Count of distinct substrings of a string using Suffix Trie

Given a string of length n of lowercase alphabet characters, we need to count total number of distinct substrings of this string. Examples:

Input  : str = “ababa”
Output : 10
Total number of distinct substring are 10, which are,
"", "a", "b", "ab", "ba", "aba", "bab", "abab", "baba"
and "ababa"

The idea is create a Trie of all suffixes of given string. Once the Trie is constricted, our answer is total number of nodes in the constructed Trie. For example below diagram represent Trie of all suffixes for “ababa”. Total number of nodes is 10 which is our answer. 

How does this work?

• Each root to node path of a Trie represents a prefix of words present in Trie. Here we words are suffixes. So each node represents a prefix of suffixes.
• Every substring of a string “str” is a prefix of a suffix of “str”.

Below is implementation based on above idea. 

C++

// A C++ program to find the count of distinct substring
// of a string using trie data structure
#include <bits/stdc++.h>
#define MAX_CHAR 26
using namespace std;

// A Suffix Trie (A Trie of all suffixes) Node
class SuffixTrieNode
{
public:
    SuffixTrieNode *children[MAX_CHAR];
    SuffixTrieNode() // Constructor
    {
        // 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 s
    // in subtree rooted with this node
    void insertSuffix(string suffix);
};

// A Trie of all suffixes
class SuffixTrie
{
    SuffixTrieNode *root;
    int _countNodesInTrie(SuffixTrieNode *);
public:
    // Constructor (Builds a trie of suffies of the given text)
    SuffixTrie(string s)
    {
        root = new SuffixTrieNode();

        // 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 < s.length(); i++)
            root->insertSuffix(s.substr(i));
    }

    //  method to count total nodes in suffix trie
    int countNodesInTrie() { return _countNodesInTrie(root); }
};

// A recursive function to insert a suffix of the s in
// subtree rooted with this node
void SuffixTrieNode::insertSuffix(string s)
{
    // If string has more characters
    if (s.length() > 0)
    {
        // Find the first character and convert it
        // into 0-25 range.
        char cIndex = s.at(0) - 'a';

        // 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));
    }
}

// A recursive function to count nodes in trie
int SuffixTrie::_countNodesInTrie(SuffixTrieNode* node)
{
    // If all characters of pattern have been processed,
    if (node == NULL)
        return 0;

    int count = 0;
    for (int i = 0; i < MAX_CHAR; i++)
    {
        // if children is not NULL then find count
        // of all nodes in this subtrie
        if (node->children[i] != NULL)
            count += _countNodesInTrie(node->children[i]);
    }

    // return count of nodes of subtrie and plus
    // 1 because of node's own count
    return (1 + count);
}

// Returns count of distinct substrings of str
int countDistinctSubstring(string str)
{
    // Construct a Trie of all suffixes
    SuffixTrie sTrie(str);

    // Return count of nodes in Trie of Suffixes
    return sTrie.countNodesInTrie();
}

// Driver program to test above function
int main()
{
    string str = "ababa";
    cout << "Count of distinct substrings is "
         << countDistinctSubstring(str);
    return 0;
}

Java

// A Java program to find the count of distinct substring
// of a string using trie data structure
public class Suffix
{
    // A Suffix Trie (A Trie of all suffixes) Node
    static class SuffixTrieNode
    {
        static final int MAX_CHAR = 26;
        SuffixTrieNode[] children = new SuffixTrieNode[MAX_CHAR];

        SuffixTrieNode() // Constructor
        {
            // 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 s in
        // subtree rooted with this node
        void insertSuffix(String s)
        {
            // If string has more characters
            if (s.length() > 0)
            {
                // Find the first character and convert it
                // into 0-25 range.
                char cIndex = (char) (s.charAt(0) - 'a');

                // 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));
                }
        }
    }

    // A Trie of all suffixes
    static class Suffix_trie
    {
        static final int MAX_CHAR = 26;
        SuffixTrieNode root;

        // Constructor (Builds a trie of suffies of the given text)
        Suffix_trie(String s) {
            root = new SuffixTrieNode();

            // 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 < s.length(); i++)
                root.insertSuffix(s.substring(i));
        }

        // A recursive function to count nodes in trie
        int _countNodesInTrie(SuffixTrieNode node)
        {
            // If all characters of pattern have been processed,
            if (node == null)
                return 0;

            int count = 0;
            for (int i = 0; i < MAX_CHAR; i++) {

                // if children is not NULL then find count
                // of all nodes in this subtrie
                if (node.children[i] != null)
                    count += _countNodesInTrie(node.children[i]);
            }

            // return count of nodes of subtrie and plus
            // 1 because of node's own count
            return (1 + count);
        }

        // method to count total nodes in suffix trie
        int countNodesInTrie()
        {
            return _countNodesInTrie(root);
        }

    }

    // Returns count of distinct substrings of str
    static int countDistinctSubstring(String str)
    {
        // Construct a Trie of all suffixes
        Suffix_trie sTrie = new Suffix_trie(str);

        // Return count of nodes in Trie of Suffixes
        return sTrie.countNodesInTrie();
    }

    // Driver program to test above function
    public static void main(String args[])
    {
        String str = "ababa";
        System.out.println("Count of distinct substrings is "
                + countDistinctSubstring(str));

    }
}
// This code is contributed by Sumit Ghosh

Python3

# Python program to find the count of distinct substring
# of a string using trie data structure

# A Suffix Trie (A Trie of all suffixes) Node
class SuffixTrieNode:
    def __init__(self):
        # Initialize all child pointers as NULL
        self.children = [None] * 26

    # A recursive function to insert a suffix of the s in
    # subtree rooted with this node
    def insert_suffix(self, suffix):
        # If string has more characters
        if suffix:
            # Find the first character and convert it
            # into 0-25 range.
            c_index = ord(suffix[0]) - ord('a')
            # If there is no edge for this character,
            # add a new edge
            if not self.children[c_index]:
                self.children[c_index] = SuffixTrieNode()
            # Recur for next suffix
            self.children[c_index].insert_suffix(suffix[1:])

# A Trie of all suffixes
class SuffixTrie:
    def __init__(self, s):
        # Constructor (Builds a trie of suffies of the given text)
        self.root = SuffixTrieNode()
        for i in range(len(s)):
            # Consider all suffixes of given string and insert
            # them into the Suffix Trie using recursive function
            # insertSuffix() in SuffixTrieNode class
            self.root.insert_suffix(s[i:])

    # method to count total nodes in suffix trie
    def countNodesInTrie(self):
        return self._countNodesInTrie(self.root)

    def _countNodesInTrie(self, node):
        # If all characters of pattern have been processed,
        if node is None:
            return 0
        count = 0
        for i in range(26):
            # if children is not NULL then find count
            # of all nodes in this subtrie
            if node.children[i]:
                count += self._countNodesInTrie(node.children[i])
        # return count of nodes of subtrie and plus
        # 1 because of node's own count
        return count + 1

# Returns count of distinct substrings of str
def countDistinctSubstring(str):
    # Construct a Trie of all suffixes
    s_trie = SuffixTrie(str)
    # Return count of nodes in Trie of Suffixes
    return s_trie.countNodesInTrie()

# Driver program to test above function
if __name__ == '__main__':
    str = "ababa"
    print("Count of distinct substrings is", countDistinctSubstring(str))

# This code is contributed by Aman Kumar.

C#

// C# program to find the count of distinct substring
// of a string using trie data structure
using System;

public class Suffix
{
    // A Suffix Trie (A Trie of all suffixes) Node
    public class SuffixTrieNode
    {
        static readonly int MAX_CHAR = 26;
        public SuffixTrieNode[] children = new SuffixTrieNode[MAX_CHAR];

        public SuffixTrieNode() // Constructor
        {
            // 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 s in
        // subtree rooted with this node
        public void insertSuffix(String s)
        {
            // If string has more characters
            if (s.Length > 0)
            {
                // Find the first character and convert it
                // into 0-25 range.
                char cIndex = (char) (s[0] - 'a');

                // 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));
                }
        }
    }

    // A Trie of all suffixes
    public class Suffix_trie
    {
        static readonly int MAX_CHAR = 26;
        public SuffixTrieNode root;

        // Constructor (Builds a trie of suffies of the given text)
        public Suffix_trie(String s)
        {
            root = new SuffixTrieNode();

            // 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 < s.Length; i++)
                root.insertSuffix(s.Substring(i));
        }

        // A recursive function to count nodes in trie
        public int _countNodesInTrie(SuffixTrieNode node)
        {
            // If all characters of pattern have been processed,
            if (node == null)
                return 0;

            int count = 0;
            for (int i = 0; i < MAX_CHAR; i++)
            {

                // if children is not NULL then find count
                // of all nodes in this subtrie
                if (node.children[i] != null)
                    count += _countNodesInTrie(node.children[i]);
            }

            // return count of nodes of subtrie and plus
            // 1 because of node's own count
            return (1 + count);
        }

        // method to count total nodes in suffix trie
        public int countNodesInTrie()
        {
            return _countNodesInTrie(root);
        }

    }

    // Returns count of distinct substrings of str
    static int countDistinctSubstring(String str)
    {
        // Construct a Trie of all suffixes
        Suffix_trie sTrie = new Suffix_trie(str);

        // Return count of nodes in Trie of Suffixes
        return sTrie.countNodesInTrie();
    }

    // Driver program to test above function
    public static void Main(String []args)
    {
        String str = "ababa";
        Console.WriteLine("Count of distinct substrings is "
                + countDistinctSubstring(str));

    }
}

// This code contributed by Rajput-Ji

Javascript

// A Javascript program to find the count of distinct substring
// of a string using trie data structure
// A Suffix Trie (A Trie of all suffixes) Node
class SuffixTrieNode {
    constructor() {
        // Initialize all child pointers as null
        this.children = new Array(26).fill(null);
    }

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

        // If string has more characters
        if (suffix.length > 0) {
            // Find the first character and convert it
            // into 0-25 range.
            const cIndex = suffix.charCodeAt(0) - 'a'.charCodeAt(0);
            // If there is no edge for this character,
            // add a new edge
            if (!this.children[cIndex]) {
                this.children[cIndex] = new SuffixTrieNode();
            }
            // Recur for next suffix
            this.children[cIndex].insertSuffix(suffix.slice(1));
        }
    }
}

// A Trie of all suffixes
class SuffixTrie {
    constructor(s) {
        // Constructor (Builds a trie of suffies of the given text)
        this.root = new SuffixTrieNode();
        for (let i = 0; i < s.length; i++) {

            // Consider all suffixes of given string and insert
            // them into the Suffix Trie using recursive function
            // insertSuffix() in SuffixTrieNode class
            this.root.insertSuffix(s.slice(i));
        }
    }

    // method to count total nodes in suffix trie
    countNodesInTrie() {
        return this._countNodesInTrie(this.root);
    }

    _countNodesInTrie(node) {
        // If all characters of pattern have been processed,
        if (node === null) {
            return 0;
        }
        let count = 0;
        for (let i = 0; i < 26; i++) {

            // if children is not null then find count
            // of all nodes in this subtrie
            if (node.children[i]) {
                count += this._countNodesInTrie(node.children[i]);
            }
        }

        // return count of nodes of subtrie and plus
        // 1 because of node's own count
        return count + 1;
    }
}

// Returns count of distinct substrings of str
function countDistinctSubstring(str) {

    // Construct a Trie of all suffixes
    const sTrie = new SuffixTrie(str);

    // Return count of nodes in Trie of Suffixes
    return sTrie.countNodesInTrie();
}

// Driver program to test above function
const str = 'ababa';
console.log('Count of distinct substrings is', countDistinctSubstring(str));

Output

Count of distinct substrings is 10

Time Complexity: O(n²), where n is the length of string.
Auxiliary Space: O(n)

We will soon be discussing Suffix Array and Suffix Tree based approaches for this problem. This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.