Program to construct a DFA to check if a given integer is unsigned or not

Last Updated : 20 Jul, 2022

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.

Suggest improvement

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Program to construct a DFA to check if a given integer is unsigned or not

C++

Java

Python3

C#

Javascript

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