NFA which accepts set of strings over an alphabet {0, 1, 2} such that the final digit has appeared before

Prerequisite – Introduction of Finite Automata
C++ Program to construct an NFA which accepts the set of strings over an alphabet {0, 1, 2} such that the final digit has appeared before.

Examples :

Input : 01101 
Output : Accepted

Input : 012
Output : Not Accepted

Input : 2
Output : Not Accepted

Input : 0122
Output : Accepted

Explanation:
In the first example, 01101, the last digit ‘1’ occurred at letter number 2 and 3 of the string. Hence it is accepted. In second example, 012, the occurrence of ‘2’ is only at the last place. Hence it is rejected. Similarly with the third example, 2 is rejected. In the last example, the last digit ‘2’ occured befor end of the string hence it is Accepted.

Approach:

Construct a start state.
Construct 3 states for input of 0, 1 and 2.
Repeat the loops in all state for all the inputs.
Connect all the state with a final state.

NFA State Transaction Diagram:

Implementation :

#include <bits/stdc++.h> 
using namespace std; 
  
// function of state one or starting state 
void q1(string s, int pos, int len);  
  
// function of state two 
void q2(string s, int pos, int len); 
  
// function of state three  
void q3(string s, int pos, int len);  
  
// function of state four 
void q4(string s, int pos, int len);  
  
// function of state five 
void q5(string s, int pos, int len);  
  
// See diagram for help 
  
vector<string> states; 
int accepted = 0; 
  
// Uncomment this function and the function calls to see 
// the path of string from the start state to end state 
/* 
void printVector() 
{ 
    for (auto i = states.begin(); i != states.end(); i++) 
        cout << *i << " "; 
    cout << endl; 
} 
*/
void q5(string s, int pos, int len) 
{ 
    states.push_back("Q5->"); 
    if (pos == len) { 
        // printVector(); 
        accepted = 1; 
    } 
    else { 
        states.push_back("Dead"); 
        // printVector(); 
        states.pop_back(); 
    } 
    states.pop_back(); 
    return; 
} 
  
void q4(string s, int pos, int len) 
{ 
    states.push_back("Q4->"); 
    if (pos == len) { 
        // printVector(); 
        states.pop_back(); 
        return; 
    } 
    if (s[pos] == '2') 
        q5(s, pos + 1, len); 
    q4(s, pos + 1, len); 
    states.pop_back(); 
    return; 
} 
  
void q3(string s, int pos, int len) 
{ 
    states.push_back("Q3->"); 
    if (pos == len) { 
        // printVector(); 
        states.pop_back(); 
        return; 
    } 
    if (s[pos] == '1') 
        q5(s, pos + 1, len); 
    q3(s, pos + 1, len); 
    states.pop_back(); 
    return; 
} 
  
void q2(string s, int pos, int len) 
{ 
    states.push_back("Q2->"); 
    if (pos == len) { 
        // printVector(); 
        states.pop_back(); 
        return; 
    } 
    if (s[pos] == '0') 
        q5(s, pos + 1, len); 
    q2(s, pos + 1, len); 
    states.pop_back(); 
    return; 
} 
  
void q1(string s, int pos, int len) 
{ 
    states.push_back("Q1->"); 
    if (pos == len) { 
        // printVector(); 
        states.pop_back(); 
        return; 
    } 
    if (s[pos] == '0') 
        q2(s, pos + 1, len); 
    else if (s[pos] == '1') 
        q3(s, pos + 1, len); 
    else if (s[pos] == '2') 
        q4(s, pos + 1, len); 
  
    q1(s, pos + 1, len); 
    states.pop_back(); 
    return; 
} 
  
int main() 
{ 
    string s; 
    // cin >> s; 
    s = "01101"; 
  
    int pos = 0; 
    q1(s, pos, s.length()); 
  
    if (accepted) 
        cout << "Accepted" << endl; 
    else
        cout << "Not Accepted" << endl; 
    return 0; 
} 

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