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Code Algorithm

String matching with finite automata

String matching with finite automata is a pattern matching algorithm that uses a finite automaton (also called a finite state machine) to search for a given pattern within a text. The algorithm works by constructing a finite automaton that recognizes the pattern and then using it to scan the text, character by character, to determine if the pattern occurs in the text.

To build the finite automaton, the algorithm first constructs a set of states that represent the different possible matches of the pattern within the text. Each state corresponds to a particular position in the pattern, and the transitions between the states are determined by the characters in the pattern. Specifically, each transition represents the next possible state that the automaton can reach based on the next character in the text.

Once the finite automaton is constructed, the algorithm scans the text one character at a time, updating the state of the automaton based on the current character. If the automaton reaches an accepting state (which represents a complete match of the pattern), the algorithm reports a match.

The advantage of using a finite automaton for string matching is that the algorithm can recognize patterns in linear time, regardless of the length of the text. This makes it an efficient algorithm for searching large amounts of text for a given pattern.

Here given code implementation process.

// Java program for
// String matching with finite automata
public class Matching
{
	public int findNextState(String text, int m, int state, int x)
	{
		if (state < m && x == text.charAt(state))
		{
			return state + 1;
		}
		int i = 0;
		for (int p = state; p > 0; --p)
		{
			if (text.charAt(p - 1) == x)
			{
				while (i < p - 1 && 
                       text.charAt(i) == text.charAt(state - p + 1 + i))
				{
					i++;
				}
				if (i == p - 1)
				{
					return p;
				}
				i = 0;
			}
		}
		return 0;
	}
	public void construction(String text, int m, int[][] track)
	{
		for (int state = 0; state <= m; ++state)
		{
			// 256 indicate all possible characters
			for (int x = 0; x < 256; ++x)
			{
				track[state][x] = findNextState(text, m, state, x);
			}
		}
	}
	public void findPattern(String text, String pattern)
	{
		// Get the length of given text
		int m = text.length();
		// Get the length of given pattern
		int n = pattern.length();
		// m is a length of given text 
		// and 256 are indicate possible characters
		int[][] track = new int[m + 1][256];
		construction(text, m, track);
		int state = 0;
		for (int i = 0; i < n; i++)
		{
			state = track[state][pattern.charAt(i)];
			if (state == m)
			{
				System.out.println("Pattern found at index " + (i - m + 1));
			}
		}
	}
	public static void main(String[] args)
	{
		Matching task = new Matching();
		// Given text
		String text = "LXYZHEQXYZXYZQQHE11HXYZ1E";
		// Search pattern
		String pattern = "XYZ";
		// Find pattern which occurs in given text
		/*
		    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
		    Pattern = XYZ
		    --------------------------------
		    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
		        ---
		    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
		              ---
		    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
		                 ---
		    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
		                            ---
		*/
		task.findPattern(pattern, text);
	}
}

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20
// Include header file
#include <iostream>
#include <string>

using namespace std;
// C++ program for
// String matching with finite automata
class Matching
{
	public: int findNextState(
      string text, 
      int m, 
      int state, 
      int x)
	{
		if (state < m && x == text[state])
		{
			return state + 1;
		}
		int i = 0;
		for (int p = state; p > 0; --p)
		{
			if (text[p - 1] == x)
			{
				while (i < p - 1 && 
                       text[i] == text[state - p + 1 + i])
				{
					i++;
				}
				if (i == p - 1)
				{
					return p;
				}
				i = 0;
			}
		}
		return 0;
	}
	void construction(string text, 
                      int m, 
                      int track[][256])
	{
		for (int state = 0; state <= m; ++state)
		{
			// 256 indicate all possible characters
			for (int x = 0; x < 256; ++x)
			{
				track[state][x] = 
                  this->findNextState(text, m, state, x);
			}
		}
	}
	void findPattern(string text, string pattern)
	{
		// Get the length of given text
		int m = text.length();
		// Get the length of given pattern
		int n = pattern.length();
		// m is a length of given text
		// and 256 are indicate possible characters
		int track[m + 1][256];
		this->construction(text, m, track);
		int state = 0;
		for (int i = 0; i < n; i++)
		{
			state = track[state][pattern[i]];
			if (state == m)
			{
				cout << "Pattern found at index " 
                     << (i - m + 1) << endl;
			}
		}
	}
};
int main()
{
	Matching *task = new Matching();
	// Given text
	string text = "LXYZHEQXYZXYZQQHE11HXYZ1E";
	// Search pattern
	string pattern = "XYZ";
	// Find pattern which occurs in given text
	/*
	    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	    Pattern = XYZ
	    --------------------------------
	    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	        ---
	    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	              ---
	    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                 ---
	    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                            ---
	*/
	task->findPattern(pattern, text);
	return 0;
}

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20
// Include namespace system
using System;
// Csharp program for
// String matching with finite automata
public class Matching
{
	public int findNextState(String text, 
                             int m, 
							 int state, 
                             int x)
	{
		if (state < m && x == text[state])
		{
			return state + 1;
		}
		int i = 0;
		for (int p = state; p > 0; --p)
		{
			if (text[p - 1] == x)
			{
				while (i < p - 1 && 
                       text[i] == text[state - p + 1 + i])
				{
					i++;
				}
				if (i == p - 1)
				{
					return p;
				}
				i = 0;
			}
		}
		return 0;
	}
	public void construction(String text, 
                              int m, 
                              int[,] track)
	{
		for (int state = 0; state <= m; ++state)
		{
			// 256 indicate all possible characters
			for (int x = 0; x < 256; ++x)
			{
				track[state,x] = 
                  this.findNextState(text, m, state, x);
			}
		}
	}
	public void findPattern(String text, String pattern)
	{
		// Get the length of given text
		int m = text.Length;
		// Get the length of given pattern
		int n = pattern.Length;
		// m is a length of given text
		// and 256 are indicate possible characters
		int[,] track = new int[m + 1,256];
		this.construction(text, m, track);
		int state = 0;
		for (int i = 0; i < n; i++)
		{
			state = track[state,pattern[i]];
			if (state == m)
			{
				Console.WriteLine("Pattern found at index " + 
                                  (i - m + 1));
			}
		}
	}
	public static void Main(String[] args)
	{
		Matching task = new Matching();
		// Given text
		String text = "LXYZHEQXYZXYZQQHE11HXYZ1E";
		// Search pattern
		String pattern = "XYZ";
		// Find pattern which occurs in given text
		/*
		    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
		    Pattern = XYZ
		    --------------------------------
		    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
		        ---
		    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
		              ---
		    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
		                 ---
		    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
		                            ---
		*/
		task.findPattern(pattern, text);
	}
}

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20
package main
import "fmt"
// Go program for
// String matching with finite automata
type Matching struct {}
func getMatching() * Matching {
	var me *Matching = &Matching {}
	return me
}
func(this Matching) findNextState(text string, 
	m int, 
	state int, 
	x int) int {
	if state < m && x == int(text[state]) {
		return state + 1
	}
	var i int = 0
	for p := state ; p > 0 ; p-- {
		if int(text[p - 1]) == x {
			for (i < p - 1 && text[i] == text[state - p + 1 + i]) {
				i++
			}
			if i == p - 1 {
				return p
			}
			i = 0
		}
	}
	return 0
}
func(this Matching) construction(text string, 
	m int, track[][] int) {
	for state := 0 ; state <= m ; state++ {
		// 256 indicate all possible characters
		for x := 0 ; x < 256 ; x++ {
			track[state][x] = this.findNextState(text, m, state, x)
		}
	}
}
func(this Matching) findPattern(text, pattern string) {
	// Get the length of given text
	var m int = len(text)
	// Get the length of given pattern
	var n int = len(pattern)
	// m is a length of given text
	// and 256 are indicate possible characters
	var track = make([][] int, m + 1)
	for i := 0;i < m + 1;i++{
		track[i] = make([] int, 256)
	}
	this.construction(text, m, track)
	var state int = 0
	for i := 0 ; i < n ; i++ {
		state = track[state][pattern[i]]
		if state == m {
			fmt.Println("Pattern found at index ", (i - m + 1))
		}
	}
}
func main() {
	var task * Matching = getMatching()
	// Given text
	var text string = "LXYZHEQXYZXYZQQHE11HXYZ1E"
	// Search pattern
	var pattern string = "XYZ"
	// Find pattern which occurs in given text
	/*
	    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	    Pattern = XYZ
	    --------------------------------
	    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	        ---
	    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	              ---
	    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                 ---
	    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                            ---
	*/
	task.findPattern(pattern, text)
}

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20
<?php
// Php program for
// String matching with finite automata
class Matching
{
	public	function findNextState($text, $m, $state, $x)
	{
		if ($state < $m && $x == ord($text[$state]))
		{
			return $state + 1;
		}
		$i = 0;
		for ($p = $state; $p > 0; --$p)
		{
			if (ord($text[$p - 1]) == $x)
			{
				while ($i < $p - 1 && 
                       $text[$i] == $text[$state - $p + 1 + $i])
				{
					$i++;
				}
				if ($i == $p - 1)
				{
					return $p;
				}
				$i = 0;
			}
		}
		return 0;
	}
	public	function construction($text, $m, &$track)
	{
		for ($state = 0; $state <= $m; ++$state)
		{
			// 256 indicate all possible characters
			for ($x = 0; $x < 256; ++$x)
			{
				$track[$state][$x] = 
                  $this->findNextState($text, $m, $state, $x);
			}
		}
	}
	public	function findPattern($text, $pattern)
	{
		// Get the length of given text
		$m = strlen($text);
		// Get the length of given pattern
		$n = strlen($pattern);
		// m is a length of given text
		// and 256 are indicate possible characters
		$track = array_fill(0, $m + 1, array_fill(0, 256, 0));
		$this->construction($text, $m, $track);
		$state = 0;
		for ($i = 0; $i < $n; $i++)
		{
			$state = $track[$state][ord($pattern[$i])];
			if ($state == $m)
			{
				echo("Pattern found at index ".($i - $m + 1)."\n");
			}
		}
	}
}

function main()
{
	$task = new Matching();
	// Given text
	$text = "LXYZHEQXYZXYZQQHE11HXYZ1E";
	// Search pattern
	$pattern = "XYZ";
	// Find pattern which occurs in given text
	/*
	    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	    Pattern = XYZ
	    --------------------------------
	    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	        ---
	    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	              ---
	    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                 ---
	    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                            ---
	*/
	$task->findPattern($pattern, $text);
}
main();

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20
// Node JS program for
// String matching with finite automata
class Matching
{
	findNextState(text, m, state, x)
	{
		if (state < m && x == text.charAt(state).charCodeAt(0))
		{
			return state + 1;
		}
		var i = 0;
		for (var p = state; p > 0; --p)
		{
			if (text.charAt(p - 1).charCodeAt(0) == x)
			{
				while (i < p - 1 && 
                       text.charAt(i) == text.charAt(state - p + 1 + i))
				{
					i++;
				}
				if (i == p - 1)
				{
					return p;
				}
				i = 0;
			}
		}
		return 0;
	}
	construction(text, m, track)
	{
		for (var state = 0; state <= m; ++state)
		{
			// 256 indicate all possible characters
			for (var x = 0; x < 256; ++x)
			{
				track[state][x] = 
                  this.findNextState(text, m, state, x);
			}
		}
	}
	findPattern(text, pattern)
	{
		// Get the length of given text
		var m = text.length;
		// Get the length of given pattern
		var n = pattern.length;
		// m is a length of given text
		// and 256 are indicate possible characters
		var track = Array(m + 1).fill(0).map(() => 
                                             new Array(256).fill(0));
		this.construction(text, m, track);
		var state = 0;
		for (var i = 0; i < n; i++)
		{
			state = track[state][pattern.charAt(i).charCodeAt(0)];
			if (state == m)
			{
				console.log("Pattern found at index " + 
                            (i - m + 1));
			}
		}
	}
}

function main()
{
	var task = new Matching();
	// Given text
	var text = "LXYZHEQXYZXYZQQHE11HXYZ1E";
	// Search pattern
	var pattern = "XYZ";
	// Find pattern which occurs in given text
	/*
	    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	    Pattern = XYZ
	    --------------------------------
	    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	        ---
	    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	              ---
	    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                 ---
	    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                            ---
	*/
	task.findPattern(pattern, text);
}
main();

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20
#  Python 3 program for
#  String matching with finite automata
class Matching :
	def findNextState(self, text, m, state, x) :
		if (state < m and x == ord(text[state])) :
			return state + 1
		
		i = 0
		p = state
		while (p > 0) :
			if (ord(text[p - 1]) == x) :
				while (i < p - 1 and 
                       text[i] == text[state - p + 1 + i]) :
					i += 1
				
				if (i == p - 1) :
					return p
				
				i = 0
			
			p -= 1
		
		return 0
	
	def construction(self, text, m, track) :
		state = 0
		while (state <= m) :
			x = 0
			#  256 indicate all possible characters
			while (x < 256) :
				track[state][x] = self.findNextState(text, m, state, x)
				x += 1
			
			state += 1
		
	
	def findPattern(self, text, pattern) :
		#  Get the length of given text
		m = len(text)
		#  Get the length of given pattern
		n = len(pattern)
		#  m is a length of given text
		#  and 256 are indicate possible characters
		track = [[0] * (256) for _ in range(m + 1) ]
		self.construction(text, m, track)
		state = 0
		i = 0
		while (i < n) :
			state = track[state][ord(pattern[i])]
			if (state == m) :
				print("Pattern found at index ", (i - m + 1))
			
			i += 1
		
	

def main() :
	task = Matching()
	#  Given text
	text = "LXYZHEQXYZXYZQQHE11HXYZ1E"
	#  Search pattern
	pattern = "XYZ"
	#  Find pattern which occurs in given text
	#    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	#    Pattern = XYZ
	#    --------------------------------
	#    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	#        ---
	#    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	#              ---
	#    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	#                 ---
	#    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	#                            ---
	task.findPattern(pattern, text)

if __name__ == "__main__": main()

Output

Pattern found at index  1
Pattern found at index  7
Pattern found at index  10
Pattern found at index  20
#  Ruby program for
#  String matching with finite automata
class Matching 
	def findNextState(text, m, state, x) 
		if (state < m && x == text[state].ord) 
			return state + 1
		end

		i = 0
		p = state
		while (p > 0) 
			if (text[p - 1].ord == x) 
				while (i < p - 1 && 
                       text[i] == text[state - p + 1 + i]) 
					i += 1
				end

				if (i == p - 1) 
					return p
				end

				i = 0
			end

			p -= 1
		end

		return 0
	end

	def construction(text, m, track) 
		state = 0
		while (state <= m) 
			x = 0
			#  256 indicate all possible characters
			while (x < 256) 
				track[state][x] = self.findNextState(text, m, state, x)
				x += 1
			end

			state += 1
		end

	end

	def findPattern(text, pattern) 
		#  Get the length of given text
		m = text.length
		#  Get the length of given pattern
		n = pattern.length
		#  m is a length of given text
		#  and 256 are indicate possible characters
		track = Array.new(m + 1) {Array.new(256) {0}}
		self.construction(text, m, track)
		state = 0
		i = 0
		while (i < n) 
			state = track[state][pattern[i].ord]
			if (state == m) 
				print("Pattern found at index ", 
                      (i - m + 1), "\n")
			end

			i += 1
		end

	end

end

def main() 
	task = Matching.new()
	#  Given text
	text = "LXYZHEQXYZXYZQQHE11HXYZ1E"
	#  Search pattern
	pattern = "XYZ"
	#  Find pattern which occurs in given text
	#    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	#    Pattern = XYZ
	#    --------------------------------
	#    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	#        ---
	#    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	#              ---
	#    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	#                 ---
	#    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	#                            ---
	task.findPattern(pattern, text)
end

main()

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20

import scala.collection.mutable._;
// Scala program for
// String matching with finite automata
class Matching()
{
	def findNextState(text: String, 
                      m: Int, 
                      state: Int, 
                      x: Int): Int = {
		if (state < m && x == text.charAt(state).toInt)
		{
			return state + 1;
		}
		var i: Int = 0;
		var p: Int = state;
		while (p > 0)
		{
			if (text.charAt(p - 1).toInt == x)
			{
				while (i < p - 1 && 
                       text.charAt(i) == text.charAt(state - p + 1 + i))
				{
					i += 1;
				}
				if (i == p - 1)
				{
					return p;
				}
				i = 0;
			}
			p -= 1;
		}
		return 0;
	}
	def construction(text: String, 
                     m: Int, 
                     track: Array[Array[Int]]): Unit = {
		var state: Int = 0;
		while (state <= m)
		{
			var x: Int = 0;
			// 256 indicate all possible characters
			while (x < 256)
			{
				track(state)(x) = findNextState(text, m, state, x);
				x += 1;
			}
			state += 1;
		}
	}
	def findPattern(text: String, pattern: String): Unit = {
		// Get the length of given text
		var m: Int = text.length();
		// Get the length of given pattern
		var n: Int = pattern.length();
		// m is a length of given text
		// and 256 are indicate possible characters
		var track: Array[Array[Int]] = Array.fill[Int](m + 1, 256)(0);
		construction(text, m, track);
		var state: Int = 0;
		var i: Int = 0;
		while (i < n)
		{
			state = track(state)(pattern.charAt(i));
			if (state == m)
			{
				println("Pattern found at index " + (i - m + 1));
			}
			i += 1;
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Matching = new Matching();
		// Given text
		var text: String = "LXYZHEQXYZXYZQQHE11HXYZ1E";
		// Search pattern
		var pattern: String = "XYZ";
		// Find pattern which occurs in given text
		/*
		    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
		    Pattern = XYZ
		    --------------------------------
		    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
		        ---
		    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
		              ---
		    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
		                 ---
		    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
		                            ---
		*/
		task.findPattern(pattern, text);
	}
}

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20
import Foundation;
// Swift 4 program for
// String matching with finite automata
class Matching
{
	func findNextState(_ text: [Character], 
                        _ m: Int, 
                        _ state: Int, 
                        _ x: Int) -> Int
	{
		if (state < m && 
            x == Int(UnicodeScalar(String(text[state]))!.value))
		{
			return state + 1;
		}
		var i: Int = 0;
		var p: Int = state;
		while (p > 0)
		{
			if (Int(UnicodeScalar(String(text[p - 1]))!.value) == x)
			{
				while (i < p - 1 && text[i] == text[state - p + 1 + i])
				{
					i += 1;
				}
				if (i == p - 1)
				{
					return p;
				}
				i = 0;
			}
			p -= 1;
		}
		return 0;
	}
	func construction(_ text: [Character], 
                      _ m: Int, 
                      _ track: inout[[Int]])
	{
		var state: Int = 0;
		while (state <= m)
		{
			var x: Int = 0;
			// 256 indicate all possible characters
			while (x < 256)
			{
				track[state][x] = self.findNextState(text, m, state, x);
				x += 1;
			}
			state += 1;
		}
	}
	func findPattern(_ t: String, _ p: String)
	{
      	let text = Array(t);
      	let pattern = Array(p);
		// Get the length of given text
		let m: Int = text.count;
		// Get the length of given pattern
		let n: Int = pattern.count;
      
      	
		// m is a length of given text
		// and 256 are indicate possible characters
		var track: [[Int]] = 
          Array(repeating: Array(repeating: 0, count: 256), 
          count: m + 1);
		self.construction(text, m, &track);
		var state: Int = 0;
		var i: Int = 0;
		while (i < n)
		{
			state = track[state][Int(
              UnicodeScalar(String(pattern[i]))!.value)];
			if (state == m)
			{
				print("Pattern found at index ", (i - m + 1));
			}
			i += 1;
		}
	}
}
func main()
{
	let task: Matching = Matching();
	// Given text
	let text: String = "LXYZHEQXYZXYZQQHE11HXYZ1E";
	// Search pattern
	let pattern: String = "XYZ";
	// Find pattern which occurs in given text
	/*
	    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	    Pattern = XYZ
	    --------------------------------
	    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	        ---
	    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	              ---
	    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                 ---
	    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                            ---
	*/
	task.findPattern(pattern, text);
}
main();

Output

Pattern found at index  1
Pattern found at index  7
Pattern found at index  10
Pattern found at index  20
// Kotlin program for
// String matching with finite automata
class Matching
{
	fun findNextState(text: String, 
                       m: Int, 
                       state: Int, 
                       x: Int): Int
	{
		if (state < m && x == text.get(state).toInt())
		{
			return state + 1;
		}
		var i: Int = 0;
		var p: Int = state;
		while (p > 0)
		{
			if (text.get(p - 1).toInt() == x)
			{
				while (i < p - 1 && 
                       text.get(i) == text.get(state - p + 1 + i))
				{
					i += 1;
				}
				if (i == p - 1)
				{
					return p;
				}
				i = 0;
			}
			p -= 1;
		}
		return 0;
	}
	fun construction(text: String, 
                     m: Int, 
                     track: Array < Array < Int >> ): Unit
	{
		var state: Int = 0;
		while (state <= m)
		{
			var x: Int = 0;
			// 256 indicate all possible characters
			while (x < 256)
			{
				track[state][x] = 
                  this.findNextState(text, m, state, x);
				x += 1;
			}
			state += 1;
		}
	}
	fun findPattern(text: String, pattern: String): Unit
	{
		// Get the length of given text
		val m: Int = text.length;
		// Get the length of given pattern
		val n: Int = pattern.length;
		// m is a length of given text
		// and 256 are indicate possible characters
		val track: Array < Array < Int >> = Array(m + 1)
		{
			Array(256)
			{
				0
			}
		};
		this.construction(text, m, track);
		var state: Int = 0;
		var i: Int = 0;
		while (i < n)
		{
			state = track[state][pattern.get(i).toInt()];
			if (state == m)
			{
				println("Pattern found at index " + (i - m + 1));
			}
			i += 1;
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: Matching = Matching();
	// Given text
	val text: String = "LXYZHEQXYZXYZQQHE11HXYZ1E";
	// Search pattern
	val pattern: String = "XYZ";
	// Find pattern which occurs in given text
	/*
	    Text = LXYZHEQXYZXYZQQHE11HXYZ1E
	    Pattern = XYZ
	    --------------------------------
	    ➀  LXYZHEQXYZXYZQQHE11HXYZ1E
	        ---
	    ➁  LXYZHEQXYZXYZQQHE11HXYZ1E 
	              ---
	    ➂  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                 ---
	    ➃  LXYZHEQXYZXYZQQHE11HXYZ1E 
	                            ---
	*/
	task.findPattern(pattern, text);
}

Output

Pattern found at index 1
Pattern found at index 7
Pattern found at index 10
Pattern found at index 20

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