DFA for Strings not ending with “THE”

• Difficulty Level : Easy
• Last Updated : 10 Jul, 2021

Problem – Accept Strings that not ending with substring “THE”. Check if a given string is ending with “the” or not. The different forms of “the” which are avoided in the end of the string are:

"THE", "ThE", "THe", "tHE", "thE", "The", "tHe" and "the"

All those strings that are ending with any of the above mentioned forms of “the” are not accepted.

Determinitis finite automata (DFA) of strings that not ending with “THE” –
The initial and starting state in this dfa is Qo Approach used in the program –
In this program, consider the 4 states to be 0, 1, 2 and 3. 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 0, 1 or 2 then our string will be accepted otherwise not.

Input : XYzabCthe
Output : NOT ACCEPTED

Input :  Themaliktth
Output :  ACCEPTED

C++

 // C++ program to implement DFS that accepts// all string that do not end with "THE"#include using namespace std; // dfa tells the number associated// with the present stateint dfa = 0; // This function is for// the starting state (zeroth) of DFAvoid start(char c){         // On receiving 'T' or 't' goto    // first state (1)    if (c == 't' || c == 'T')        dfa = 1;} // This function is for the first state of DFAvoid state1(char c){         // On receiving 'T' or 't' goto    // first state (1)    if (c == 't' || c == 'T')        dfa = 1;     // On receiving 'H' or 'h'    // goto second state (2)    else if (c == 'h' || c == 'H')        dfa = 2;     // Else goto starting state (0)    else        dfa = 0;} // This function is for the second state of DFAvoid state2(char c){         // On receiving 'E' or 'e' goto third state (3)    // else goto starting state (0)    if (c == 'e' || c == 'E')        dfa = 3;    else if (c == 't' || c == 'T')        dfa = 1;      else        dfa = 0;} // This function is for the third state of DFAvoid state3(char c){         // On receiving 'T' or 't' goto first state (1)    // else goto starting state (0)    if (c == 't' || c == 'T')        dfa = 1;    else        dfa = 0;} bool isAccepted(string str){         // Store length of string    int len = str.length();     for(int i = 0; i < len; i++)    {        if (dfa == 0)            start(str[i]);         else if (dfa == 1)            state1(str[i]);         else if (dfa == 2)            state2(str[i]);         else            state3(str[i]);           }    return (dfa != 3);} // Driver codeint main(){    string str = "forTHEgeeks";    if (isAccepted(str) == true)        cout << "ACCEPTED\n";    else        cout << "NOT ACCEPTED\n";             return 0;} // This code is contributed by ShubhamSingh10

C

 // C program to implement DFS that accepts// all string that do not end with "THE"#include #include  // dfa tells the number associated// with the present stateint dfa = 0; // This function is for// the starting state (zeroth) of DFAvoid start(char c){    // On receiving 'T' or 't' goto first state (1)    if (c == 't' || c == 'T')        dfa = 1;} // This function is for the first state of DFAvoid state1(char c){    // On receiving 'T' or 't' goto first state (1)    if (c == 't' || c == 'T')        dfa = 1;     // On receiving 'H' or 'h' goto second state (2)    else if (c == 'h' || c == 'H')        dfa = 2;     // else goto starting state (0)    else        dfa = 0;} // This function is for the second state of DFAvoid state2(char c){    // On receiving 'E' or 'e' goto third state (3)    // else goto starting state (0)    if (c == 'e' || c == 'E')        dfa = 3;    else if (c == 't' || c == 'T')        dfa = 1;      else        dfa = 0;} // This function is for the third state of DFAvoid state3(char c){    // On receiving 'T' or 't' goto first state (1)    // else goto starting state (0)    if (c == 't' || c == 'T')        dfa = 1;    else        dfa = 0;} bool isAccepted(char str[]){    // store length of string    int len = strlen(str);     for (int i=0; i < len; i++) {            if (dfa == 0)                start(str[i]);             else if (dfa == 1)                state1(str[i]);             else if (dfa == 2)                state2(str[i]);             else                state3(str[i]);           }     return (dfa != 3);} // driver codeint main(){    char str[] = "forTHEgeeks";    if (isAccepted(str) == true)        printf("ACCEPTED\n");    else        printf("NOT ACCEPTED\n");    return 0;}

Java

 // Java program to implement DFS that accepts// all string that do not end with "THE"import java.util.*; class GFG{ // dfa tells the number associated// with the present statestatic int dfa = 0; // This function is for// the starting state (zeroth) of DFAstatic void start(char c){    // On receiving 'T' or 't' goto first state (1)    if (c == 't' || c == 'T')        dfa = 1;} // This function is for the first state of DFAstatic void state1(char c){    // On receiving 'T' or 't' goto first state (1)    if (c == 't' || c == 'T')        dfa = 1;     // On receiving 'H' or 'h' goto second state (2)    else if (c == 'h' || c == 'H')        dfa = 2;     // else goto starting state (0)    else        dfa = 0;} // This function is for the second state of DFAstatic void state2(char c){    // On receiving 'E' or 'e' goto third state (3)    // else goto starting state (0)    if (c == 'e' || c == 'E')        dfa = 3;    else        dfa = 0;} // This function is for the third state of DFAstatic void state3(char c){    // On receiving 'T' or 't' goto first state (1)    // else goto starting state (0)    if (c == 't' || c == 'T')        dfa = 1;    else        dfa = 0;} static boolean isAccepted(char str[]){    // store length of string    int len = str.length;     for (int i=0; i < len; i++)    {            if (dfa == 0)                start(str[i]);             else if (dfa == 1)                state1(str[i]);             else if (dfa == 2)                state2(str[i]);             else                state3(str[i]);        }     return (dfa != 3);} // Driver codepublic static void main(String[] args){    char str[] = "forTHEgeeks".toCharArray();    if (isAccepted(str) == true)        System.out.println("ACCEPTED\n");    else        System.out.println("NOT ACCEPTED\n");}} /* This code is contributed by PrinciRaj1992 */

Python3

 # Python3 program to implement DFS that accepts# all stringing that do not end with "THE" # This function is for the starting# state (zeroth) of DFAdef start(c):         # On receiving 'T' or 't' goto    # first state (1)    if (c == 't' or c == 'T'):        dfa=1 # This function is for the first state of DFAdef state1(c):         # On receiving 'T' or 't' goto first state (1)    if (c == 't' or c == 'T'):        dfa = 1     # On receiving 'H' or 'h' goto second state (2)    elif (c == 'h' or c == 'H'):        dfa = 2     # else goto starting state (0)    else:        dfa = 0 # This function is for the second state of DFAdef state2(c):         # On receiving 'E' or 'e' goto third    # state (3) else goto starting state (0)    if (c == 'e' or c == 'E'):        dfa = 3    else:        dfa = 0         # This function is for the third state of DFAdef state3(c):         # On receiving 'T' or 't' goto first    # state (1) else goto starting state (0)    if (c == 't' or c == 'T'):        dfa = 1    else:        dfa = 0 def isAccepted(string):         # store length of stringing    length = len(string)     for i in range(length):        if (dfa == 0):            start(string[i])        elif (dfa == 1):            state1(string[i])        elif (dfa == 2):            state2(string[i])        else:            state3(string[i])            return (dfa != 3) # Driver Codeif __name__ == "__main__" :    string="forTHEgeeks"         # dfa tells the number associated    # with the present state    dfa = 0    if isAccepted(string):        print("ACCEPTED")    else:        print("NOT ACCEPTED") # This code is contributed by SHUBHAMSINGH10

C#

 // C# program to implement DFS that accepts// all string that do not end with "THE"using System; class GFG{     // dfa tells the number associated// with the present statestatic int dfa = 0; // This function is for// the starting state (zeroth) of DFAstatic void start(char c){    // On receiving 'T' or 't' goto first state (1)    if (c == 't' || c == 'T')        dfa = 1;} // This function is for the first state of DFAstatic void state1(char c){    // On receiving 'T' or 't' goto first state (1)    if (c == 't' || c == 'T')        dfa = 1;     // On receiving 'H' or 'h' goto second state (2)    else if (c == 'h' || c == 'H')        dfa = 2;     // else goto starting state (0)    else        dfa = 0;} // This function is for the second state of DFAstatic void state2(char c){    // On receiving 'E' or 'e' goto third state (3)    // else goto starting state (0)    if (c == 'e' || c == 'E')        dfa = 3;    else        dfa = 0;} // This function is for the third state of DFAstatic void state3(char c){    // On receiving 'T' or 't' goto first state (1)    // else goto starting state (0)    if (c == 't' || c == 'T')        dfa = 1;    else        dfa = 0;} static bool isAccepted(char []str){    // store length of string    int len = str.Length;     for (int i=0; i < len; i++)    {            if (dfa == 0)                start(str[i]);             else if (dfa == 1)                state1(str[i]);             else if (dfa == 2)                state2(str[i]);             else                state3(str[i]);    }     return (dfa != 3);} // Driver codestatic public void Main (){    char []str = "forTHEgeeks".ToCharArray();    if (isAccepted(str) == true)        Console.WriteLine("ACCEPTED\n");    else        Console.WriteLine("NOT ACCEPTED\n");}} /* This code is contributed by ajit. */



Javascript


Output :
ACCEPTED

The time complexity of this program is O(n)

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