# 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 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: Wordhisappears from 1 to 3 Wordheappears from 4 to 5 Wordsheappears from 3 to 5 Wordhersappears 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 arrayg[][]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 arrayf[]where we store next state for current state. Output : Stores indexes of all words that end at current state. It is represented as 1D arrayo[]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.

- 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

`// 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` |

## Python3

`# 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#

`// 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` |

**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

**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.

**Source:**

http://www.cs.uku.fi/~kilpelai/BSA05/lectures/slides04.pdf

This article is contributed by **Ayush Govil**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above