Program to construct DFA accepting odd number of 0s and odd number of 1s

Given a binary string S, the task is to write a program for DFA Machine that accepts a string with odd numbers of 0s and 1s.

Examples:

Input: S = "010011"
Output: Accepted
Explanation:
The given string S contains odd number of zeros and ones.

Input: S = "00000"
Output: Not Accepted
Explanation:
The given string S doesn't contains odd number of zeros and ones.

Approach: Below is the designed DFA Machine for the given problem. Construct a transition table for DFA states and analyze the transitions between each state. Below are the steps:

There are 4 states q₀, q₁, q₂, q₃ where q₀ is the initial state and q₃ is the final state.
The transition table of the above DFA is as follows:

Current state	Final state
Current state	0	1
q₀	q₁	q₂
q₁	q₀	q₃
q₂	q₃	q₀
q₃	q₂	q₁

Through this table, understand the transitions in the DFA.
If the final state(q₃) is reached after reading the whole string, then the string is accepted otherwise not-accepted.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to check whether the given
// string is accepted by DFA or not
void checkValidDFA(string s)
{
    // Stores initial state of DFA
    int initial_state = 0;

    // Stores final state of DFA
    int final_state;

    // Stores previous state of DFA
    int previous_state = 0;

    // Iterate through the string
    for (int i = 0; i < s.length(); i++) {

        // Checking for all combinations
        if ((s[i] == '0'
             && previous_state == 0)
            || (s[i] == '1'
                && previous_state == 3)) {
            final_state = 1;
        }
        else if ((s[i] == '0'
                  && previous_state == 3)
                 || (s[i] == '1'
                     && previous_state == 0)) {
            final_state = 2;
        }
        else if ((s[i] == '0'
                  && previous_state == 1)
                 || (s[i] == '1'
                     && previous_state == 2)) {
            final_state = 0;
        }
        else if ((s[i] == '0'
                  && previous_state == 2)
                 || (s[i] == '1'
                     && previous_state == 1)) {
            final_state = 3;
        }

        // Update the previous_state
        previous_state = final_state;
    }

    // If final state is reached
    if (final_state == 3) {
        cout << "Accepted" << endl;
    }

    // Otherwise
    else {
        cout << "Not Accepted" << endl;
    }
}

// Driver Code
int main()
{
    // Given string
    string s = "010011";

    // Function Call
    checkValidDFA(s);

    return 0;
}

Python3

# Python3 program for the above approach

# Function to check whether the given
# is accepted by DFA or not
def checkValidDFA(s):
    
    # Stores initial state of DFA
    initial_state = 0

    # Stores final state of DFA
    final_state = 0

    # Stores previous state of DFA
    previous_state = 0

    # Iterate through the string
    for i in range(len(s)):
        
        # Checking for all combinations
        if ((s[i] == '0' and previous_state == 0) or 
            (s[i] == '1' and previous_state == 3)):
            final_state = 1
        elif ((s[i] == '0' and previous_state == 3) or 
              (s[i] == '1' and previous_state == 0)):
            final_state = 2
        elif ((s[i] == '0' and previous_state == 1) or 
              (s[i] == '1' and previous_state == 2)):
            final_state = 0
        elif ((s[i] == '0' and previous_state == 2) or
              (s[i] == '1' and previous_state == 1)):
            final_state = 3

        # Update the previous_state
        previous_state = final_state

    # If final state is reached
    if (final_state == 3):
        print("Accepted")
        
    # Otherwise
    else:
        print("Not Accepted")

# Driver Code
if __name__ == '__main__':
    
    # Given string
    s = "010011"

    # Function Call
    checkValidDFA(s)

# This code is contributed by mohit kumar 29

Java

// Java program for the above approach
import java.util.*;

class GFG{
  
// Function to check whether the given
// string is accepted by DFA or not
static void checkValidDFA(String s)
{
    
    // Stores initial state of DFA
    int initial_state = 0;

    // Stores final state of DFA
    int final_state = 0;

    // Stores previous state of DFA
    int previous_state = 0;

    // Iterate through the string
    for(int i = 0; i < s.length(); i++) 
    {
        
        // Checking for all combinations
        if ((s.charAt(i) == '0' && previous_state == 0) ||
            (s.charAt(i) == '1' && previous_state == 3))
        {
            final_state = 1;
        }
        else if ((s.charAt(i) == '0' && previous_state == 3) ||
                 (s.charAt(i) == '1' && previous_state == 0)) 
        {
            final_state = 2;
        }
        else if ((s.charAt(i) == '0' && previous_state == 1) ||
                 (s.charAt(i) == '1' && previous_state == 2))
        {
            final_state = 0;
        }
        else if ((s.charAt(i) == '0' && previous_state == 2) ||
                 (s.charAt(i) == '1' && previous_state == 1))
        {
            final_state = 3;
        }

        // Update the previous_state
        previous_state = final_state;
    }

    // If final state is reached
    if (final_state == 3) 
    {
        System.out.println("Accepted");
    }

    // Otherwise
    else 
    {
        System.out.println("Not Accepted");
    }
}

// Driver Code
public static void main(String args[])
{
    
    // Given string
    String s = "010011";

    // Function Call
    checkValidDFA(s);
}
}

// This code is contributed by bgangwar59

// C# program for the above approach
using System;
 
class GFG{
    
// Function to check whether the given
// string is accepted by DFA or not
static void checkValidDFA(string s)
{
    
    // Stores initial state of DFA
    //int initial_state = 0;
 
    // Stores final state of DFA
    int final_state = 0;
 
    // Stores previous state of DFA
    int previous_state = 0;
 
    // Iterate through the string
    for(int i = 0; i < s.Length; i++) 
    {
        
        // Checking for all combinations
        if ((s[i] == '0' && previous_state == 0) || 
            (s[i] == '1' && previous_state == 3))
        {
            final_state = 1;
        }
        else if ((s[i] == '0' && previous_state == 3) ||
                 (s[i] == '1' && previous_state == 0))
        {
            final_state = 2;
        }
        else if ((s[i] == '0' && previous_state == 1) || 
                 (s[i] == '1' && previous_state == 2))
        {
            final_state = 0;
        }
        else if ((s[i] == '0' && previous_state == 2) ||
                 (s[i] == '1' && previous_state == 1))
        {
            final_state = 3;
        }
 
        // Update the previous_state
        previous_state = final_state;
    }
 
    // If final state is reached
    if (final_state == 3)
    {
        Console.WriteLine("Accepted");
    }
 
    // Otherwise
    else 
    {
        Console.WriteLine("Not Accepted");
    }
}
 
// Driver Code
public static void Main()
{
    
    // Given string
    string s = "010011";
 
    // Function Call
    checkValidDFA(s);
}
}

// This code is contributed by sanjoy_62

JavaScript

<script>

      // JavaScript program for the above approach
      // Function to check whether the given
      // string is accepted by DFA or not
      function checkValidDFA(s) {
        // Stores initial state of DFA
        // int initial_state = 0;

        // Stores final state of DFA
        var final_state = 0;

        // Stores previous state of DFA
        var previous_state = 0;

        // Iterate through the string
        for (var i = 0; i < s.length; i++) {
          // Checking for all combinations
          if (
            (s[i] === "0" && previous_state === 0) ||
            (s[i] === "1" && previous_state === 3)
          ) {
            final_state = 1;
          } else if (
            (s[i] === "0" && previous_state === 3) ||
            (s[i] === "1" && previous_state === 0)
          ) {
            final_state = 2;
          } else if (
            (s[i] === "0" && previous_state === 1) ||
            (s[i] === "1" && previous_state === 2)
          ) {
            final_state = 0;
          } else if (
            (s[i] === "0" && previous_state === 2) ||
            (s[i] === "1" && previous_state === 1)
          ) {
            final_state = 3;
          }

          // Update the previous_state
          previous_state = final_state;
        }

        // If final state is reached
        if (final_state === 3) {
          document.write("Accepted");
        }

        // Otherwise
        else {
          document.write("Not Accepted");
        }
      }

      // Driver Code
      // Given string
      var s = "010011";

      // Function Call
      checkValidDFA(s);
      
</script>

Output:

Accepted

Time Complexity: O(N)
Auxiliary Space: O(1)

Program to construct DFA accepting odd number of 0s and odd number of 1s

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