Insertion in a Trie recursively

02 Dec, 2021
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++
Java
Python3
C#
Javascript
#include<bits/stdc++.h>using namespace std;# define CHILDREN 26# define MAX 100 // Trie nodestruct 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 recursivelyvoid 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 stringvoid insert(trie* itr, string str){        // Function call with necessary arguments    insertRecursively(itr, str, 0); } // Function to check whether the node is leaf or notbool isLeafNode(trie* root){    return root->endOfWord != false;} // Function to display the content of trievoid 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 contentvoid display(trie* itr){    int level = 0;    char str[MAX];     // Function call with necessary arguments    displayContent(itr, str, level);} // Driver codeint 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 program to traverse in bottom up mannerimport 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 program to traverse in bottom up mannerCHILDREN = 26MAX = 100 # Trie nodeclass 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 recursivelydef 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 stringdef insert(itr, str):     # Function call with necessary arguments    insertRecursively(itr, str, 0);   # Function to check whether the node is leaf or notdef isLeafNode(root):     return root.endOfWord != False;  # Function to display the content of triedef 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 contentdef display(itr):     level = 0;    str = ['' for i in range(MAX)];      # Function call with necessary arguments    displayContent(itr, str, level);    # Driver codeif __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# program to traverse in bottom up mannerusing 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.
<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
 
Akanksha_Rai
rutvik_56
arorakashish0911
mukesh07
surindertarika1234
suresh07
divyeshrabadiya07
Trie
Advanced Data Structure
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Recursion
Trie
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