Aho-Corasick Algorithm for Pattern Searching
Last Updated : 11 Mar, 2024
Given an input text and an array of k words, arr[], find all occurrences of all words in the input text. Let n be the length of text and m be the total number of characters in all words, i.e. m = length(arr[0]) + length(arr[1]) + ... + length(arr[k-1]). Here k is total numbers of input words.
Example:
Input: text = "ahishers" arr[] = {"he", "she", "hers", "his"} Output: Word his appears from 1 to 3 Word he appears from 4 to 5 Word she appears from 3 to 5 Word hers appears from 4 to 7
If we use a linear time searching algorithm like KMP, then we need to one by one search all words in text[]. This gives us total time complexity as O(n + length(word[0]) + O(n + length(word[1]) + O(n + length(word[2]) + ... O(n + length(word[k-1]). This time complexity can be written as O(n*k + m).
Aho-Corasick Algorithm finds all words in O(n + m + z) time where z is total number of occurrences of words in text. The Aho–Corasick string matching algorithm formed the basis of the original Unix command fgrep.
- Preprocessing : Build an automaton of all words in arr[] The automaton has mainly three functions:
Go To : This function simply follows edges of Trie of all words in arr[]. It is represented as 2D array g[][] where we store next state for current state and character. Failure : This function stores all edges that are followed when current character doesn't have edge in Trie. It is represented as 1D array f[] where we store next state for current state. Output : Stores indexes of all words that end at current state. It is represented as 1D array o[] where we store indexes of all matching words as a bitmap for current state.
- Matching : Traverse the given text over built automaton to find all matching words.
Preprocessing:
- We first Build a Trie (or Keyword Tree) of all words.
Trie- This part fills entries in goto g[][] and output o[].
- Next we extend Trie into an automaton to support linear time matching.
- This part fills entries in failure f[] and output o[].
Go to :
We build Trie. And for all characters which don't have an edge at root, we add an edge back to root.
Failure :
For a state s, we find the longest proper suffix which is a proper prefix of some pattern. This is done using Breadth First Traversal of Trie.
Output :
For a state s, indexes of all words ending at s are stored. These indexes are stored as bitwise map (by doing bitwise OR of values). This is also computing using Breadth First Traversal with Failure.
Below is the implementation of Aho-Corasick Algorithm
C++ // C++ program for implementation of Aho Corasick algorithm // for string matching using namespace std; #include <bits/stdc++.h> // Max number of states in the matching machine. // Should be equal to the sum of the length of all keywords. const int MAXS = 500; // Maximum number of characters in input alphabet const int MAXC = 26; // OUTPUT FUNCTION IS IMPLEMENTED USING out[] // Bit i in this mask is one if the word with index i // appears when the machine enters this state. int out[MAXS]; // FAILURE FUNCTION IS IMPLEMENTED USING f[] int f[MAXS]; // GOTO FUNCTION (OR TRIE) IS IMPLEMENTED USING g[][] int g[MAXS][MAXC]; // Builds the string matching machine. // arr - array of words. The index of each keyword is important: // "out[state] & (1 << i)" is > 0 if we just found word[i] // in the text. // Returns the number of states that the built machine has. // States are numbered 0 up to the return value - 1, inclusive. int buildMatchingMachine(string arr[], int k) { // Initialize all values in output function as 0. memset(out, 0, sizeof out); // Initialize all values in goto function as -1. memset(g, -1, sizeof g); // Initially, we just have the 0 state int states = 1; // Construct values for goto function, i.e., fill g[][] // This is same as building a Trie for arr[] for (int i = 0; i < k; ++i) { const string &word = arr[i]; int currentState = 0; // Insert all characters of current word in arr[] for (int j = 0; j < word.size(); ++j) { int ch = word[j] - 'a'; // Allocate a new node (create a new state) if a // node for ch doesn't exist. if (g[currentState][ch] == -1) g[currentState][ch] = states++; currentState = g[currentState][ch]; } // Add current word in output function out[currentState] |= (1 << i); } // For all characters which don't have an edge from // root (or state 0) in Trie, add a goto edge to state // 0 itself for (int ch = 0; ch < MAXC; ++ch) if (g[0][ch] == -1) g[0][ch] = 0; // Now, let's build the failure function // Initialize values in fail function memset(f, -1, sizeof f); // Failure function is computed in breadth first order // using a queue queue<int> q; // Iterate over every possible input for (int ch = 0; ch < MAXC; ++ch) { // All nodes of depth 1 have failure function value // as 0. For example, in above diagram we move to 0 // from states 1 and 3. if (g[0][ch] != 0) { f[g[0][ch]] = 0; q.push(g[0][ch]); } } // Now queue has states 1 and 3 while (q.size()) { // Remove the front state from queue int state = q.front(); q.pop(); // For the removed state, find failure function for // all those characters for which goto function is // not defined. for (int ch = 0; ch <= MAXC; ++ch) { // If goto function is defined for character 'ch' // and 'state' if (g[state][ch] != -1) { // Find failure state of removed state int failure = f[state]; // Find the deepest node labeled by proper // suffix of string from root to current // state. while (g[failure][ch] == -1) failure = f[failure]; failure = g[failure][ch]; f[g[state][ch]] = failure; // Merge output values out[g[state][ch]] |= out[failure]; // Insert the next level node (of Trie) in Queue q.push(g[state][ch]); } } } return states; } // Returns the next state the machine will transition to using goto // and failure functions. // currentState - The current state of the machine. Must be between // 0 and the number of states - 1, inclusive. // nextInput - The next character that enters into the machine. int findNextState(int currentState, char nextInput) { int answer = currentState; int ch = nextInput - 'a'; // If goto is not defined, use failure function while (g[answer][ch] == -1) answer = f[answer]; return g[answer][ch]; } // This function finds all occurrences of all array words // in text. void searchWords(string arr[], int k, string text) { // Preprocess patterns. // Build machine with goto, failure and output functions buildMatchingMachine(arr, k); // Initialize current state int currentState = 0; // Traverse the text through the built machine to find // all occurrences of words in arr[] for (int i = 0; i < text.size(); ++i) { currentState = findNextState(currentState, text[i]); // If match not found, move to next state if (out[currentState] == 0) continue; // Match found, print all matching words of arr[] // using output function. for (int j = 0; j < k; ++j) { if (out[currentState] & (1 << j)) { cout << "Word " << arr[j] << " appears from " << i - arr[j].size() + 1 << " to " << i << endl; } } } } // Driver program to test above int main() { string arr[] = {"he", "she", "hers", "his"}; string text = "ahishers"; int k = sizeof(arr)/sizeof(arr[0]); searchWords(arr, k, text); return 0; } // Java program for implementation of // Aho Corasick algorithm for String // matching import java.util.*; class GFG{ // Max number of states in the matching // machine. Should be equal to the sum // of the length of all keywords. static int MAXS = 500; // Maximum number of characters // in input alphabet static int MAXC = 26; // OUTPUT FUNCTION IS IMPLEMENTED USING out[] // Bit i in this mask is one if the word with // index i appears when the machine enters // this state. static int []out = new int[MAXS]; // FAILURE FUNCTION IS IMPLEMENTED USING f[] static int []f = new int[MAXS]; // GOTO FUNCTION (OR TRIE) IS // IMPLEMENTED USING g[][] static int [][]g = new int[MAXS][MAXC]; // Builds the String matching machine. // arr - array of words. The index of each keyword is important: // "out[state] & (1 << i)" is > 0 if we just found word[i] // in the text. // Returns the number of states that the built machine has. // States are numbered 0 up to the return value - 1, inclusive. static int buildMatchingMachine(String arr[], int k) { // Initialize all values in output function as 0. Arrays.fill(out, 0); // Initialize all values in goto function as -1. for(int i = 0; i < MAXS; i++) Arrays.fill(g[i], -1); // Initially, we just have the 0 state int states = 1; // Convalues for goto function, i.e., fill g[][] // This is same as building a Trie for arr[] for(int i = 0; i < k; ++i) { String word = arr[i]; int currentState = 0; // Insert all characters of current // word in arr[] for(int j = 0; j < word.length(); ++j) { int ch = word.charAt(j) - 'a'; // Allocate a new node (create a new state) // if a node for ch doesn't exist. if (g[currentState][ch] == -1) g[currentState][ch] = states++; currentState = g[currentState][ch]; } // Add current word in output function out[currentState] |= (1 << i); } // For all characters which don't have // an edge from root (or state 0) in Trie, // add a goto edge to state 0 itself for(int ch = 0; ch < MAXC; ++ch) if (g[0][ch] == -1) g[0][ch] = 0; // Now, let's build the failure function // Initialize values in fail function Arrays.fill(f, -1); // Failure function is computed in // breadth first order // using a queue Queue<Integer> q = new LinkedList<>(); // Iterate over every possible input for(int ch = 0; ch < MAXC; ++ch) { // All nodes of depth 1 have failure // function value as 0. For example, // in above diagram we move to 0 // from states 1 and 3. if (g[0][ch] != 0) { f[g[0][ch]] = 0; q.add(g[0][ch]); } } // Now queue has states 1 and 3 while (!q.isEmpty()) { // Remove the front state from queue int state = q.peek(); q.remove(); // For the removed state, find failure // function for all those characters // for which goto function is // not defined. for(int ch = 0; ch < MAXC; ++ch) { // If goto function is defined for // character 'ch' and 'state' if (g[state][ch] != -1) { // Find failure state of removed state int failure = f[state]; // Find the deepest node labeled by proper // suffix of String from root to current // state. while (g[failure][ch] == -1) failure = f[failure]; failure = g[failure][ch]; f[g[state][ch]] = failure; // Merge output values out[g[state][ch]] |= out[failure]; // Insert the next level node // (of Trie) in Queue q.add(g[state][ch]); } } } return states; } // Returns the next state the machine will transition to using goto // and failure functions. // currentState - The current state of the machine. Must be between // 0 and the number of states - 1, inclusive. // nextInput - The next character that enters into the machine. static int findNextState(int currentState, char nextInput) { int answer = currentState; int ch = nextInput - 'a'; // If goto is not defined, use // failure function while (g[answer][ch] == -1) answer = f[answer]; return g[answer][ch]; } // This function finds all occurrences of // all array words in text. static void searchWords(String arr[], int k, String text) { // Preprocess patterns. // Build machine with goto, failure // and output functions buildMatchingMachine(arr, k); // Initialize current state int currentState = 0; // Traverse the text through the // built machine to find all // occurrences of words in arr[] for(int i = 0; i < text.length(); ++i) { currentState = findNextState(currentState, text.charAt(i)); // If match not found, move to next state if (out[currentState] == 0) continue; // Match found, print all matching // words of arr[] // using output function. for(int j = 0; j < k; ++j) { if ((out[currentState] & (1 << j)) > 0) { System.out.print("Word " + arr[j] + " appears from " + (i - arr[j].length() + 1) + " to " + i + "\n"); } } } } // Driver code public static void main(String[] args) { String arr[] = { "he", "she", "hers", "his" }; String text = "ahishers"; int k = arr.length; searchWords(arr, k, text); } } // This code is contributed by Princi Singh # Python program for implementation of # Aho-Corasick algorithm for string matching # defaultdict is used only for storing the final output # We will return a dictionary where key is the matched word # and value is the list of indexes of matched word from collections import defaultdict # For simplicity, Arrays and Queues have been implemented using lists. # If you want to improve performance try using them instead class AhoCorasick: def __init__(self, words): # Max number of states in the matching machine. # Should be equal to the sum of the length of all keywords. self.max_states = sum([len(word) for word in words]) # Maximum number of characters. # Currently supports only alphabets [a,z] self.max_characters = 26 # OUTPUT FUNCTION IS IMPLEMENTED USING out [] # Bit i in this mask is 1 if the word with # index i appears when the machine enters this state. # Lets say, a state outputs two words "he" and "she" and # in our provided words list, he has index 0 and she has index 3 # so value of out[state] for this state will be 1001 # It has been initialized to all 0. # We have taken one extra state for the root. self.out = [0]*(self.max_states+1) # FAILURE FUNCTION IS IMPLEMENTED USING fail [] # There is one value for each state + 1 for the root # It has been initialized to all -1 # This will contain the fail state value for each state self.fail = [-1]*(self.max_states+1) # GOTO FUNCTION (OR TRIE) IS IMPLEMENTED USING goto [[]] # Number of rows = max_states + 1 # Number of columns = max_characters i.e 26 in our case # It has been initialized to all -1. self.goto = [[-1]*self.max_characters for _ in range(self.max_states+1)] # Convert all words to lowercase # so that our search is case insensitive for i in range(len(words)): words[i] = words[i].lower() # All the words in dictionary which will be used to create Trie # The index of each keyword is important: # "out[state] & (1 << i)" is > 0 if we just found word[i] # in the text. self.words = words # Once the Trie has been built, it will contain the number # of nodes in Trie which is total number of states required <= max_states self.states_count = self.__build_matching_machine() # Builds the String matching machine. # Returns the number of states that the built machine has. # States are numbered 0 up to the return value - 1, inclusive. def __build_matching_machine(self): k = len(self.words) # Initially, we just have the 0 state states = 1 # Convalues for goto function, i.e., fill goto # This is same as building a Trie for words[] for i in range(k): word = self.words[i] current_state = 0 # Process all the characters of the current word for character in word: ch = ord(character) - 97 # Ascii value of 'a' = 97 # Allocate a new node (create a new state) # if a node for ch doesn't exist. if self.goto[current_state][ch] == -1: self.goto[current_state][ch] = states states += 1 current_state = self.goto[current_state][ch] # Add current word in output function self.out[current_state] |= (1<<i) # For all characters which don't have # an edge from root (or state 0) in Trie, # add a goto edge to state 0 itself for ch in range(self.max_characters): if self.goto[0][ch] == -1: self.goto[0][ch] = 0 # Failure function is computed in # breadth first order using a queue queue = [] # Iterate over every possible input for ch in range(self.max_characters): # All nodes of depth 1 have failure # function value as 0. For example, # in above diagram we move to 0 # from states 1 and 3. if self.goto[0][ch] != 0: self.fail[self.goto[0][ch]] = 0 queue.append(self.goto[0][ch]) # Now queue has states 1 and 3 while queue: # Remove the front state from queue state = queue.pop(0) # For the removed state, find failure # function for all those characters # for which goto function is not defined. for ch in range(self.max_characters): # If goto function is defined for # character 'ch' and 'state' if self.goto[state][ch] != -1: # Find failure state of removed state failure = self.fail[state] # Find the deepest node labeled by proper # suffix of String from root to current state. while self.goto[failure][ch] == -1: failure = self.fail[failure] failure = self.goto[failure][ch] self.fail[self.goto[state][ch]] = failure # Merge output values self.out[self.goto[state][ch]] |= self.out[failure] # Insert the next level node (of Trie) in Queue queue.append(self.goto[state][ch]) return states # Returns the next state the machine will transition to using goto # and failure functions. # current_state - The current state of the machine. Must be between # 0 and the number of states - 1, inclusive. # next_input - The next character that enters into the machine. def __find_next_state(self, current_state, next_input): answer = current_state ch = ord(next_input) - 97 # Ascii value of 'a' is 97 # If goto is not defined, use # failure function while self.goto[answer][ch] == -1: answer = self.fail[answer] return self.goto[answer][ch] # This function finds all occurrences of all words in text. def search_words(self, text): # Convert the text to lowercase to make search case insensitive text = text.lower() # Initialize current_state to 0 current_state = 0 # A dictionary to store the result. # Key here is the found word # Value is a list of all occurrences start index result = defaultdict(list) # Traverse the text through the built machine # to find all occurrences of words for i in range(len(text)): current_state = self.__find_next_state(current_state, text[i]) # If match not found, move to next state if self.out[current_state] == 0: continue # Match found, store the word in result dictionary for j in range(len(self.words)): if (self.out[current_state] & (1<<j)) > 0: word = self.words[j] # Start index of word is (i-len(word)+1) result[word].append(i-len(word)+1) # Return the final result dictionary return result # Driver code if __name__ == "__main__": words = ["he", "she", "hers", "his"] text = "ahishers" # Create an Object to initialize the Trie aho_chorasick = AhoCorasick(words) # Get the result result = aho_chorasick.search_words(text) # Print the result for word in result: for i in result[word]: print("Word", word, "appears from", i, "to", i+len(word)-1) # This code is contributed by Md Azharuddin // C# program for implementation of // Aho Corasick algorithm for String // matching using System; using System.Collections.Generic; class GFG{ // Max number of states in the matching // machine. Should be equal to the sum // of the length of all keywords. static int MAXS = 500; // Maximum number of characters // in input alphabet static int MAXC = 26; // OUTPUT FUNCTION IS IMPLEMENTED USING out[] // Bit i in this mask is one if the word with // index i appears when the machine enters // this state. static int[] out = new int[MAXS]; // FAILURE FUNCTION IS IMPLEMENTED USING f[] static int[] f = new int[MAXS]; // GOTO FUNCTION (OR TRIE) IS // IMPLEMENTED USING g[,] static int[,] g = new int[MAXS, MAXC]; // Builds the String matching machine. // arr - array of words. The index of each keyword is // important: // "out[state] & (1 << i)" is > 0 if we just // found word[i] in the text. // Returns the number of states that the built machine // has. States are numbered 0 up to the return value - // 1, inclusive. static int buildMatchingMachine(String[] arr, int k) { // Initialize all values in output function as 0. for(int i = 0; i < outt.Length; i++) outt[i] = 0; // Initialize all values in goto function as -1. for(int i = 0; i < MAXS; i++) for(int j = 0; j < MAXC; j++) g[i, j] = -1; // Initially, we just have the 0 state int states = 1; // Convalues for goto function, i.e., fill g[,] // This is same as building a Trie for []arr for(int i = 0; i < k; ++i) { String word = arr[i]; int currentState = 0; // Insert all characters of current // word in []arr for(int j = 0; j < word.Length; ++j) { int ch = word[j] - 'a'; // Allocate a new node (create a new state) // if a node for ch doesn't exist. if (g[currentState, ch] == -1) g[currentState, ch] = states++; currentState = g[currentState, ch]; } // Add current word in output function outt[currentState] |= (1 << i); } // For all characters which don't have // an edge from root (or state 0) in Trie, // add a goto edge to state 0 itself for(int ch = 0; ch < MAXC; ++ch) if (g[0, ch] == -1) g[0, ch] = 0; // Now, let's build the failure function // Initialize values in fail function for(int i = 0; i < MAXC; i++) f[i] = 0; // Failure function is computed in // breadth first order // using a queue Queue<int> q = new Queue<int>(); // Iterate over every possible input for(int ch = 0; ch < MAXC; ++ch) { // All nodes of depth 1 have failure // function value as 0. For example, // in above diagram we move to 0 // from states 1 and 3. if (g[0, ch] != 0) { f[g[0, ch]] = 0; q.Enqueue(g[0, ch]); } } // Now queue has states 1 and 3 while (q.Count != 0) { // Remove the front state from queue int state = q.Peek(); q.Dequeue(); // For the removed state, find failure // function for all those characters // for which goto function is // not defined. for(int ch = 0; ch < MAXC; ++ch) { // If goto function is defined for // character 'ch' and 'state' if (g[state, ch] != -1) { // Find failure state of removed state int failure = f[state]; // Find the deepest node labeled by // proper suffix of String from root to // current state. while (g[failure, ch] == -1) failure = f[failure]; failure = g[failure, ch]; f[g[state, ch]] = failure; // Merge output values outt[g[state, ch]] |= outt[failure]; // Insert the next level node // (of Trie) in Queue q.Enqueue(g[state, ch]); } } } return states; } // Returns the next state the machine will transition to // using goto and failure functions. currentState - The // current state of the machine. Must be between // 0 and the number of states - 1, // inclusive. // nextInput - The next character that enters into the // machine. static int findNextState(int currentState, char nextInput) { int answer = currentState; int ch = nextInput - 'a'; // If goto is not defined, use // failure function while (g[answer, ch] == -1) answer = f[answer]; return g[answer, ch]; } // This function finds all occurrences of // all array words in text. static void searchWords(String[] arr, int k, String text) { // Preprocess patterns. // Build machine with goto, failure // and output functions buildMatchingMachine(arr, k); // Initialize current state int currentState = 0; // Traverse the text through the // built machine to find all // occurrences of words in []arr for(int i = 0; i < text.Length; ++i) { currentState = findNextState(currentState, text[i]); // If match not found, move to next state if (outt[currentState] == 0) continue; // Match found, print all matching // words of []arr // using output function. for(int j = 0; j < k; ++j) { if ((outt[currentState] & (1 << j)) > 0) { Console.Write("Word " + arr[j] + " appears from " + (i - arr[j].Length + 1) + " to " + i + "\n"); } } } } // Driver code public static void Main(String[] args) { String[] arr = { "he", "she", "hers", "his" }; String text = "ahishers"; int k = arr.Length; searchWords(arr, k, text); } } // This code is contributed by Amit Katiyar // Max number of states in the matching machine. // Should be equal to the sum of the length of all keywords. const MAXS = 500; // Maximum number of characters in input alphabet const MAXC = 26; // OUTPUT FUNCTION IS IMPLEMENTED USING out[] // Bit i in this mask is one if the word with index i // appears when the machine enters this state. const out = new Array(MAXS).fill(0); // FAILURE FUNCTION IS IMPLEMENTED USING f[] const f = new Array(MAXS).fill(-1); // GOTO FUNCTION (OR TRIE) IS IMPLEMENTED USING g[][] let g = new Array(MAXS).fill(null).map(() => new Array(MAXC).fill(-1)); // Builds the string matching machine. // arr - array of words. The index of each keyword is important: // "out[state] & (1 << i)" is > 0 if we just found word[i] // in the text. // Returns the number of states that the built machine has. // States are numbered 0 up to the return value - 1, inclusive. function buildMatchingMachine(arr, k) { // Initialize all values in output function as 0. out.fill(0); // Initialize all values in goto function as -1. g = new Array(MAXS).fill(null).map(() => new Array(MAXC).fill(-1)); // Initially, we just have the 0 state let states = 1; // Construct values for goto function, i.e., fill g[][] // This is same as building a Trie for arr[] for (let i = 0; i < k; ++i) { const word = arr[i]; let currentState = 0; // Insert all characters of current word in arr[] for (let j = 0; j < word.length; ++j) { let ch = word.charCodeAt(j) - 'a'.charCodeAt(0); // Allocate a new node (create a new state) if a // node for ch doesn't exist. if (g[currentState][ch] == -1) g[currentState][ch] = states++; currentState = g[currentState][ch]; } // Add current word in output function out[currentState] |= (1 << i); } // For all characters which don't have an edge from // root (or state 0) in Trie, add a goto edge to state // 0 itself for (let ch = 0; ch < MAXC; ++ch) if (g[0][ch] == -1) g[0][ch] = 0; // Now, let's build the failure function // Initialize values in fail function f.fill(-1); // Failure function is computed in breadth first order // using a queue let q = []; // Iterate over every possible input for (let ch = 0; ch < MAXC; ++ch) { // All nodes of depth 1 have failure function value // as 0. For example, in above diagram we move to 0 // from states 1 and 3. if (g[0][ch] != 0) { f[g[0][ch]] = 0; q.push(g[0][ch]); } } // Now queue has states 1 and 3 while (q.length) { // Remove the front state from queue let state = q.shift(); // For the removed state, find failure function for // all those characters for which goto function is // not defined. for (let ch = 0; ch < 26; ++ch) { // If goto function is defined for character 'ch' // and 'state' if (g[state][ch] != -1) { // Find failure state of removed state let failure = f[state]; // Find the deepest node labeled by proper // suffix of string from root to current // state. while (g[failure][ch] == -1) failure = f[failure]; failure = g[failure][ch]; f[g[state][ch]] = failure; // Merge output values out[g[state][ch]] |= out[failure]; // Insert the next level node (of Trie) in Queue q.push(g[state][ch]); } } } return states; } // Returns the next state the machine will transition to using goto // and failure functions. // currentState - The current state of the machine. Must be between // 0 and the number of states - 1, inclusive. // nextInput - The next character that enters into the machine. function findNextState(currentState, nextInput) { let answer = currentState; const ch = nextInput.charCodeAt(0) - 'a'.charCodeAt(0); // If goto is not defined, use failure function while (g[answer][ch] === -1) answer = f[answer]; return g[answer][ch]; } // This function finds all occurrences of all array words // in text. function searchWords(arr, k, text) { // Preprocess patterns. // Build machine with goto, failure and output functions buildMatchingMachine(arr, k); // Initialize current state let currentState = 0; // Traverse the text through the built machine to find // all occurrences of words in arr[] for (let i = 0; i < text.length; ++i) { currentState = findNextState(currentState, text[i]); // If match not found, move to next state if (out[currentState] === 0) continue; // Match found, print all matching words of arr[] // using output function. for (let j = 0; j < k; ++j) { if (out[currentState] & (1 << j)) { console.log("Word " + arr[j] + " appears from " + (i - arr[j].length + 1) + " to " + i); } } } } // Driver program to test above const arr = ["he", "she", "hers", "his"]; const text = "ahishers"; const k = arr.length; searchWords(arr, k, text); OutputWord his appears from 1 to 3 Word he appears from 4 to 5 Word she appears from 3 to 5 Word hers appears from 4 to 7
Time Complexity: O(n + l + z), where ‘n’ is the length of the text, ‘l' is the length of keywords, and ‘z’ is the number of matches.
Auxiliary Space: O(l * q), where ‘q’ is the length of the alphabet since that is the maximum number of children a node can have.
Applications:
? Detecting plagiarism
? Text mining
? Bioinformatics
? Intrusion Detection
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Introduction to Pattern Searching - Data Structure and Algorithm Tutorial Pattern searching is an algorithm that involves searching for patterns such as strings, words, images, etc. We use certain algorithms to do the search process. The complexity of pattern searching varies from algorithm to algorithm. They are very useful when performing a search in a database. The Pat
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Naive algorithm for Pattern Searching Given text string with length n and a pattern with length m, the task is to prints all occurrences of pattern in text. Note: You may assume that n > m. Examples:Â Input: Â text = "THIS IS A TEST TEXT", pattern = "TEST"Output: Pattern found at index 10 Input: Â text = Â "AABAACAADAABAABA", pattern =
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Rabin-Karp Algorithm for Pattern Searching Given two strings text and pattern string, your task is to find all starting positions where the pattern appears as a substring within the text. The strings will only contain lowercase English alphabets.While reporting the results, use 1-based indexing (i.e., the first character of the text is at po
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KMP Algorithm for Pattern Searching Given two strings txt and pat, the task is to return all indices of occurrences of pat within txt. Examples:Input: txt = "abcab", pat = "ab"Output: [0, 3]Explanation: The string "ab" occurs twice in txt, first occurrence starts from index 0 and second from index 3.Input: txt= "aabaacaadaabaaba", pat
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Z algorithm (Linear time pattern searching Algorithm) This algorithm efficiently locates all instances of a specific pattern within a text in linear time. If the length of the text is "n" and the length of the pattern is "m," then the total time taken is O(m + n), with a linear auxiliary space. It is worth noting that the time and auxiliary space of th
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Finite Automata algorithm for Pattern Searching Given a text txt[0..n-1] and a pattern pat[0..m-1], write a function search(char pat[], char txt[]) that prints all occurrences of pat[] in txt[]. You may assume that n > m.Examples: Input: txt[] = "THIS IS A TEST TEXT" pat[] = "TEST" Output: Pattern found at index 10 Input: txt[] = "AABAACAADAAB
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Boyer Moore Algorithm for Pattern Searching Pattern searching is an important problem in computer science. When we do search for a string in a notepad/word file, browser, or database, pattern searching algorithms are used to show the search results. A typical problem statement would be-Â " Given a text txt[0..n-1] and a pattern pat[0..m-1] whe
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Aho-Corasick Algorithm for Pattern Searching Given an input text and an array of k words, arr[], find all occurrences of all words in the input text. Let n be the length of text and m be the total number of characters in all words, i.e. m = length(arr[0]) + length(arr[1]) + ... + length(arr[k-1]). Here k is total numbers of input words. Exampl
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ÂÂkasai’s Algorithm for Construction of LCP array from Suffix Array Background Suffix Array : A suffix array is a sorted array of all suffixes of a given string. Let the given string be "banana". 0 banana 5 a1 anana Sort the Suffixes 3 ana2 nana ----------------> 1 anana 3 ana alphabetically 0 banana 4 na 4 na 5 a 2 nanaThe suffix array for "banana" :suffix[] = {
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