Pattern Searching | Set 6 (Efficient Construction of Finite Automata)
Last Updated :
09 Sep, 2023
In the previous post, we discussed the Finite Automata-based pattern searching algorithm. The FA (Finite Automata) construction method discussed in the previous post takes O((m^3)*NO_OF_CHARS) time. FA can be constructed in O(m*NO_OF_CHARS) time. In this post, we will discuss the O(m*NO_OF_CHARS) algorithm for FA construction. The idea is similar to LPs (longest prefix suffix) array construction discussed in the KMP algorithm. We use previously filled rows to fill a new row.
The above diagrams represent graphical and tabular representations of pattern ACACAGA.
Algorithm:
1) Fill the first row. All entries in the first row are always 0 except the entry for the pat[0] character. For pat[0] character, we always need to go to state 1.
2) Initialize lps as 0. lps for the first index is always 0.
3) Do following for rows at index i = 1 to M. (M is the length of the pattern)
.....a) Copy the entries from the row at index equal to lps.
.....b) Update the entry for pat[i] character to i+1.
.....c) Update lps "lps = TF[lps][pat[i]]" where TF is the 2D array which is being constructed.
Following is the implementation for the above algorithm.
Implementation
C++
#include <bits/stdc++.h>
using namespace std;
#define NO_OF_CHARS 256
/* This function builds the TF table
which represents Finite Automata for a
given pattern */
void computeTransFun(char* pat, int M, int TF[][NO_OF_CHARS])
{
int i, lps = 0, x;
// Fill entries in first row
for (x = 0; x < NO_OF_CHARS; x++)
TF[0][x] = 0;
TF[0][pat[0]] = 1;
// Fill entries in other rows
for (i = 1; i <= M; i++) {
// Copy values from row at index lps
for (x = 0; x < NO_OF_CHARS; x++)
TF[i][x] = TF[lps][x];
// Update the entry corresponding to this character
TF[i][pat[i]] = i + 1;
// Update lps for next row to be filled
if (i < M)
lps = TF[lps][pat[i]];
}
}
/* Prints all occurrences of pat in txt */
void search(char pat[], char txt[])
{
int M = strlen(pat);
int N = strlen(txt);
int TF[M + 1][NO_OF_CHARS];
computeTransFun(pat, M, TF);
// process text over FA.
int i, j = 0;
for (i = 0; i < N; i++) {
j = TF[j][txt[i]];
if (j == M) {
cout << "pattern found at index " << i - M + 1 << endl;
}
}
}
/* Driver code */
int main()
{
char txt[] = "ACACACACAGAAGA ACACAGAACACAGA GEEKS";
char pat[] = "ACACAGA";
search(pat, txt);
return 0;
}
// This is code is contributed by rathbhupendra
#include <stdio.h>
#include <string.h>
#define NO_OF_CHARS 256
/* This function builds the TF table which represents Finite Automata for a
given pattern */
void computeTransFun(char* pat, int M, int TF[][NO_OF_CHARS])
{
int i, lps = 0, x;
// Fill entries in first row
for (x = 0; x < NO_OF_CHARS; x++)
TF[0][x] = 0;
TF[0][pat[0]] = 1;
// Fill entries in other rows
for (i = 1; i <= M; i++) {
// Copy values from row at index lps
for (x = 0; x < NO_OF_CHARS; x++)
TF[i][x] = TF[lps][x];
// Update the entry corresponding to this character
TF[i][pat[i]] = i + 1;
// Update lps for next row to be filled
if (i < M)
lps = TF[lps][pat[i]];
}
}
/* Prints all occurrences of pat in txt */
void search(char* pat, char* txt)
{
int M = strlen(pat);
int N = strlen(txt);
int TF[M + 1][NO_OF_CHARS];
computeTransFun(pat, M, TF);
// process text over FA.
int i, j = 0;
for (i = 0; i < N; i++) {
j = TF[j][txt[i]];
if (j == M) {
printf("\n pattern found at index %d", i - M + 1);
}
}
}
/* Driver program to test above function */
int main()
{
char* txt = "GEEKS FOR GEEKS";
char* pat = "GEEKS";
search(pat, txt);
getchar();
return 0;
}
/* A Java program to answer queries to check whether
the substrings are palindrome or not efficiently */
class GFG
{
static int NO_OF_CHARS = 256;
/* This function builds the TF table
which represents Finite Automata for a
given pattern */
static void computeTransFun(char[] pat,
int M, int TF[][])
{
int i, lps = 0, x;
// Fill entries in first row
for (x = 0; x < NO_OF_CHARS; x++)
{
TF[0][x] = 0;
}
TF[0][pat[0]] = 1;
// Fill entries in other rows
for (i = 1; i < M; i++)
{
// Copy values from row at index lps
for (x = 0; x < NO_OF_CHARS; x++)
{
TF[i][x] = TF[lps][x];
}
// Update the entry corresponding to this character
TF[i][pat[i]] = i + 1;
// Update lps for next row to be filled
if (i < M)
{
lps = TF[lps][pat[i]];
}
}
}
/* Prints all occurrences of pat in txt */
static void search(char pat[], char txt[])
{
int M = pat.length;
int N = txt.length;
int[][] TF = new int[M + 1][NO_OF_CHARS];
computeTransFun(pat, M, TF);
// process text over FA.
int i, j = 0;
for (i = 0; i < N; i++)
{
j = TF[j][txt[i]];
if (j == M)
{
System.out.println("pattern found at index " +
(i - M + 1));
}
}
}
/* Driver code */
public static void main(String[] args)
{
char txt[] = "GEEKS FOR GEEKS".toCharArray();
char pat[] = "GEEKS".toCharArray();
search(pat, txt);
}
}
// This code is contributed by Princi Singh
""" A Python3 program to answer queries to check whether
the substrings are palindrome or not efficiently """
NO_OF_CHARS = 256
""" This function builds the TF table
which represents Finite Automata for a
given pattern """
def computeTransFun(pat, M, TF):
lps = 0
# Fill entries in first row
for x in range(NO_OF_CHARS):
TF[0][x] = 0
TF[0][ord(pat[0])] = 1
# Fill entries in other rows
for i in range(1, M+1):
# Copy values from row at index lps
for x in range(NO_OF_CHARS):
TF[i][x] = TF[lps][x]
if (i < M):
# Update the entry corresponding to this character
TF[i][ord(pat[i])] = i + 1
# Update lps for next row to be filled
lps = TF[lps][ord(pat[i])]
# Prints all occurrences of pat in txt
def search(pat, txt):
M = len(pat)
N = len(txt)
TF = [[0 for i in range(NO_OF_CHARS)] for j in range(M + 1)]
computeTransFun(pat, M, TF)
# process text over FA.
j = 0
for i in range(N):
j = TF[j][ord(txt[i])]
if (j == M):
print("pattern found at index", i - M + 1)
# Driver code
txt = "ACACACACAGAAGA ACACAGAACACAGA GEEKS"
pat = "ACACAGA"
search(pat, txt)
# This code is contributed by divyeshrabadiya07
/* A C# program to answer queries to check whether
the substrings are palindrome or not efficiently */
using System;
class GFG
{
static int NO_OF_CHARS = 256;
/* This function builds the TF table
which represents Finite Automata for a
given pattern */
static void computeTransFun(char[] pat,
int M, int [,]TF)
{
int i, lps = 0, x;
// Fill entries in first row
for (x = 0; x < NO_OF_CHARS; x++)
{
TF[0,x] = 0;
}
TF[0,pat[0]] = 1;
// Fill entries in other rows
for (i = 1; i < M; i++)
{
// Copy values from row at index lps
for (x = 0; x < NO_OF_CHARS; x++)
{
TF[i,x] = TF[lps,x];
}
// Update the entry corresponding to this character
TF[i,pat[i]] = i + 1;
// Update lps for next row to be filled
if (i < M)
{
lps = TF[lps,pat[i]];
}
}
}
/* Prints all occurrences of pat in txt */
static void search(char []pat, char []txt)
{
int M = pat.Length;
int N = txt.Length;
int[,] TF = new int[M + 1,NO_OF_CHARS];
computeTransFun(pat, M, TF);
// process text over FA.
int i, j = 0;
for (i = 0; i < N; i++)
{
j = TF[j,txt[i]];
if (j == M)
{
Console.WriteLine("pattern found at index " +
(i - M + 1));
}
}
}
/* Driver code */
public static void Main(String[] args)
{
char []txt = "GEEKS FOR GEEKS".ToCharArray();
char []pat = "GEEKS".ToCharArray();
search(pat, txt);
}
}
// This code is contributed by Rajput-Ji
<script>
/* A Javascript program to answer queries to check whether
the substrings are palindrome or not efficiently */
let NO_OF_CHARS = 256;
/* This function builds the TF table
which represents Finite Automata for a
given pattern */
function computeTransFun(pat,M,TF)
{
let i, lps = 0, x;
// Fill entries in first row
for (x = 0; x < NO_OF_CHARS; x++)
{
TF[0][x] = 0;
}
TF[0][pat[0].charCodeAt(0)] = 1;
// Fill entries in other rows
for (i = 1; i < M; i++)
{
// Copy values from row at index lps
for (x = 0; x < NO_OF_CHARS; x++)
{
TF[i][x] = TF[lps][x];
}
// Update the entry corresponding to this character
TF[i][pat[i].charCodeAt(0)] = i + 1;
// Update lps for next row to be filled
if (i < M)
{
lps = TF[lps][pat[i].charCodeAt(0)];
}
}
}
/* Prints all occurrences of pat in txt */
function search(pat,txt)
{
let M = pat.length;
let N = txt.length;
let TF = new Array(M + 1);
for(let i=0;i<M+1;i++)
{
TF[i]=new Array(NO_OF_CHARS);
for(let j=0;j<NO_OF_CHARS;j++)
{
TF[i][j]=0;
}
}
computeTransFun(pat, M, TF);
// process text over FA.
let i, j = 0;
for (i = 0; i < N; i++)
{
j = TF[j][txt[i].charCodeAt(0)];
if (j == M)
{
document.write("pattern found at index " +
(i - M + 1)+"<br>");
}
}
}
/* Driver code */
let txt = "GEEKS FOR GEEKS".split("");
let pat = "GEEKS".split("");
search(pat, txt);
// This code is contributed by avanitrachhadiya2155
</script>
Output:
pattern found at index 0
pattern found at index 10
Time Complexity for FA construction is O(M*NO_OF_CHARS). The code for search is the same as the previous post and the time complexity for it is O(n).
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