Count of distinct substrings of a string using Suffix Trie

Last Updated : 19 Sep, 2023

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# 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));