Pattern Searching using a Trie of all Suffixes

Problem Statement: 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.
As discussed in the previous post, we discussed that there are two ways efficiently solve the above problem.
1) Preprocess Pattern: KMP Algorithm, Rabin Karp Algorithm, Finite Automata, Boyer Moore Algorithm.
2) Preprocess Text: Suffix Tree

The best possible time complexity achieved by first (preprocessing pattern) is O(n) and by second (preprocessing text) is O(m) where m and n are lengths of pattern and text respectively.
Note that the second way does the searching only in O(m) time and it is preferred when text doesn’t change very frequently and there are many search queries. We have discussed Suffix Tree (A compressed Trie of all suffixes of Text) .
Implementation of Suffix Tree may be time consuming for problems to be coded in a technical interview or programming contexts. In this post simple implementation of a Standard Trie of all Suffixes is discussed. The implementation is close to suffix tree, the only thing is, it’s a simple Trie instead of compressed Trie.

As discussed in Suffix Tree post, the idea is, every pattern that is present in text (or we can say every substring of text) must be a prefix of one of all possible suffixes. So if we build a Trie of all suffixes, we can find the pattern in O(m) time where m is pattern length.

Building a Trie of Suffixes
1) Generate all suffixes of given text. 
2) Consider all suffixes as individual words and build a trie.
Let us consider an example text “banana\0” where ‘\0’ is string termination character. Following are all suffixes of “banana\0” 

banana\0
anana\0
nana\0
ana\0
na\0
a\0
\0

If we consider all of the above suffixes as individual words and build a Trie, we get following. 

How to search a pattern in the built Trie?
Following are steps to search a pattern in the built Trie. 
1) Starting from the first character of the pattern and root of the Trie, do following for every character. 
…..a) For the current character of pattern, if there is an edge from the current node, follow the edge. 
…..b) If there is no edge, print “pattern doesn’t exist in text” and return. 
2) If all characters of pattern have been processed, i.e., there is a path from root for characters of the given pattern, then print all indexes where pattern is present. To store indexes, we use a list with every node that stores indexes of suffixes starting at the node.

Following is the implementation of the above idea.  

C++

// A simple C++ implementation of substring search using trie of suffixes
#include<iostream>
#include<list>
#define MAX_CHAR 256
using namespace std;

// A Suffix Trie (A Trie of all suffixes) Node
class SuffixTrieNode
{
private:
    SuffixTrieNode *children[MAX_CHAR];
    list<int> *indexes;
public:
    SuffixTrieNode() // Constructor
    {
        // Create an empty linked list for indexes of
        // suffixes starting from this node
        indexes = new list<int>;

        // Initialize all child pointers as NULL
        for (int i = 0; i < MAX_CHAR; i++)
          children[i] = NULL;
    }

    // A recursive function to insert a suffix of the txt
    // in subtree rooted with this node
    void insertSuffix(string suffix, int index);

    // A function to search a pattern in subtree rooted
    // with this node.The function returns pointer to a linked
    // list containing all indexes where pattern is present.
    // The returned indexes are indexes of last characters
    // of matched text.
    list<int>* search(string pat);
};

// A Trie of all suffixes
class SuffixTrie
{
private:
    SuffixTrieNode root;
public:
    // Constructor (Builds a trie of suffixes of the given text)
    SuffixTrie(string txt)
    {
        // Consider all suffixes of given string and insert
        // them into the Suffix Trie using recursive function
        // insertSuffix() in SuffixTrieNode class
        for (int i = 0; i < txt.length(); i++)
            root.insertSuffix(txt.substr(i), i);
    }

    // Function to searches a pattern in this suffix trie.
    void search(string pat);
};

// A recursive function to insert a suffix of the txt in
// subtree rooted with this node
void SuffixTrieNode::insertSuffix(string s, int index)
{
    // Store index in linked list
    indexes->push_back(index);

    // If string has more characters
    if (s.length() > 0)
    {
        // Find the first character
        char cIndex = s.at(0);

        // If there is no edge for this character, add a new edge
        if (children[cIndex] == NULL)
            children[cIndex] = new SuffixTrieNode();

        // Recur for next suffix
        children[cIndex]->insertSuffix(s.substr(1), index+1);
    }
}

// A recursive function to search a pattern in subtree rooted with
// this node
list<int>* SuffixTrieNode::search(string s)
{
    // If all characters of pattern have been processed,
    if (s.length() == 0)
        return indexes;

    // if there is an edge from the current node of suffix trie,
    // follow the edge.
    if (children[s.at(0)] != NULL)
        return (children[s.at(0)])->search(s.substr(1));

    // If there is no edge, pattern doesn’t exist in text
    else return NULL;
}

/* Prints all occurrences of pat in the Suffix Trie S (built for text)*/
void SuffixTrie::search(string pat)
{
    // Let us call recursive search function for root of Trie.
    // We get a list of all indexes (where pat is present in text) in
    // variable 'result'
    list<int> *result = root.search(pat);

    // Check if the list of indexes is empty or not
    if (result == NULL)
        cout << "Pattern not found" << endl;
    else
    {
       list<int>::iterator i;
       int patLen = pat.length();
       for (i = result->begin(); i != result->end(); ++i)
         cout << "Pattern found at position " << *i - patLen<< endl;
    }
}

// driver program to test above functions
int main()
{
    // Let us build a suffix trie for text "geeksforgeeks.org"
    string txt = "geeksforgeeks.org";
    SuffixTrie S(txt);

    cout << "Search for 'ee'" << endl;
    S.search("ee");

    cout << "\nSearch for 'geek'" << endl;
    S.search("geek");

    cout << "\nSearch for 'quiz'" << endl;
    S.search("quiz");

    cout << "\nSearch for 'forgeeks'" << endl;
    S.search("forgeeks");

    return 0;
}

Java

import java.util.LinkedList;
import java.util.List;
class SuffixTrieNode {

    final static int MAX_CHAR = 256;

    SuffixTrieNode[] children = new SuffixTrieNode[MAX_CHAR];
    List<Integer> indexes;

    SuffixTrieNode() // Constructor
    {
        // Create an empty linked list for indexes of
        // suffixes starting from this node
        indexes = new LinkedList<Integer>();

        // Initialize all child pointers as NULL
        for (int i = 0; i < MAX_CHAR; i++)
            children[i] = null;
    }

    // A recursive function to insert a suffix of
    // the text in subtree rooted with this node
    void insertSuffix(String s, int index) {

        // Store index in linked list
        indexes.add(index);

        // If string has more characters
        if (s.length() > 0) {

            // Find the first character
            char cIndex = s.charAt(0);

            // If there is no edge for this character,
            // add a new edge
            if (children[cIndex] == null)
                children[cIndex] = new SuffixTrieNode();

            // Recur for next suffix
            children[cIndex].insertSuffix(s.substring(1),
                                              index + 1);
        }
    }

    // A function to search a pattern in subtree rooted
    // with this node.The function returns pointer to a
    // linked list containing all indexes where pattern
    // is present. The returned indexes are indexes of
    // last characters of matched text.
    List<Integer> search(String s) {

        // If all characters of pattern have been
        // processed,
        if (s.length() == 0)
            return indexes;

        // if there is an edge from the current node of
        // suffix tree, follow the edge.
        if (children[s.charAt(0)] != null)
            return (children[s.charAt(0)]).search(s.substring(1));

        // If there is no edge, pattern doesnt exist in
        // text
        else
            return null;
    }
}

// A Trie of all suffixes
class Suffix_tree{

    SuffixTrieNode root = new SuffixTrieNode();

    // Constructor (Builds a trie of suffixes of the
    // given text)
    Suffix_tree(String txt) {

        // Consider all suffixes of given string and
        // insert them into the Suffix Trie using
        // recursive function insertSuffix() in
        // SuffixTrieNode class
        for (int i = 0; i < txt.length(); i++)
            root.insertSuffix(txt.substring(i), i);
    }

    /* Prints all occurrences of pat in the Suffix Trie S
    (built for text) */
    void search_tree(String pat) {

        // Let us call recursive search function for
        // root of Trie.
        // We get a list of all indexes (where pat is
        // present in text) in variable 'result'
        List<Integer> result = root.search(pat);

        // Check if the list of indexes is empty or not
        if (result == null)
            System.out.println("Pattern not found");
        else {

            int patLen = pat.length();

            for (Integer i : result)
                System.out.println("Pattern found at position " +
                                                (i - patLen));
        }
    }

    // driver program to test above functions
    public static void main(String args[]) {

        // Let us build a suffix trie for text
        // "geeksforgeeks.org"
        String txt = "geeksforgeeks.org";
        Suffix_tree S = new Suffix_tree(txt);

        System.out.println("Search for 'ee'");
        S.search_tree("ee");

        System.out.println("\nSearch for 'geek'");
        S.search_tree("geek");

        System.out.println("\nSearch for 'quiz'");
        S.search_tree("quiz");

        System.out.println("\nSearch for 'forgeeks'");
        S.search_tree("forgeeks");
    }
}
// This code is contributed by Sumit Ghosh

C#

// C# implementation of the approach
using System;
using System.Collections.Generic;
class SuffixTrieNode
{
    static int MAX_CHAR = 256;

    public SuffixTrieNode[] children = new SuffixTrieNode[MAX_CHAR];
    public List<int> indexes;

    public SuffixTrieNode() // Constructor
    {
        // Create an empty linked list for indexes of
        // suffixes starting from this node
        indexes = new List<int>();

        // Initialize all child pointers as NULL
        for (int i = 0; i < MAX_CHAR; i++)
            children[i] = null;
    }

    // A recursive function to insert a suffix of
    // the text in subtree rooted with this node
    public void insertSuffix(String s, int index)
    {

        // Store index in linked list
        indexes.Add(index);

        // If string has more characters
        if (s.Length > 0)
        {

            // Find the first character
            char cIndex = s[0];

            // If there is no edge for this character,
            // add a new edge
            if (children[cIndex] == null)
                children[cIndex] = new SuffixTrieNode();

            // Recur for next suffix
            children[cIndex].insertSuffix(s.Substring(1),
                                              index + 1);
        }
    }

    // A function to search a pattern in subtree rooted
    // with this node.The function returns pointer to a
    // linked list containing all indexes where pattern
    // is present. The returned indexes are indexes of
    // last characters of matched text.
    public List<int> search(String s)
    {

        // If all characters of pattern have been
        // processed,
        if (s.Length == 0)
            return indexes;

        // if there is an edge from the current node of
        // suffix tree, follow the edge.
        if (children[s[0]] != null)
            return (children[s[0]]).search(s.Substring(1));

        // If there is no edge, pattern doesnt exist in
        // text
        else
            return null;
    }
}

// A Trie of all suffixes
public class Suffix_tree
{

    SuffixTrieNode root = new SuffixTrieNode();

    // Constructor (Builds a trie of suffixes of the
    // given text)
    Suffix_tree(String txt)
    {

        // Consider all suffixes of given string and
        // insert them into the Suffix Trie using
        // recursive function insertSuffix() in
        // SuffixTrieNode class
        for (int i = 0; i < txt.Length; i++)
            root.insertSuffix(txt.Substring(i), i);
    }

    /* Prints all occurrences of pat in the
    Suffix Trie S (built for text) */
    void search_tree(String pat)
    {

        // Let us call recursive search function
        // for root of Trie.
        // We get a list of all indexes (where pat is
        // present in text) in variable 'result'
        List<int> result = root.search(pat);

        // Check if the list of indexes is empty or not
        if (result == null)
            Console.WriteLine("Pattern not found");
        else
        {
            int patLen = pat.Length;

            foreach (int i in result)
                Console.WriteLine("Pattern found at position " +
                                                  (i - patLen));
        }
    }

    // Driver Code
    public static void Main(String []args)
    {

        // Let us build a suffix trie for text
        // "geeksforgeeks.org"
        String txt = "geeksforgeeks.org";
        Suffix_tree S = new Suffix_tree(txt);

        Console.WriteLine("Search for 'ee'");
        S.search_tree("ee");

        Console.WriteLine("\nSearch for 'geek'");
        S.search_tree("geek");

        Console.WriteLine("\nSearch for 'quiz'");
        S.search_tree("quiz");

        Console.WriteLine("\nSearch for 'forgeeks'");
        S.search_tree("forgeeks");
    }
}

// This code is contributed by 29AjayKumar

Javascript

<script>
let MAX_CHAR = 256;

class SuffixTrieNode
{

    // Constructor
    constructor()
    {
        this.indexes = [];
        this.children = new Array(MAX_CHAR);

        for(let i = 0; i < MAX_CHAR; i++)
        {
            this.children[i] = 0;
        }
    }

// A recursive function to insert a suffix of
// the text in subtree rooted with this node
insertSuffix(s,index)
{

    // Store index in linked list
    this.indexes.push(index);

    // If string has more characters
    if (s.length > 0)
    {

        // Find the first character
        let cIndex = s[0];

        // If there is no edge for this character,
        // add a new edge
        if (this.children[cIndex] == null)
            this.children[cIndex] = new SuffixTrieNode();

        // Recur for next suffix
        this.children[cIndex].insertSuffix(s.substring(1),
                                           index + 1);
    }
}

// A function to search a pattern in subtree rooted
// with this node.The function returns pointer to a
// linked list containing all indexes where pattern
// is present. The returned indexes are indexes of
// last characters of matched text.
search(s)
{

    // If all characters of pattern have been
    // processed,
    if (s.length == 0)
        return this.indexes;

    // If there is an edge from the current node of
    // suffix tree, follow the edge.
    if (this.children[s[0]] != null)
        return(this.children[s[0]].search(
                  s.substring(1)));

    // If there is no edge, pattern doesnt exist in
    // text
    else
        return null;
}
}

let root = new SuffixTrieNode();

// Constructor (Builds a trie of suffixes of the
// given text)
function Suffix_tree(txt)
{

    // Consider all suffixes of given string and
    // insert them into the Suffix Trie using
    // recursive function insertSuffix() in
    // SuffixTrieNode class
    for(let i = 0; i < txt.length; i++)
        root.insertSuffix(txt.substring(i), i);
}

/* Prints all occurrences of pat in the Suffix
Trie S (built for text) */
function search_tree(pat)
{

    // Let us call recursive search function for
    // root of Trie.
    // We get a list of all indexes (where pat is
    // present in text) in variable 'result'
    let result = root.search(pat);

    // Check if the list of indexes is empty or not
    if (result == null)
        document.write("Pattern not found<br>");
    else
    {
        let patLen = pat.length;

        for(let i of result.values())
            document.write("Pattern found at position " +
                           (i - patLen)+"<br>");
    }
}

// Driver code

// Let us build a suffix trie for text
// "geeksforgeeks.org"
let txt = "geeksforgeeks.org";
Suffix_tree(txt);

document.write("Search for 'ee'<br>");
search_tree("ee");

document.write("<br>Search for 'geek'<br>");
search_tree("geek");

document.write("<br>Search for 'quiz'<br>");
search_tree("quiz");

document.write("<br>Search for 'forgeeks'<br>");
search_tree("forgeeks");

// This code is contributed by unknown2108

</script>

Python3

class SuffixTrieNode:
    def __init__(self):
        self.children = [None] * 256
        self.indexes = []

    def insert_suffix(self, suffix, index):
        self.indexes.append(index)
        if suffix:
            c_index = ord(suffix[0])
            if not self.children[c_index]:
                self.children[c_index] = SuffixTrieNode()
            self.children[c_index].insert_suffix(suffix[1:], index + 1)

    def search(self, pat):
        if not pat:
            return self.indexes
        c_index = ord(pat[0])
        if self.children[c_index]:
            return self.children[c_index].search(pat[1:])
        return None

class SuffixTrie:
    def __init__(self, txt):
        self.root = SuffixTrieNode()
        for i in range(len(txt)):
            self.root.insert_suffix(txt[i:], i)

    def search(self, pat):
        result = self.root.search(pat)
        if not result:
            print("Pattern not found")
        else:
            pat_len = len(pat)
            for i in result:
                print(f"Pattern found at position {i - pat_len}")

if __name__ == "__main__":
    # Let us build the suffix trie for text "geeksforgeeks.org"
    txt = "geeksforgeeks.org"
    st = SuffixTrie(txt)

    # Let us search for different patterns
    pat = "ee"
    print(f"Search for '{pat}'")
    st.search(pat)
    print()

    pat = "geek"
    print(f"Search for '{pat}'")
    st.search(pat)
    print()

    pat = "quiz"
    print(f"Search for '{pat}'")
    st.search(pat)
    print()

    pat = "forgeeks"
    print(f"Search for '{pat}'")
    st.search(pat)
    print()

Output:

Search for 'ee'
Pattern found at position 1
Pattern found at position 9

Search for 'geek'
Pattern found at position 0
Pattern found at position 8

Search for 'quiz'
Pattern not found

Search for 'forgeeks'
Pattern found at position 5

Time Complexity of the above search function is O(m+k) where m is length of the pattern and k is the number of occurrences of pattern in text.

Space Complexity: O(n * MAX_CHAR) where n is the length of the input text.