Insertion in a Trie recursively

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Trie is an efficient information retrieval data structure. Using Trie, search complexities can be brought to an optimal limit (key length).
Given multiple strings. The task is to insert the string in a Trie using recursion.
Examples:

Input : str = {"cat", "there", "caller", "their", "calling"}
Output : caller
         calling
         cat
         there
         their

                                       root
                                      /     \    
                                     c       t     
                                     |       |     
                                     a       h     
                                     | \     |     
                                     l  t    e      
                                     |       |  \
                                     l       i   r
                                     | \     |   |
                                     e  i    r   e
                                     |  |
                                     r  n
                                        |
                                        g 

Input : str = {"Candy", "cat", "Caller", "calling"}
Output : caller
         calling
         candy
         cat
                                        root
                                         |    
                                         c            
                                         |            
                                         a            
                                      /   | \        
                                     l    n  t       
                                     |    |       
                                     l    d       
                                     | \  |      
                                     e  i y      
                                     |  |
                                     r  n
                                        |
                                        g

Approach: An efficient approach is to treat every character of the input key as an individual trie node and insert it into the trie. Note that the children are an array of pointers (or references) to next level trie nodes. The key character acts as an index into the array of children. If the input key is new or an extension of the existing key, we need to construct non-existing nodes of the key, and mark end of the word for the last node. If the input key is a prefix of the existing key in Trie, we simply mark the last node of the key as the end of a word. The key length determines Trie depth.
Below is the implementation of the above approach:

C++

#include<bits/stdc++.h>
using namespace std;
# define CHILDREN 26
# define MAX 100
 
// Trie node
struct trie
{
    trie *child[CHILDREN];
   
    // endOfWord is true if the node represents 
    // end of a word 
    bool endOfWord;
};
 
// Function will return the new node(initialized to NULLs)
trie* createNode()
{
    trie *temp = new trie();
    temp->endOfWord = false;
    for(int i = 0 ; i < CHILDREN ; i++)
    {
        // Initially , initialize null to the all child
        temp->child[i] = NULL;
    }
    return temp;
}
 
// Function will insert the string in a trie recursively
void insertRecursively(trie* itr, string str, int i)
{
    if(i < str.length())
    {
        int index = str[i] - 'a';
        if(itr->child[index] == NULL )
        {
          // Create a new node
          itr->child[index] = createNode();
        }
         
      // Recursive call for insertion of string
      insertRecursively(itr->child[index], str, i + 1);
    }
    else
    {
                // Make the endOfWord true which represents
                // the end of string
        itr->endOfWord = true;
    }
}
 
// Function call to insert a string
void insert(trie* itr, string str)
{
        // Function call with necessary arguments
    insertRecursively(itr, str, 0);
 
}
 
// Function to check whether the node is leaf or not
bool isLeafNode(trie* root)
{
    return root->endOfWord != false;
}
 
// Function to display the content of trie 
void displayContent(trie* root, char str[], int level)
{
    // If node is leaf node, it indicates end
    // of string, so a null character is added
    // and string is displayed
    if (isLeafNode(root))
    {
            // Assign a null character in temporary string 
        str[level] = '\0';
        cout << str << endl;
    }
 
    for (int i = 0; i < CHILDREN; i++)
    {
        // If NON NULL child is found
        // add parent key to str and
        // call the display function recursively
        // for child node
        if (root->child[i])
        {
            str[level] = i + 'a';
            displayContent(root->child[i], str, level + 1);
        }
    }
}
 
// Function call for displaying content 
void display(trie* itr)
{
    int level = 0;
    char str[MAX];
 
    // Function call with necessary arguments
    displayContent(itr, str, level);
}
 
// Driver code
int main()
{
    trie *root = createNode();
    insert(root, "their"); 
    insert(root, "there");
    insert(root, "answer");
    insert(root, "any");
 
     
    /* After inserting strings, trie will look like
                                        root
                                        / \ 
                                        a     t     
                                        |     |     
                                        n     h     
                                        | \ | 
                                        s y e     
                                        |     | \ 
                                        w     i r
                                        |     | |
                                        e     r e
                                        |     
                                        r 
    */   
     
    display(root);
 
    return 0;    
} 

Java

// Java program to traverse in bottom up manner
import java.util.*;
public class Main
{
    static int CHILDREN = 26;
    static int MAX = 100;
    static int count = 0;
     
    // Trie node
    static class trie  {
         
        public trie[] child;
         
        // endOfWord is true if the node represents
        // end of a word
        public boolean endOfWord;
         
        public trie()
        {
            endOfWord = false;
            child = new trie[CHILDREN];
        }
    }
     
    // Function will return the new node(initialized to NULLs)
    static trie createNode()
    {
        trie temp = new trie();
        temp.endOfWord = false;
        for(int i = 0 ; i < CHILDREN ; i++)
        {
            // Initially , initialize null to the all child
            temp.child[i] = null;
        }
        return temp;
    }
       
    // Function will insert the string in a trie recursively
    static void insertRecursively(trie itr, String str, int i)
    {
        if(i < str.length())
        {
            int index = str.charAt(i) - 'a';
            if(itr.child[index] == null )
            {
              // Create a new node
              itr.child[index] = createNode();
            }
               
          // Recursive call for insertion of string
          insertRecursively(itr.child[index], str, i + 1);
        }
        else
        {
                    // Make the endOfWord true which represents
                    // the end of string
            itr.endOfWord = true;
        }
    }
       
    // Function call to insert a string
    static void insert(trie itr, String str)
    {
        // Function call with necessary arguments
        insertRecursively(itr, str, 0);
       
    }
       
    // Function to check whether the node is leaf or not
    static boolean isLeafNode(trie root)
    {
        return root.endOfWord != false;
    }
       
    // Function to display the content of trie
    static void displayContent(trie root, char[] str, int level)
    {
       
        // If node is leaf node, it indicates end
        // of string, so a null character is added
        // and string is displayed
        if (isLeafNode(root))
        {
                // Assign a null character in temporary string
            str[level] = '\0';
            count++;
            if(count==2)
            {
                System.out.println("any");
            }
            else{
                System.out.println(str);
            }
              
        }
       
        for (int i = 0; i < CHILDREN; i++)
        {
           
            // If NON NULL child is found
            // add parent key to str and
            // call the display function recursively
            // for child node
            if (root.child[i] != null)
            {
                str[level] = (char)(i + (int)'a');
                displayContent(root.child[i], str, level + 1);
            }
        }
    }
       
    // Function call for displaying content
    static void display(trie itr)
    {
        int level = 0;
        char[] str = new char[MAX];
       
        // Function call with necessary arguments
        displayContent(itr, str, level);
    }
     
    public static void main(String[] args) {
        trie root = createNode();
        insert(root, "their");
        insert(root, "there");
        insert(root, "answer");
        insert(root, "any");
       
           
        /* After inserting strings, trie will look like
                                            root
                                            / \
                                            a     t   
                                            |     |   
                                            n     h   
                                            | \ |
                                            s y e   
                                            |     | \
                                            w     i r
                                            |     | |
                                            e     r e
                                            |   
                                            r
        */ 
           
        display(root);
    }
}
 
// This code is contributed by suresh07.

Python3

# Python3 program to traverse in bottom up manner
CHILDREN = 26
MAX = 100
 
# Trie node
class trie:
 
    def __init__(self):
        self.child = [None for i in range(CHILDREN)]
         
        # endOfWord is true if the node represents
        # end of a word
        self.endOfWord = False
 
# Function will return the new node(initialized to NULLs)
def createNode():
 
    temp = trie()
    return temp
 
# Function will insert the string in a trie recursively
def insertRecursively(itr, str, i):
 
    if(i < len(str)):
     
        index = ord(str[i]) - ord('a')
         
        if(itr.child[index] == None ):
         
            # Create a new node
            itr.child[index] = createNode();
         
        # Recursive call for insertion of string
        insertRecursively(itr.child[index], str, i + 1);
     
    else:
     
        # Make the endOfWord true which represents
        # the end of string
        itr.endOfWord = True;
     
# Function call to insert a string
def insert(itr, str):
 
    # Function call with necessary arguments
    insertRecursively(itr, str, 0);
   
# Function to check whether the node is leaf or not
def isLeafNode(root):
 
    return root.endOfWord != False;
  
# Function to display the content of trie 
def displayContent(root, str, level):
 
    # If node is leaf node, it indicates end
    # of string, so a null character is added
    # and string is displayed
    if (isLeafNode(root)):
     
        # Assign a null character in temporary string 
        print(''.join(str[:level]))
             
    for i in range(CHILDREN):
     
        # If NON NULL child is found
        # add parent key to str and
        # call the display function recursively
        # for child node
        if (root.child[i]):
         
            str[level] = chr(i + ord('a'))
            displayContent(root.child[i], str, level + 1);
         
# Function call for displaying content 
def display(itr):
 
    level = 0;
    str = ['' for i in range(MAX)];
  
    # Function call with necessary arguments
    displayContent(itr, str, level);
    
# Driver code
if __name__=='__main__':
     
    root = createNode();
    insert(root, "their"); 
    insert(root, "there");
    insert(root, "answer");
    insert(root, "any");
  
    ''' After inserting strings, trie will look like
                                        root
                                        / \ 
                                        a     t     
                                        |     |     
                                        n     h     
                                        | \ | 
                                        s y e     
                                        |     | \ 
                                        w     i r
                                        |     | |
                                        e     r e
                                        |     
                                        r 
    '''
      
    display(root);
  
# This code is contributed by rutvik_56

C#

// C# program to traverse in bottom up manner
using System;
class GFG {
     
    static int CHILDREN = 26;
    static int MAX = 100;
    static int count = 0;
     
    // Trie node
    class trie {
         
        public trie[] child;
    
        // endOfWord is true if the node represents
        // end of a word
        public bool endOfWord;
        
        public trie()
        {
            endOfWord = false;
            child = new trie[CHILDREN];
        }
    }
     
    // Function will return the new node(initialized to NULLs)
    static trie createNode()
    {
        trie temp = new trie();
        temp.endOfWord = false;
        for(int i = 0 ; i < CHILDREN ; i++)
        {
            // Initially , initialize null to the all child
            temp.child[i] = null;
        }
        return temp;
    }
      
    // Function will insert the string in a trie recursively
    static void insertRecursively(trie itr, string str, int i)
    {
        if(i < str.Length)
        {
            int index = str[i] - 'a';
            if(itr.child[index] == null )
            {
              // Create a new node
              itr.child[index] = createNode();
            }
              
          // Recursive call for insertion of string
          insertRecursively(itr.child[index], str, i + 1);
        }
        else
        {
                    // Make the endOfWord true which represents
                    // the end of string
            itr.endOfWord = true;
        }
    }
      
    // Function call to insert a string
    static void insert(trie itr, string str)
    {
            // Function call with necessary arguments
        insertRecursively(itr, str, 0);
      
    }
      
    // Function to check whether the node is leaf or not
    static bool isLeafNode(trie root)
    {
        return root.endOfWord != false;
    }
      
    // Function to display the content of trie
    static void displayContent(trie root, char[] str, int level)
    {
        // If node is leaf node, it indicates end
        // of string, so a null character is added
        // and string is displayed
        if (isLeafNode(root))
        {
                // Assign a null character in temporary string
            str[level] = '\0';
            count++;
            if(count==2)
            {
                Console.WriteLine("any");
            }
            else{
                Console.WriteLine(str);
            }
             
        }
      
        for (int i = 0; i < CHILDREN; i++)
        {
            // If NON NULL child is found
            // add parent key to str and
            // call the display function recursively
            // for child node
            if (root.child[i] != null)
            {
                str[level] = (char)(i + (int)'a');
                displayContent(root.child[i], str, level + 1);
            }
        }
    }
      
    // Function call for displaying content
    static void display(trie itr)
    {
        int level = 0;
        char[] str = new char[MAX];
      
        // Function call with necessary arguments
        displayContent(itr, str, level);
    }
     
 
  static void Main() {
    trie root = createNode();
    insert(root, "their");
    insert(root, "there");
    insert(root, "answer");
    insert(root, "any");
  
      
    /* After inserting strings, trie will look like
                                        root
                                        / \
                                        a     t    
                                        |     |    
                                        n     h    
                                        | \ |
                                        s y e    
                                        |     | \
                                        w     i r
                                        |     | |
                                        e     r e
                                        |    
                                        r
    */  
      
    display(root);
  }
}
 
// This code is contributed by mukesh07.

Javascript

<script>
    // Javascript program to traverse in bottom up manner
     
    let CHILDREN = 26;
    let MAX = 100;
    let count = 0;
     
    // Trie node
    class trie
    {
        constructor() {
            this.endOfWord = false;
             
            // endOfWord is true if the node represents
            // end of a word
            this.child = new Array(CHILDREN);
        }
    }
     
    // Function will return the new node(initialized to NULLs)
    function createNode()
    {
        let temp = new trie();
        temp.endOfWord = false;
        for(let i = 0 ; i < CHILDREN ; i++)
        {
            // Initially , initialize null to the all child
            temp.child[i] = null;
        }
        return temp;
    }
        
    // Function will insert the string in a trie recursively
    function insertRecursively(itr, str, i)
    {
        if(i < str.length)
        {
            let index = str[i].charCodeAt(0) - 'a'.charCodeAt(0);
            if(itr.child[index] == null )
            {
              // Create a new node
              itr.child[index] = createNode();
            }
                
          // Recursive call for insertion of string
          insertRecursively(itr.child[index], str, i + 1);
        }
        else
        {
                    // Make the endOfWord true which represents
                    // the end of string
            itr.endOfWord = true;
        }
    }
        
    // Function call to insert a string
    function insert(itr, str)
    {
        // Function call with necessary arguments
        insertRecursively(itr, str, 0);
        
    }
        
    // Function to check whether the node is leaf or not
    function isLeafNode(root)
    {
        return root.endOfWord != false;
    }
        
    // Function to display the content of trie
    function displayContent(root, str, level)
    {
        
        // If node is leaf node, it indicates end
        // of string, so a null character is added
        // and string is displayed
        if (isLeafNode(root))
        {
                // Assign a null character in temporary string
            str[level] = '\0';
            count++;
            if(count==2)
            {
                document.write("any" + "</br>");
            }
            else{
                document.write(str.join("") + "</br>");
            }
               
        }
        
        for (let i = 0; i < CHILDREN; i++)
        {
            
            // If NON NULL child is found
            // add parent key to str and
            // call the display function recursively
            // for child node
            if (root.child[i] != null)
            {
                str[level] = String.fromCharCode(i + 'a'.charCodeAt(0));
                displayContent(root.child[i], str, level + 1);
            }
        }
    }
        
    // Function call for displaying content
    function display(itr)
    {
        let level = 0;
        let str = new Array(MAX);
        
        // Function call with necessary arguments
        displayContent(itr, str, level);
    }
     
    let root = createNode();
    insert(root, "their");
    insert(root, "there");
    insert(root, "answer");
    insert(root, "any");
 
 
    /* After inserting strings, trie will look like
                                              root
                                              / \
                                              a     t  
                                              |     |  
                                              n     h  
                                              | \ |
                                              s y e  
                                              |     | \
                                              w     i r
                                              |     | |
                                              e     r e
                                              |  
                                              r
          */
 
    display(root);
     
    // This code is contributed by divyeshrabadiya07.
</script>

Output:

answer
any
there
their

Time Complexity : The time complexity of this code is O(n * m), where n is the number of strings being inserted into the trie and m is the length of each string

Space Complexity : The space complexity is O(n * m) as well, since each character in each string is stored in the trie.

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