Trie Bottom-Up Traversal

The Trie Bottom-Up Traversal is a technique used to traverse and display the contents of a trie data structure in a specific order. A trie (also known as a prefix tree) is a tree-like data structure used to store a dynamic set of strings, where the keys are usually 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. Tries are commonly used for tasks like autocomplete suggestions, spell checking, and searching.

Problem Statement

Given a trie containing various words, the task is to traverse and display the characters in a bottom-up manner. Bottom-up traversal means starting from the deepest levels of the trie and moving towards the root while displaying the characters encountered.

Description with Example

Let's consider a scenario where we have a trie containing the words "war," "cooky," "cool," "code," and "cow." The trie would look like this:

     root
    /   \
   c     w   
   |     |
   o     a  
   | \   |
   o  w  r
 / | \ 
 d k  l
 | |
 e y

Idea to Solve the Problem

The idea to solve this problem is to perform a recursive traversal of the trie in a bottom-up manner. Starting from the deepest levels (leaf nodes) of the trie, we traverse upwards while printing the characters we encounter. We can implement this traversal using a recursive function.

Pseudocode

function traverse(node):
 if node is not null:
     for each child in node's children:
         traverse(child)
         print character associated with the child node

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 display function in the Trie class to perform the bottom-up traversal and display characters. This function starts from the root and recursively traverses through the children nodes, printing characters as it goes.

5. In the main function, create an instance of the Trie class, insert the words "war," "cooky," "cool," "code," and "cow," and then call the display function to perform the bottom-up traversal and display the characters.

Code Solution

• C++
• Java
• C#
• Python
• Ruby
• Php
• Node Js

/*
Java program
Trie Bottom-Up Traversal
*/
#include <iostream>

#include <string.h>

#define ALPHABETS 26

using namespace std;
class Node {
  public:
  bool end;
  Node *children[ALPHABETS];
  Node() {
    this->end = false;
    for (int i = 0; i < ALPHABETS; ++i) {
      this->children[i] = NULL;
    }
  }
};
class Trie {
  public:
    Node *root;
  Trie() {
    this->root = new Node();
  }
  void insert(string text) {
    int length = text.size();
    int index = 0;
    Node *head = this->root;
    int level = 0;
    while (level < length) {
      index = text[level] - 'a';
      if (head->children[index] == NULL) {
        head->children[index] = new Node();
      }
      head = head->children[index];
      level++;
    }
    if (head != NULL) {
      head->end = true;
    }
  }
  void display(Node *head) {
    if (head != NULL) {
      int i = 0;
      while (i < ALPHABETS) {
        if (head->children[i] != NULL) {
          this->display(head->children[i]);
          cout <<"  "<< (char)(i + 97);
        }
        i++;
      }
    }
  }
};
int main() {
  Trie obj;
  /*
       root
       /   \
      c     w   
      |     |
      o     a  
      | \   |
      o  w  r
    / | \ 
    d k  l
    | |
    e y
  */
  obj.insert("war");
  obj.insert("cooky");
  obj.insert("cool");
  obj.insert("code");
  obj.insert("cow");
  obj.display(obj.root);
}

 e  d  y  k  l  o  w  o  c  r  a  w

/*
Java program
Trie Bottom-Up Traversal
*/
class Node {
  //Indicates end of string
  public boolean end;

  public Node[] children;

  public Node(int size) {
    end = false;
    children = new Node[size];
  }
}
public class Trie 
{ 
  public 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 void display(Node root)
  {

    if(root!=null)
    {

      for (int i = 0; i < ALPHABETS ; i++ ) 
      {
        if(root.children[i] != null)
        {
          display(root.children[i]);

          System.out.print(" "+(char)(i+97));
        }    
      }
    }
  }

  public static void main(String[] args) 
  {
    //Make object
    Trie obj = new Trie();
    obj.insert("war");
    obj.insert("cooky");
    obj.insert("cool");
    obj.insert("code");
    obj.insert("cow");


  /*
       root
       /   \
      c     w   
      |     |
      o     a  
      | \   |
      o  w  r
    / | \ 
    d k  l
    | |
    e y
  */

    obj.display(obj.root);
  }
}

 e d y k l o w o c r a w

/*
C# program
Trie Bottom-Up Traversal
*/
using System;
public class Node {
	//Indicates end of string
	public Boolean end;

	public Node[] children;

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

	public Node root;

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

	public void insert(String text) {
		//first get the.Length of text
		int size = 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 < size; 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 void display(Node root)
	{

		if(root!=null)
		{

			for (int i = 0; i < ALPHABETS ; i++ ) 
			{
				if(root.children[i] != null)
				{
					display(root.children[i]);

					Console.Write(" "+(char)(i+97));
				}    
			}
		}
	}

	public static void Main(String[] args) 
	{
		//Make object
		Trie obj = new Trie();
		obj.insert("war");
		obj.insert("cooky");
		obj.insert("cool");
		obj.insert("code");
		obj.insert("cow");


		/*
       root
       /   \
      c     w   
      |     |
      o     a  
      | \   |
      o  w  r
    / | \ 
    d k  l
    | |
    e y
    */

		obj.display(obj.root);
	}
}

 e d y k l o w o c r a w

#Python3 Program
#Trie Bottom-Up Traversal
class Node :

  def __init__(self, size) :
    self.end = False
    self.children = [None]*size
  

class Trie :

  def __init__(self) :
    self.ALPHABETS = 26
    self.root = Node(self.ALPHABETS)
  
  def insert(self, text) :
    length = len(text)
    index = 0
    head = self.root
    level = 0
    while (level < length) :
      index = ord(text[level]) - ord('a')
      if (head.children[index] == None) :
        head.children[index] = Node(self.ALPHABETS)
      
      head = head.children[index]
      level += 1
    
    if (head != None) :
      head.end = True
    
  
  def display(self, head) :
    if (head != None) :
      i = 0
      while (i < self.ALPHABETS) :
        if (head.children[i] != None) :
          self.display(head.children[i])
          print(chr(i + 97),end=" ")
        
        i += 1
      
    
  
def main() :
  obj = Trie()

  #       root
  #       /   \
  #      c     w
  #      |     |
  #      o     a
  #      | \   |
  #      o  w  r
  #    / | \
  #    d k  l
  #    | |
  #    e y

  obj.insert("war")
  obj.insert("cooky")
  obj.insert("cool")
  obj.insert("code")
  obj.insert("cow")
  obj.display(obj.root)
  

if __name__ == "__main__":
  main()

e d y k l o w o c r a w

# Java program
# Trie Bottom-Up Traversal

class Node
	attr_reader :end, :children
	attr_accessor :end, :children
	def initialize(size) 
		@end = false
		@children = Array.new(size){nil}
	end
end

class Trie
	attr_reader :ALPHABETS, :root
	attr_accessor :ALPHABETS, :root
	def initialize() 
		@ALPHABETS = 26
		@root = Node.new(@ALPHABETS)
	end
	def insert(text) 
		size = text.length
		location = 0
		head = @root
		level = 0
		while (level < size) 
			location = text[level].ord - 'a'.ord
			if (head.children[location] == nil) 
				head.children[location] = Node.new(@ALPHABETS)
			end
			head = head.children[location]
			level += 1
		end
		if (head != nil) 
			head.end = true
		end
	end
	def display(head) 
		if (head != nil) 
			i = 0
			while (i < @ALPHABETS) 
				if (head.children[i] != nil) 
					self.display(head.children[i])
					print(" " , (i + 97).chr)
				end
				i += 1
			end
		end
	end
end

def main() 
	obj = Trie.new()

	#
	#       root
	#       /   \
	#      c     w
	#      |     |
	#      o     a
	#      | \   |
	#      o  w  r
	#    / | \
	#    d k  l
	#    | |
	#    e y
	#    
	obj.insert("war")
	obj.insert("cooky")
	obj.insert("cool")
	obj.insert("code")
	obj.insert("cow")
	obj.display(obj.root)
end
main()

 e d y k l o w o c r a w

<?php
/*
  Php Program
  Trie Bottom-Up Traversal
*/
class Node {
  public $end;
  public $children = [];

  function __construct($size) {
    $this->end = false;
    $this->children = array_fill(0, $size, null);
  }
}
class Trie {
  private $ALPHABETS;
  public $root;

  function __construct() {
    $this->ALPHABETS = 26;
    $this->root = new Node($this->ALPHABETS);
  }

  public  function insert($text) {
    $size = strlen($text);
    $index = 0;
    $head = $this->root;
    $level = 0;
    while ($level < $size) {
      $index =  ord($text[$level]) - ord('a');
      if ($head->children[$index] == null) {
        $head->children[$index] = new Node($this->ALPHABETS);
      }
      $head = $head->children[$index];
      $level++;
    }
    if ($head != null) {
      $head->end = true;
    }
  }
  public  function display($head) {
    if ($head != null) {
      $i = 0;
      while ($i < $this->ALPHABETS) {
        if ($head->children[$i] != null) {
          $this->display($head->children[$i]);
          echo (" ". chr($i + 97));
        }
        $i++;
      }
    }
  }
}

function main() {
  $obj = new Trie();
  /*
        root
       /   \
      c     w
      |     |
      o     a
      | \   |
      o  w  r
    / | \ 
    d k  l
    | |
    e y
  */
  $obj->insert("war");
  $obj->insert("cooky");
  $obj->insert("cool");
  $obj->insert("code");
  $obj->insert("cow");
  $obj->display($obj->root);
}
main();

 e d y k l o w o c r a w

/*
  Node Js Program
  Trie Bottom-Up Traversal
*/
class Node {
	
	constructor(size) {
		this.end = false;
		this.children = new Array(size).fill(null);
	}
}
class Trie {
	
	constructor() {
		this.ALPHABETS = 26;
		this.root = new Node(this.ALPHABETS);
	}
	insert(text) {
		var size = text.length;
		var index = 0;
		var head = this.root;
		var level = 0;
		while (level < size) {
			index = text.charCodeAt(level) - 'a'.charCodeAt(0);
			if (head.children[index] == null) {
				head.children[index] = new Node(this.ALPHABETS);
			}
			head = head.children[index];
			level++;
		}
		if (head != null) {
			head.end = true;
		}
	}
	display(head) {
		if (head != null) {
			var i = 0;
			while (i < this.ALPHABETS) {
				if (head.children[i] != null) {
					this.display(head.children[i]);
					process.stdout.write(" " + String.fromCharCode(i + 97));
				}
				i++;
			}
		}
	}



}
function main() {
	var obj = new Trie();
	/*
	        root
	       /   \
	      c     w
	      |     |
	      o     a
	      | \   |
	      o  w  r
	    / | \ 
	    d k  l
	    | |
	    e y
	 */
	obj.insert("war");
	obj.insert("cooky");
	obj.insert("cool");
	obj.insert("code");
	obj.insert("cow");
	obj.display(obj.root);
}
main();

 e d y k l o w o c r a w

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 bottom-up traversal (displaying characters) is also 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.