Pattern Searching | Set 6 (Efficient Construction of Finite Automata)
Last Updated : 23 Jul, 2025
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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