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Program to construct a DFA which accepts the language L = {aN | N ≥ 1}
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Program to construct a DFA to check if a given integer is unsigned or not

Last Updated : 20 Jul, 2022
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Given a string S that represents an integer, the task is to check if the given string S represents an unsigned integer or not by constructing the DFA. If the given string represents an unsigned integer, then print "Unsigned integer". Otherwise, print "Not an unsigned integer".

Examples:

Input: S = "+4554"
Output: Not an unsigned integer

Input: S = "1729"
Output: unsigned integer

Approach: Below is the transition states of DFA for the given problem:

Follow the steps below to solve the problem:

  • Declare a function to build and connect DFA states as per the given conditions. Below are the representation of the transitions states:
    • 0 represents a digit.
    • 1 represents sign "+/-".
    • 2 represents "." or dot.
    • 3 represents any other character.
    • 4 represents exponent(e/E sign).
  • Initialize a variable, say currentState as 0, that stores the current state in the DFA.
  • Traverse the string S and based on the current state and present character at the current index decide the next state of the DFA.
  • After completing the above steps, if the value of currentState is either 1 or 4 or 8, then print "Unsigned integer". Otherwise, print "Not an unsigned integer".

Below is the implementation of the above approach:

C++ 
// C++ program for the above approach  #include "bits/stdc++.h" using namespace std;  string digits = "0123456789", sign = "+-"; string dot = ".", ex = "eE"; int dfa[11][5];  // Function to construct DFA as per the // given conditions void makeDFA() {     // If at state 0 and a digit has     // occurred then set it to state 1     dfa[0][0] = 1;      // Similarly for all other states     dfa[1][0] = 1;     dfa[1][2] = 3;     dfa[1][3] = 2;     dfa[1][4] = 6;      dfa[3][0] = 4;      dfa[4][0] = 4;     dfa[4][3] = 5;     dfa[4][4] = 6;      dfa[6][0] = 8;     dfa[6][1] = 7;      dfa[7][0] = 8;      dfa[8][0] = 8;     dfa[8][3] = 9; }  // Function to build and connect // the DFA states void buildDFA() {     // Connect all the states to the     // dead state     for (int i = 0; i < 11; i++)         for (int j = 0; j < 5; j++)             dfa[i][j] = 10;      // Function call to make DFA as     // per the given conditions     makeDFA(); }  // Function call to check whether an // integer in the form of string is // unsigned integer or not void checkDFA(string s) {     // Build the DFA     buildDFA();      // Stores the current state     int currentstate = 0;      // Traverse the string     for (int i = 0; i < s.size(); i++) {          if (digits.find(s[i])             != digits.npos)              // If at a certain state a             // digit occurs then change             // the current state according             // to the DFA             currentstate                 = dfa[currentstate][0];          // Or +/- sign         else if (sign.find(s[i])                  != sign.npos)             currentstate                 = dfa[currentstate][1];          // Or decimal occurred         else if (dot.find(s[i])                  != dot.npos)             currentstate                 = dfa[currentstate][2];          // Or any other character         else if (ex.find(s[i])                  != ex.npos)             currentstate                 = dfa[currentstate][4];          // Or e/E or exponent sign         else             currentstate                 = dfa[currentstate][3];     }      // State 1, 4, 8 will give     // the final answer     if (currentstate == 1         || currentstate == 4         || currentstate == 8) {         cout << "Unsigned integer";     }     else {         cout << "Not an unsigned integer";     } }  // Driver Code int main() {     string S = "1729";     checkDFA(S);      return 0; }
Java 
// Java program for the above approach import java.io.*; import java.lang.*; import java.util.*;  class GFG{  static String digits = "0123456789", sign = "+-"; static String dot = ".", ex = "eE"; static int dfa[][] = new int[11][5];  // Function to construct DFA as per the // given conditions static void makeDFA() {          // If at state 0 and a digit has     // occurred then set it to state 1     dfa[0][0] = 1;      // Similarly for all other states     dfa[1][0] = 1;     dfa[1][2] = 3;     dfa[1][3] = 2;     dfa[1][4] = 6;      dfa[3][0] = 4;      dfa[4][0] = 4;     dfa[4][3] = 5;     dfa[4][4] = 6;      dfa[6][0] = 8;     dfa[6][1] = 7;      dfa[7][0] = 8;      dfa[8][0] = 8;     dfa[8][3] = 9; }  // Function to build and connect // the DFA states static void buildDFA() {          // Connect all the states to the     // dead state     for(int i = 0; i < 11; i++)         for(int j = 0; j < 5; j++)             dfa[i][j] = 10;      // Function call to make DFA as     // per the given conditions     makeDFA(); }  // Function call to check whether an // integer in the form of string is // unsigned integer or not static void checkDFA(String s) {          // Build the DFA     buildDFA();      // Stores the current state     int currentstate = 0;      // Traverse the string     for(int i = 0; i < s.length(); i++)     {         if (digits.indexOf(s.charAt(i)) != -1)              // If at a certain state a             // digit occurs then change             // the current state according             // to the DFA             currentstate = dfa[currentstate][0];          // Or +/- sign         else if (sign.indexOf(s.charAt(i)) != -1)             currentstate = dfa[currentstate][1];          // Or decimal occurred         else if (dot.indexOf(s.charAt(i)) != -1)             currentstate = dfa[currentstate][2];          // Or any other character         else if (ex.indexOf(s.charAt(i)) != -1)             currentstate = dfa[currentstate][4];          // Or e/E or exponent sign         else             currentstate = dfa[currentstate][3];     }      // State 1, 4, 8 will give     // the final answer     if (currentstate == 1 || currentstate == 4 ||          currentstate == 8)      {         System.out.println("Unsigned integer");     }     else      {         System.out.println("Not an unsigned integer");     } }  // Driver Code public static void main(String[] args) {     String S = "1729";          checkDFA(S); } }  // This code is contributed by Kingash
Python3 
# Python3 program for the above approach digits,sign = "0123456789", "+-" dot, ex = ".", "eE" dfa = [[0 for i in range(5)] for i in range(11)]  # Function to construct DFA as per the # given conditions def makeDFA():     global dfa      # If at state 0 and a digit has     # occurred then set it to state 1     dfa[0][0] = 1      # Similarly for all other states     dfa[1][0] = 1     dfa[1][2] = 3     dfa[1][3] = 2     dfa[1][4] = 6      dfa[3][0] = 4      dfa[4][0] = 4     dfa[4][3] = 5     dfa[4][4] = 6      dfa[6][0] = 8     dfa[6][1] = 7      dfa[7][0] = 8      dfa[8][0] = 8     dfa[8][3] = 9   # Function to build and connect # the DFA states def buildDFA():     global dfa     # Connect all the states to the     # dead state     for i in range(11):         for j in range(5):             dfa[i][j] = 10      # Function call to make DFA as     # per the given conditions     makeDFA()  # Function call to check whether an # integer in the form of is # unsigned integer or not def checkDFA(s):     # Build the DFA     buildDFA()      # Stores the current state     currentstate = 0      # Traverse the string     for i in range(len(s)):          if (s[i] in digits):              # If at a certain state a             # digit occurs then change             # the current state according             # to the DFA             currentstate = dfa[currentstate][0]          # Or +/- sign         elif (s[i] in sign):             currentstate = dfa[currentstate][1]          # Or decimal occurred         elif (s[i] in dot):             currentstate = dfa[currentstate][2]          # Or any other character         elif (s[i] in ex):             currentstate = dfa[currentstate][4]          # Or e/E or exponent sign         else:             currentstate = dfa[currentstate][3]      # State 1, 4, 8 will give     # the final answer     if (currentstate == 1 or currentstate == 4 or currentstate == 8):         print("Unsigned integer")     else:         print("Not an unsigned integer")  # Driver Code if __name__ == '__main__':     S = "1729"     checkDFA(S)      # This code is contributed by mohit kumar 29.
C# 
// C# program for the above approach using System;  class GFG{  static string digits = "0123456789", sign = "+-"; static string dot = ".", ex = "eE"; static int[,] dfa = new int[11, 5];  // Function to construct DFA as per the // given conditions static void makeDFA() {      // If at state 0 and a digit has     // occurred then set it to state 1     dfa[0, 0] = 1;      // Similarly for all other states     dfa[1, 0] = 1;     dfa[1, 2] = 3;     dfa[1, 3] = 2;     dfa[1, 4] = 6;      dfa[3, 0] = 4;      dfa[4, 0] = 4;     dfa[4, 3] = 5;     dfa[4, 4] = 6;      dfa[6, 0] = 8;     dfa[6, 1] = 7;      dfa[7, 0] = 8;      dfa[8, 0] = 8;     dfa[8, 3] = 9; }  // Function to build and connect // the DFA states static void buildDFA() {      // Connect all the states to the     // dead state     for(int i = 0; i < 11; i++)         for(int j = 0; j < 5; j++)             dfa[i, j] = 10;      // Function call to make DFA as     // per the given conditions     makeDFA(); }  // Function call to check whether an // integer in the form of string is // unsigned integer or not static void checkDFA(string s) {      // Build the DFA     buildDFA();      // Stores the current state     int currentstate = 0;      // Traverse the string     for(int i = 0; i < s.Length; i++)      {         if (digits.IndexOf(s[i]) != -1)              // If at a certain state a             // digit occurs then change             // the current state according             // to the DFA             currentstate = dfa[currentstate, 0];          // Or +/- sign         else if (sign.IndexOf(s[i]) != -1)             currentstate = dfa[currentstate, 1];          // Or decimal occurred         else if (dot.IndexOf(s[i]) != -1)             currentstate = dfa[currentstate, 2];          // Or any other character         else if (ex.IndexOf(s[i]) != -1)             currentstate = dfa[currentstate, 4];          // Or e/E or exponent sign         else             currentstate = dfa[currentstate, 3];     }      // State 1, 4, 8 will give     // the final answer     if (currentstate == 1 || currentstate == 4 ||          currentstate == 8)     {         Console.WriteLine("Unsigned integer");     }     else      {         Console.WriteLine("Not an unsigned integer");     } }  // Driver Code public static void Main(string[] args) {     string S = "1729";      checkDFA(S); } }  // This code is contributed by ukasp
JavaScript 
<script>  // JavaScript program for the above approach  let digits = "0123456789", sign = "+-"; let dot = ".", ex = "eE";  let dfa = new Array(11); for(let i=0;i<11;i++) {     dfa[i]=new Array(5);      }  // Function to construct DFA as per the // given conditions function makeDFA() {     // If at state 0 and a digit has     // occurred then set it to state 1     dfa[0][0] = 1;       // Similarly for all other states     dfa[1][0] = 1;     dfa[1][2] = 3;     dfa[1][3] = 2;     dfa[1][4] = 6;       dfa[3][0] = 4;       dfa[4][0] = 4;     dfa[4][3] = 5;     dfa[4][4] = 6;       dfa[6][0] = 8;     dfa[6][1] = 7;       dfa[7][0] = 8;       dfa[8][0] = 8;     dfa[8][3] = 9; }  // Function to build and connect // the DFA states function buildDFA() {     // Connect all the states to the     // dead state     for(let i = 0; i < 11; i++)         for(let j = 0; j < 5; j++)             dfa[i][j] = 10;       // Function call to make DFA as     // per the given conditions     makeDFA(); }  // Function call to check whether an // integer in the form of string is // unsigned integer or not function  checkDFA(s) {     // Build the DFA     buildDFA();       // Stores the current state     let currentstate = 0;       // Traverse the string     for(let i = 0; i < s.length; i++)     {         if (digits.indexOf(s[i]) != -1)               // If at a certain state a             // digit occurs then change             // the current state according             // to the DFA             currentstate = dfa[currentstate][0];           // Or +/- sign         else if (sign.indexOf(s[i]) != -1)             currentstate = dfa[currentstate][1];           // Or decimal occurred         else if (dot.indexOf(s[i]) != -1)             currentstate = dfa[currentstate][2];           // Or any other character         else if (ex.indexOf(s[i]) != -1)             currentstate = dfa[currentstate][4];           // Or e/E or exponent sign         else             currentstate = dfa[currentstate][3];     }       // State 1, 4, 8 will give     // the final answer     if (currentstate == 1 || currentstate == 4 ||         currentstate == 8)     {         document.write("Unsigned integer<br>");     }     else     {         document.write("Not an unsigned integer");     } } // Driver Code let S = "1729";       checkDFA(S);   // This code is contributed by avanitrachhadiya2155  </script>

Output: 
Unsigned integer

 

Time Complexity: O(N)
Auxiliary Space: O(1),  since no extra space has been taken.


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