Count Total words in Trie

The problem involves working with a trie data structure to determine the total number of words it contains. A trie (also known as a prefix tree) is a tree-like data structure used to store a dynamic set of strings. Each node of the trie represents a single character of a string, and paths from the root to a node represent the characters in a string. The problem here is to count the total number of complete words present in the trie.

Problem Statement

Given a trie containing various words, the task is to count the total number of complete words present in the trie.

Description with Example

Consider a scenario where we have a trie containing the words: "how," "many," "code," "co," "club," "run," "rule," and "set." The trie would look like this:

           root  

       /  / |  \    \
      /  /  |   \    \ 
     /  /   |    \    \
    h   m   c     r    s
    |   |   | \   |    |
    o   a   o  l  u    e
    |   |   |  |  | \  |
    w   n   d  u  n  l t
        |   |  |     |
        y   e  b     e

Idea to Solve the Problem

The idea to solve this problem is to recursively traverse the trie and count the nodes where the end flag is set to true. The end flag indicates the end of a complete word.

Pseudocode

function countWords(node):
 if node is not null:
     counter = 0
     if node.end is true:
         increment counter
     for each child in node's children:
         increment counter by countWords(child)
     return counter
 return 0

Algorithm Explanation

1. Define a Node class to represent nodes in the trie. Each node has a boolean variable end to mark the end of a word and an array children to store references to its child nodes.

2. Define a Trie class to encapsulate the trie structure. The Trie class has a root node as its member.

3. Implement the insert function in the Trie class to insert a word into the trie. This function iterates through the characters of the word, creating new nodes as necessary.

4. Implement the words function in the Trie class to recursively count the complete words in the trie. This function starts from the root and traverses through the children nodes, incrementing the counter whenever the end flag is true.

5. In the main function, create an instance of the Trie class, insert the words, and then call the words function to count the total number of complete words.

Code Solution

• Cpp
• Java
• Python
• C#
• Php

//C++ program
//Count Total words in Trie
#include <iostream>
#include <string.h>
using namespace std;
#define ALPHABETS 26
struct Node
{
  //Indicates end of string
  int end;
  struct Node *children[ALPHABETS];
};

class Trie
{

public:
  Node *root;
  Trie()
  {
    root = new Node;

    for (int i = 0; i < ALPHABETS; ++i)
    {
      root->children[i]=NULL;
    }
    root->end=0;
  }
  void insert(string);
  int  words(Node *root);
  
};

void Trie:: insert(string text)
{
  //First get the length of text
  int length = text.size();

  //This variable are used to task find the index location of character
  int index = 0;

  //Get the root node
  Node *head = root;

  for (int level = 0; level < length ; level++ )
  {

    //Get the index
    index = text[level]-'a';

    if(head->children[index] == NULL)
    {
      //When need to add new Node
      head->children[index]= new Node;


      for (int i = 0; i < ALPHABETS; ++i)
      {
        head->children[index]->children[i]=NULL;
      }
      head->children[index]->end=0;
    }

    head =head->children[index];
  }
  if(head != NULL)
  {  
    //Indicates end of string
    head->end = 1;
  }

}

int Trie:: words(Node *root)
  {
    int counter = 0;
    if(root!=NULL)
    {

      if(root->end==1)
      {
        counter++;
      }
      for (int i = 0; i < ALPHABETS ; i++ ) 
      {
        if(root->children[i] != NULL)
        {
          counter += words(root->children[i]);
        }    
      }

    }
    return counter;
  }
int main()
{
  //Make object
  Trie obj ;
  obj.insert("how");
  obj.insert("many");
  obj.insert("code");
  obj.insert("co");
  obj.insert("club");
  obj.insert("run");
  obj.insert("rule");
  obj.insert("set");
 
  

  /*
         root  

     /  / |  \    \
    /  /  |   \    \ 
   /  /   |    \    \
  h   m   c     r    s
  |   |   | \   |    |
  o   a   o  l  u    e
  |   |  /|  |  | \  |
  w   n # d  u  n  l t
      |   |  |     |
      y   e  b     e
  */
  cout<<" Total Words : "<<obj.words(obj.root);


  return 0;
}

Total Words : 8

/*
Java program
Count Total words in Trie
*/
class Node
{
  //Indicates end of string
  public boolean end;

  public Node []children;

  public Node(int size)
  {
    children = new Node[size];
    end = false;
  }
}
public class Trie 
{ 
  static final int ALPHABETS = 26;

  public Node root; 

  public Trie()
  {
    root = new Node(ALPHABETS);
  }

  public void insert(String text)
  {
    //First get the length of text
    int length = text.length();

    //This variable are used to task find the index location of character
    int index = 0;

    //Get the root node
    Node head = root;

    for (int level = 0; level < length ; level++ )
    {
      //Get the index
      index = text.charAt(level)-'a';

      if(head.children[index] == null)
      {
        //When need to add new Node
        head.children[index] = new Node(ALPHABETS);
      }

      head = head.children[index];
    }
    if(head != null)
    {  
      //indicates end of string
      head.end = true;
    }
  }
  public int words(Node root)
  {
    int counter = 0;
    if(root!=null)
    {

      if(root.end==true)
      {
        counter++;
      }
      for (int i = 0; i < ALPHABETS ; i++ ) 
      {
        if(root.children[i] != null)
        {
          counter += words(root.children[i]);
        }    
      }

    }
    return counter;
  }

  public static void main(String[] args) 
  {
    //Make object
    Trie obj = new Trie();
     
    obj.insert("how");
    obj.insert("many");
    obj.insert("code");
    obj.insert("co");
    obj.insert("club");
    obj.insert("run");
    obj.insert("rule");
    obj.insert("set");
   
    

/*
           root  

       /  / |  \    \
      /  /  |   \    \ 
     /  /   |    \    \
    h   m   c     r    s
    |   |   | \   |    |
    o   a   o  l  u    e
    |   |  /|  |  | \  |
    w   n # d  u  n  l t
        |   |  |     |
        y   e  b     e
    */

    System.out.println(" Total Words : "+obj.words(obj.root));


  }
}

 Total Words : 8

#Python program
#Count Total words in Trie
class Node:
  def __init__(self,size):
    self.children=[None]*size
    self.end=False

    
class Trie:

  def __init__(self):
    self.ALPHABET = 26
    self.root=Node(self.ALPHABET)

  
  def insert(self,text) :

    #First get the length of text
    length=len(text)
    #This variable are used to task find the index location of character
    index=0
    #Get the root node
    head= self.root
    level=0
    while ( level< length  ) :

      #Get the index
      index=ord(text[level])-ord('a')

      if (head.children[index]== None) :

        #When need to add new Node
        head.children[index]= Node(self.ALPHABET)
      head= head.children[index]

      level+=1
    if(head != None) :

      #Indicates end of string
      head.end= True

  def words(self,root) :

    counter = 0
    if(root!=None) :

      if(root.end==True) :

        counter += 1
      i = 0
      while (i < self.ALPHABET )  :

        if(root.children[i] != None) :

          counter += self.words(root.children[i])
        i += 1
    return counter

def main():
  obj = Trie()

  obj.insert("how")
  obj.insert("many")
  obj.insert("code")
  obj.insert("co")
  obj.insert("club")
  obj.insert("run")
  obj.insert("rule")
  obj.insert("set")
  #
  #         root
  #     /  / |  \    \
  #    /  /  |   \    \
  #   /  /   |    \    \
  #  h   m   c     r    s
  #  |   |   | \   |    |
  #  o   a   o  l  u    e
  #  |   |  /|  |  | \  |
  #  w   n # d  u  n  l t
  #      |   |  |     |
  #      y   e  b     e
  #  
  print(" Total Words : ",obj.words(obj.root))


if __name__=="__main__":
  main()

 Total Words :  8

/*
C# program
Count Total words in Trie
*/
using System;
public class Node
{
  //Indicates end of string
  public Boolean end;

  public Node []children;

  public Node(int size)
  {
    children = new Node[size];
    end = false;
  }
}
public class Trie 
{ 
  public const int ALPHABETS = 26;

  public Node root; 

  public Trie()
  {
    root = new Node(ALPHABETS);
  }

  public void insert(String text)
  {
    //First get the.Length of text
    int length = text.Length;

    //This variable are used to task find the index location of character
    int index = 0;

    //Get the root node
    Node head = root;

    for (int level = 0; level < length ; level++ )
    {
      //Get the index
      index = text[level]-'a';

      if(head.children[index] == null)
      {
        //When need to add new Node
        head.children[index] = new Node(ALPHABETS);
      }

      head = head.children[index];
    }
    if(head != null)
    {  
      //indicates end of string
      head.end = true;
    }
  }
  public int words(Node root)
  {
    int counter = 0;
    if(root!=null)
    {

      if(root.end==true)
      {
        counter++;
      }
      for (int i = 0; i < ALPHABETS ; i++ ) 
      {
        if(root.children[i] != null)
        {
          counter += words(root.children[i]);
        }    
      }

    }
    return counter;
  }

  public static void Main(String[] args) 
  {
    //Make object
    Trie obj = new Trie();

    obj.insert("how");
    obj.insert("many");
    obj.insert("code");
    obj.insert("co");
    obj.insert("club");
    obj.insert("run");
    obj.insert("rule");
    obj.insert("set");



    /*
           root  

       /  / |  \    \
      /  /  |   \    \ 
     /  /   |    \    \
    h   m   c     r    s
    |   |   | \   |    |
    o   a   o  l  u    e
    |   |  /|  |  | \  |
    w   n # d  u  n  l t
        |   |  |     |
        y   e  b     e
    */

    Console.WriteLine(" Total Words : "+obj.words(obj.root));


  }
}

 Total Words : 8

<?php 
/*
* PHP Program 
* Count Total words in Trie
*/


class Node
{
  public $end;
  public $children;
  function __construct($size)
  {
    $this->children=array_fill(0, $size, NULL);
    $this->end=false;

  }
}
class Trie
{

  public $root;
  const ALPHABET = 26;

  function __construct()
  {
    $this->root=new Node(self:: ALPHABET);
  }


  public function  insert($text)
  {
    //First get the length of text
    $length=strlen($text);

    //This variable are used to task find the index location of character
    $index=0;

    //Get the root node
    $head= $this->root;

    for ($level=0; $level< $length; ++$level)
    {

      //Get the index
      $index=ord($text[$level])-ord('a');


      if ($head->children[$index]== NULL)
      {
        //When need to add new Node
        $head->children[$index]= new  Node(self::ALPHABET);
      }

      $head= $head->children[$index];
    }
    if($head != NULL)
    {  
      //Indicates end of string
      $head->end= true;
    }
  }
  public function words($root)
  {
    $counter = 0;
    if($root!=NULL)
    {

      if($root->end==true)
      {
        $counter++;
      }
      for ( $i = 0; $i < self::ALPHABET ; $i++ ) 
      {
        if($root->children[$i] != NULL)
        {
          $counter += $this->words($root->children[$i]);
        }    
      }

    }
    return $counter;
  }

}


function main()
{
  //Make object
  $obj = new Trie();


  $obj->insert("how");
  $obj->insert("many");
  $obj->insert("code");
  $obj->insert("co");
  $obj->insert("club");
  $obj->insert("run");
  $obj->insert("rule");
  $obj->insert("set");

  

  /*
         root  

     /  / |  \    \
    /  /  |   \    \ 
   /  /   |    \    \
  h   m   c     r    s
  |   |   | \   |    |
  o   a   o  l  u    e
  |   |  /|  |  | \  |
  w   n # d  u  n  l t
      |   |  |     |
      y   e  b     e
  */
  echo " Total Words : ".$obj->words($obj->root);
}
main();
?>

 Total Words : 8

Time Complexity

The time complexity of inserting a word into the trie is O(N), where N is the length of the word. The time complexity of the words function is O(N), where N is the number of nodes in the trie. Since each node corresponds to a character, the number of nodes is proportional to the number of characters. Therefore, the overall time complexity of the code is O(N), where N is the total number of characters in the trie.