'a'
        if (c == 'a')
        {

            // if there is only 1 character
            // i.e. 'a'
            if (i == max)
                System.out.print("YES\n");

            while (i < max)
            {
                c = (char) ('a' + r.nextInt()*10 % 2);
                System.out.print(c+ " ");
                i++;

                // if character is 'a' and it
                // is the last character
                if (c == 'a' && i == max)
                {
                    System.out.print("\nYES\n");
                }

                // if character is 'b' and it
                // is the last character
                else if (i == max)
                {
                    System.out.print("\nNO\n");
                }
            }
        }

        // first character is 'b' so no matter
        // what the String is, it is not going
        // to be accepted
        else
        {
            while (i < max)
            {
                c = (char) ('a' + r.nextInt()*10 % 2);
                System.out.print(c+ " ");
                i++;
            }
            System.out.print("\nNO\n");
        }
    }
}
}

// This code is contributed by PrinciRaj1992

Python3

# Python Program to DFA that accept Strings
# which starts and end with 'a' over input(a, b)
import random

# for producing different random
# numbers every time.
r = random.Random()

# random length of String from 1 - 16
# we are taking input from input stream,
# we can take delimiter to end the String
max = 1 + r.randint(0, 14)

# generating random String and processing it
i = 0
while i < max:

    # producing random character over
    # input alphabet (a, b)
    c = chr(ord('a') + r.randint(0, 1))
    print(c, end=" ")
    i += 1

    # first character is 'a'
    if c == 'a':

        # if there is only 1 character
        # i.e. 'a'
        if i == max:
            print("YES")

        while i < max:
            c = chr(ord('a') + r.randint(0, 1))
            print(c, end=" ")
            i += 1

            # if character is 'a' and it
            # is the last character
            if c == 'a' and i == max:
                print("\nYES")

            # if character is 'b' and it
            # is the last character
            elif i == max:
                print("\nNO")
    # first character is 'b' so no matter
    # what the String is, it is not going
    # to be accepted
    else:
        while i < max:
            c = chr(ord('a') + r.randint(0, 1))
            print(c, end=" ")
            i += 1
        print("\nNO")

# This code is contributed by codebraxznt

C#

// C# Program to DFA that accept Strings
// which starts and end with 'a' over i.Add(a, b)
using System;

class GFG
{

static void Main(String[] args)
{

    // random length of String from 1 - 16
    // we are taking input from input stream,
    // we can take delimiter to end the String
    int max = 1 + new Random().Next()*10 % 15;

    // generating random String and processing it
    int i = 0;
    while (i < max)
    {

        // producing random character over
        // input alphabet (a, b)
        char c = (char) ('a' + new Random().Next()*10 % 2);
        Console.Write(c + " ");
        i++;

        // first character is 'a'
        if (c == 'a')
        {

            // if there is only 1 character
            // i.e. 'a'
            if (i == max)
                Console.Write("YES\n");

            while (i < max)
            {
                c = (char) ('a' + new Random().Next()*10 % 2);
                Console.Write(c + " ");
                i++;

                // if character is 'a' and it
                // is the last character
                if (c == 'a' && i == max)
                {
                    Console.Write("\nYES\n");
                }

                // if character is 'b' and it
                // is the last character
                else if (i == max)
                {
                    Console.Write("\nNO\n");
                }
            }
        }

        // first character is 'b' so no matter
        // what the String is, it is not going
        // to be accepted
        else
        {
            while (i < max)
            {
                c = (char) ('a' + new Random().Next()*10 % 2);
                Console.Write(c + " ");
                i++;
            }
            Console.Write("\nNO\n");
        }
    }
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript program to DFA that accept strings
// which starts and end with 'a' over input(a, b)

// Random length of String from 1 - 16
// we are taking input from input stream,
// we can take delimiter to end the String
let max = 1 + Math.floor(Math.random() * 10 % 15);

// Generating random String and processing it
let i = 0;
while (i < max)
{

    // Producing random character over
    // input alphabet (a, b)
    let c = String.fromCharCode(
        'a'.charCodeAt(0) +
        Math.floor(Math.random() * 10) % 2);

    document.write(c + " ");
    i++;

    // First character is 'a'
    if (c == 'a')
    {

        // If there is only 1 character
        // i.e. 'a'
        if (i == max)
            document.write("YES<br>");

        while (i < max)
        {
            c = String.fromCharCode(
                'a'.charCodeAt(0) +
                Math.floor(Math.random() * 10) % 2);

            document.write(c + " ");
            i++;

            // If character is 'a' and it
            // is the last character
            if (c == 'a' && i == max)
            {
                document.write("<br>YES<br>");
            }

            // If character is 'b' and it
            // is the last character
            else if (i == max)
            {
                document.write("<br>NO<br>");
            }
        }
    }

    // First character is 'b' so no matter
    // what the String is, it is not going
    // to be accepted
    else
    {
        while (i < max)
        {
            c = String.fromCharCode(
                'a'.charCodeAt(0) +
                Math.floor(Math.random() * 10) % 2);

            document.write(c + " ");
            i++;
        }
        document.write("<br>NO<br>");
    }
}

// This code is contributed by rag2127

</script>

Output

a b a b a b a b b b a b a 
YES

Time Complexity: O(MAX) 

Auxiliary Space: O(1)