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# 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

``````/*
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;
int level = 0;
while (level < length) {
index = text[level] - 'a';
}
level++;
}
}
}
int i = 0;
while (i < ALPHABETS) {
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);
}```
```

#### Output

`` 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

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

//When need to add new Node
}

}
//Indicates end of string
}
}
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);
}
}```
```

#### Output

`` 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

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

//When need to add new Node
}

}
//indicates end of string
}
}
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);
}
}```
```

#### Output

`` 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
level = 0
while (level < length) :
index = ord(text[level]) - ord('a')

level += 1

i = 0
while (i < self.ALPHABETS) :
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()```
```

#### Output

``e d y k l o w o c r a w``
``````# Java program
# Trie Bottom-Up Traversal

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

class Trie
attr_accessor :ALPHABETS, :root
def initialize()
@ALPHABETS = 26
@root = Node.new(@ALPHABETS)
end
def insert(text)
size = text.length
location = 0
level = 0
while (level < size)
location = text[level].ord - 'a'.ord
end
level += 1
end
end
end
i = 0
while (i < @ALPHABETS)
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()
```
```

#### Output

`` 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;
\$level = 0;
while (\$level < \$size) {
\$index =  ord(\$text[\$level]) - ord('a');
}
\$level++;
}
}
}
\$i = 0;
while (\$i < \$this->ALPHABETS) {
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();```
```

#### Output

`` 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 level = 0;
while (level < size) {
index = text.charCodeAt(level) - 'a'.charCodeAt(0);
}
level++;
}
}
}
var i = 0;
while (i < this.ALPHABETS) {
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();```
```

#### Output

`` 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.

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