DFA for Strings not ending with “THE”



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++

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// CPP 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
        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;
}

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PHP

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<?php
// PHP program to implement DFS
// that accepts all string that
// do not end with "THE"
  
// dfa tells the number associated
// with the present state
$dfa = 0;
  
// This function is for the
// starting state (zeroth) of DFA
function start($c)
{
    global $dfa;
    // On receiving 'T' or 't' 
    // goto first state (1)
    if ($c == 't' || $c == 'T')
        $dfa = 1;
}
  
// This function is for 
// the first state of DFA
function state1($c)
{
    global $dfa;
    // On receiving 'T' or 't'
    // goto first state (1)
    if ($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
function state2($c)
{
    global $dfa;
    // On receiving 'E' or 'e' 
    // goto third state (3) else
    // goto starting state (0)
    if ($c == 'e' || $c == 'E')
        $dfa = 3;
    else
        $dfa = 0;
}
  
// This function is for 
// the third state of DFA
function state3($c)
{
    global $dfa;
    // On receiving 'T' or 't' 
    // goto first state (1) else
    // goto starting state (0)
    if ($c == 't' || $c == 'T')
        $dfa = 1;
    else
        $dfa = 0;
}
  
function isAccepted($str)
{
    global $dfa;
    // store length of string
    $len = strlen($str);
  
    for ($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
$str = "forTHEgeeks";
if (isAccepted($str) == true)
    echo "ACCEPTED\n";
else
    echo "NOT ACCEPTED\n";
  
// This code is contributed by m_kit
?>

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Output :

ACCEPTED

The time complexity of this program is O(n)



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Improved By : jit_t