DFA for Strings not ending with "THE" (original) (raw)

Last Updated : 20 Dec, 2022

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.

Deterministic 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 state int dfa = 0;

// This function is for // the starting state (zeroth) of DFA 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 DFA 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 DFA 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 if (c == 't' || c == 'T')
    dfa = 1;
  else
    dfa = 0;

}

// This function is for the third state of DFA 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;

}

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 code int 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 <stdio.h> #include <string.h>

// dfa tells the number associated // with the present state int dfa = 0;

// This function is for // the starting state (zeroth) of DFA 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 DFA 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 DFA 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 if (c == 't' || c == 'T') dfa = 1; else dfa = 0; }

// This function is for the third state of DFA 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; }

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 code int 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 state static int dfa = 0;

// This function is for // the starting state (zeroth) of DFA static 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 DFA static 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 DFA static 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 DFA static 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 code public 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 string that do not end with "THE"

This function is for the starting

state (zeroth) of DFA

def 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 DFA

def 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 DFA

def 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 DFA

def 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 string
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 Code

if 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 state static int dfa = 0;

// This function is for // the starting state (zeroth) of DFA static 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 DFA static 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 DFA static 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 DFA static 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 code static 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. */

PHP

len=strlen(len = strlen(len=strlen(str); for ($i=0; i<i < 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 Code $str = "forTHEgeeks"; if (isAccepted($str) == true) echo "ACCEPTED\n"; else echo "NOT ACCEPTED\n"; // This code is contributed by m_kit ?>

JavaScript

`

Time Complexity: O(n)
Auxiliary Space: O(1) since it is using constant space