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.
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 <iostream>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 = "forTHEzambiatek"; 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 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[] = "forTHEzambiatek"; 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[] = "forTHEzambiatek".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 = 0def 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="forTHEzambiatek" # 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 = "forTHEzambiatek".ToCharArray(); if (isAccepted(str) == true) Console.WriteLine("ACCEPTED\n"); else Console.WriteLine("NOT ACCEPTED\n");}}/* This code is contributed by ajit. */ |
PHP
<?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$dfa = 0;// This function is for the// starting state (zeroth) of DFAfunction start($c){ global $dfa; // On receiving 'T' or 't' // goto first state (1) if ($c == 't' || $c == 'T') $dfa = 1;}// This function is for // the first state of DFAfunction state1($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 $dfa = 0;}// This function is for// the second state of DFAfunction state2($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 $dfa = 0;}// This function is for // the third state of DFAfunction state3($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 = "forTHEzambiatek";if (isAccepted($str) == true) echo "ACCEPTED\n";else echo "NOT ACCEPTED\n";// This code is contributed by m_kit?> |
Javascript
<script> // Javascript program to // implement DFS that accepts // all string that do not end // with "THE" // dfa tells the number associated // with the present state let dfa = 0; // This function is for // the starting state (zeroth) of DFA function start(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 function state1(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 function state2(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 function state3(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; } function isAccepted(str) { // store length of string let len = str.length; for (let 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); } let str = "forTHEzambiatek".split(''); if (isAccepted(str) == true) document.write("ACCEPTED"); else document.write("NOT ACCEPTED"); </script> |
Output :
ACCEPTED
Time Complexity: O(n)
Auxiliary Space: O(1) since it is using constant space
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