Given a string S, the task is to design a Deterministic Finite Automata (DFA) for accepting the language L = {aNbM | N ≥ 0, M ≥ 0, N+M ≥ 1}. , i.e., a regular language L such that all ‘a’ occur before the first occurrence of ‘b’ {a, ab, aab, bb…, }. If the given string follows the given language L, then print “Accepted”. Otherwise, print “Not Accepted”.
Examples
Input: S = “aabbb”
Output: Accepted
Explanation: All the ‘a’ come before ‘b’ s.Input: S = “ba”
Output: Not Accepted
Explanation: ‘b’ comes before ‘a’.Input: S = “aaa”
Output: Accepted
Explanation: Note that ‘b’ does not need to occur in SInput: S = “b”
Output: Accepted
Explanation: Note that ‘a’ does not need to occur in S
Approach: The problem can be accepted only when the following cases are met:
- All the characters can be ‘a’.
- All the characters can be ‘b’.
- All the ‘b’ come occur after all the ‘a’.
- There is at least one character in the string.
This can be better visualized with the help of the state transition diagram of the DFA
State Transition Diagram:
State Transition Diagram of the above DFA
Below is the implementation of the above approach:
C++
// C++ Program to implement// the above approach#include <bits/stdc++.h>using namespace std; // Function for state zero Q0int startStateQ0(char s) { int state; if (s == 'a') state = 1; else if (s == 'b') state = 2; else state = -1; return state;} // Function for first state Q1int firstStateQ1(char s) { int state; if (s == 'a') state = 1; else if (s == 'b') state = 2; else state = -1; return state;} // Function for second state Q2int secondStateQ2(char s) { int state; if (s == 'b') state = 2; else if (s == 'a') state = 3; else state = -1; return state;} // Function for third state Q3int thirdStateQ3(char s) { int state = 3; return state;} // Function to check // if the string is accepted or notint isAcceptedString(string String) { int l = String.length(); // dfa tells the number associated // with the present dfa = state int state = 0; for (int i = 0; i < l; i++) { if (state == 0) state = startStateQ0(String[i]); else if (state == 1) state = firstStateQ1(String[i]); else if (state == 2) state = secondStateQ2(String[i]); else if (state == 3) state = thirdStateQ3(String[i]); else return 0; } if (state == 1 || state == 2) return 1; else return 0;}int main() { string String = "ba"; if (isAcceptedString(String)) cout << "ACCEPTED"; else cout << "NOT ACCEPTED";} // This code is contributed by Samim Hossain Mondal. |
Java
// Java Program to implement// the above approachimport java.util.*;public class GFG { // Function for state zero Q0 static int startStateQ0(char s) { int state; if (s == 'a') state = 1; else if (s == 'b') state = 2; else state = -1; return state; } // Function for first state Q1 static int firstStateQ1(char s) { int state; if (s == 'a') state = 1; else if (s == 'b') state = 2; else state = -1; return state; } // Function for second state Q2 static int secondStateQ2(char s) { int state; if (s == 'b') state = 2; else if (s == 'a') state = 3; else state = -1; return state; } // Function for third state Q3 static int thirdStateQ3(char s) { int state = 3; return state; } // Function to check // if the string is accepted or not static int isAcceptedString(String Str) { int l = Str.length(); // dfa tells the number associated // with the present dfa = state int state = 0; for (int i = 0; i < l; i++) { if (state == 0) state = startStateQ0(Str.charAt(i)); else if (state == 1) state = firstStateQ1(Str.charAt(i)); else if (state == 2) state = secondStateQ2(Str.charAt(i)); else if (state == 3) state = thirdStateQ3(Str.charAt(i)); else return 0; } if (state == 1 || state == 2) return 1; else return 0; } public static void main(String args[]) { String Str = "ba"; if (isAcceptedString(Str) != 0) System.out.println("ACCEPTED"); else System.out.println("NOT ACCEPTED"); }}// This code is contributed by Samim Hossain Mondal. |
Python3
# Function for state zero Q0def startStateQ0(s): if (s == 'a'): state = 1 elif (s == 'b'): state = 2 else: state = -1 return state# Function for first state Q1def firstStateQ1(s): if (s == 'a'): state = 1 elif (s == 'b'): state = 2 else: state = -1 return state# Function for second state Q2def secondStateQ2(s): if (s == 'b'): state = 2 elif (s == 'a'): state = 3 else: state = -1 return state# Function for third state Q3def thirdStateQ3(s): state = 3 return state#Function to check #if the string is accepted or notdef isAcceptedString(String): l = len(String) # dfa tells the number associated # with the present dfa = state state = 0 for i in range(l): if (state == 0): state = startStateQ0(String[i]) elif (state == 1): state = firstStateQ1(String[i]) elif (state == 2): state = secondStateQ2(String[i]) elif (state == 3): state = thirdStateQ3(String[i]) else: return 0 if(state == 1 or state == 2): return 1 else: return 0# Driver codeif __name__ == "__main__": String = "ba" if (isAcceptedString(String)): print("ACCEPTED") else: print("NOT ACCEPTED") |
C#
// C# Program to implement// the above approachusing System;class GFG { // Function for state zero Q0 static int startStateQ0(char s) { int state; if (s == 'a') state = 1; else if (s == 'b') state = 2; else state = -1; return state; } // Function for first state Q1 static int firstStateQ1(char s) { int state; if (s == 'a') state = 1; else if (s == 'b') state = 2; else state = -1; return state; } // Function for second state Q2 static int secondStateQ2(char s) { int state; if (s == 'b') state = 2; else if (s == 'a') state = 3; else state = -1; return state; } // Function for third state Q3 static int thirdStateQ3(char s) { int state = 3; return state; } // Function to check // if the string is accepted or not static int isAcceptedString(string Str) { int l = Str.Length; // dfa tells the number associated // with the present dfa = state int state = 0; for (int i = 0; i < l; i++) { if (state == 0) state = startStateQ0(Str[i]); else if (state == 1) state = firstStateQ1(Str[i]); else if (state == 2) state = secondStateQ2(Str[i]); else if (state == 3) state = thirdStateQ3(Str[i]); else return 0; } if (state == 1 || state == 2) return 1; else return 0; } public static void Main() { string Str = "ba"; if (isAcceptedString(Str) != 0) Console.Write("ACCEPTED"); else Console.Write("NOT ACCEPTED"); }}// This code is contributed by ukasp. |
Javascript
<script> // JavaScript Program to implement // the above approach // Function for state zero Q0 function startStateQ0(s) { if (s == 'a') state = 1 else if (s == 'b') state = 2 else state = -1 return state } // Function for first state Q1 function firstStateQ1(s) { if (s == 'a') state = 1 else if (s == 'b') state = 2 else state = -1 return state } // Function for second state Q2 function secondStateQ2(s) { if (s == 'b') state = 2 else if (s == 'a') state = 3 else state = -1 return state } // Function for third state Q3 function thirdStateQ3(s) { state = 3 return state } // Function to check // if the string is accepted or not function isAcceptedString(String) { l = String.length; // dfa tells the number associated // with the present dfa = state state = 0 for (let i = 0; i < l; i++) { if (state == 0) state = startStateQ0(String[i]) else if (state == 1) state = firstStateQ1(String[i]) else if (state == 2) state = secondStateQ2(String[i]) else if (state == 3) state = thirdStateQ3(String[i]) else return 0 } if (state == 1 || state == 2) return 1 else return 0 } let String = "ba" if (isAcceptedString(String)) document.write("ACCEPTED") else document.write("NOT ACCEPTED") // This code is contributed by Potta Lokesh </script> |
Output
NOT ACCEPTED
Time Complexity: O(N) where N is the length of the string
Auxiliary Space: O(1)
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