Bottom-up traversal of a Trie

Trie is an efficient information retrieval data structure. Using Trie, search complexities can be brought to an optimal limit (key length). 
Given a trie. The task is to print the characters in a bottom-up manner

Bottom-up traversal: 

First print string of left most subtree(from bottom to top) then print string of second left subtree(from bottom to top) then print for third left subtree and so on.

It is similar to post-order traversal of a tree

Example:

    
Input :
                                          root
                                         /    \    
                                         a     t     
                                         |     |     
                                         n     h     
                                         | \   |   
                                         s  y  e     
                                         |     |  \ 
                                         w     i   r
                                         |     |   |
                                         e     r   e
                                         |        
                                         r        
Output : r, e, w, s, y, n, a, r, i, e, r, e, h, t  

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

Output : r, e, g, n, i, l, l, t, a, c, r, i, e, r, e, h, t

Explanation : 
In the first example, the root has two parts. First part contains strings: “answer” and “any”. 
the second part with strings “their” and “there”. 

• Now first we got to left subtree containing strings “answer” and “any” which separates by character ‘n’. Now ‘n’ separates two-part of characters ‘s’, ‘w’, ‘e’, ‘r’ and ‘y’. so print ‘s’, ‘w’, ‘e’, ‘r’ in reverse order then print ‘y’ and go up and print ‘n'(which separates string) then go up and print ‘a’. Now first left subtree has printed in bottom up manner ‘r’, ‘e’, ‘w’, ‘s’, ‘y’, ‘n’, ‘a’.
• Do the same thing for another subtree of the root which contains strings “their” and “there” which is separated by character ‘e’.

Approach : 
The idea to do this is to start traversing from the root node of the trie, whenever we find a NON-NULL child node, we recursively move ahead when we get “NULL” we return simply and print the value of current node and same goes un till we find the node which is a leaf node, which actually marks the end of the string.

Below is the implementation of the above approach :

C++

// CPP program to traverse in bottom up manner
#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++) {
        // Initialise all child to the null, initially
        temp->child[i] = NULL;
    }

    // Return newly created node
    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) {
            // Assigning a newly created node
            itr->child[index] = createNode();
        }
        // Recursive call for insertion
        // of a string in a trie
        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 print traverse
// the tree in bottom to top manner
void printPattern(trie* itr)
{
    // Base condition
    if (itr == NULL)
        return;

    // Loop for printing t a value of character
    for (int i = 0; i < CHILDREN; i++) {

        // Recursive call for print pattern
        printPattern(itr->child[i]);
        if (itr->child[i] != NULL) {
            char ch = (i + 97);
            cout << ch << ", "; // Print character
        }
    }
}

// Driver code
int main()
{
    trie* root = createNode();

    // Function to insert a string
    insert(root, "their");
    insert(root, "there");
    insert(root, "answer");
    insert(root, "any");


    // Function call for printing a pattern
    printPattern(root);

    return 0;
}

Java

// Java program to traverse in bottom up manner
public class Main
{
    static int CHILDREN = 26;

    // Trie node
    static class trie {

        public boolean endOfWord;
        public trie[] child;

        public trie()
        {
            endOfWord = false;

            // endOfWord is true if the node represents
            // end of a word
            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++)
        {

            // Initialise all child to the null, initially
            temp.child[i] = null;
        }

        // Return newly created node
        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)
            {

                // Assigning a newly created node
                itr.child[index] = createNode();
            }

            // Recursive call for insertion
            // of a string in a trie
            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 print traverse
    // the tree in bottom to top manner
    static void printPattern(trie itr)
    {

        // Base condition
        if (itr == null)
            return;

        // Loop for printing t a value of character
        for (int i = 0; i < CHILDREN; i++) {

            // Recursive call for print pattern
            printPattern(itr.child[i]);
            if (itr.child[i] != null) {
                char ch = (char)(i + 97);
                System.out.print(ch + ", "); // Print character
            }
        }
    }

    public static void main(String[] args) {
        trie root = createNode();

        // Function to insert a string
        insert(root, "their");
        insert(root, "there");
        insert(root, "answer");
        insert(root, "any");


        // Function call for printing a pattern
        printPattern(root);
    }
}

// This code is contributed by divyesh072019.

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):

            # Assigning a newly created node
            itr.child[index] = createNode()

        # Recursive call for insertion
        # of a string in a trie
        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 print traverse
# the tree in bottom to top manner
def printPattern(itr):

    # Base condition
    if(itr == None):
        return

    # Loop for printing t a value of character
    for i in range(CHILDREN):

        # Recursive call for print pattern
        printPattern(itr.child[i])
        if (itr.child[i] != None):
            ch = chr(i + 97)

            # Print character
            print(ch,end=', ')

# Driver code
if __name__=='__main__':

    root = createNode()

    # Function to insert a string
    insert(root, "their")
    insert(root, "there")
    insert(root, "answer")
    insert(root, "any")

    # Function call for printing a pattern
    printPattern(root)

    # This code is countributed by rutvik_56

C#

// C# program to traverse in bottom up manner
using System;
class GFG {

    static int CHILDREN = 26;

    // Trie node
    class trie {

        public bool endOfWord;
        public trie[] child;

        public trie()
        {
            endOfWord = false;

            // endOfWord is true if the node represents
            // end of a word
            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++)
        {

            // Initialise all child to the null, initially
            temp.child[i] = null;
        }

        // Return newly created node
        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)
            {

                // Assigning a newly created node
                itr.child[index] = createNode();
            }

            // Recursive call for insertion
            // of a string in a trie
            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 print traverse
    // the tree in bottom to top manner
    static void printPattern(trie itr)
    {

        // Base condition
        if (itr == null)
            return;

        // Loop for printing t a value of character
        for (int i = 0; i < CHILDREN; i++) {

            // Recursive call for print pattern
            printPattern(itr.child[i]);
            if (itr.child[i] != null) {
                char ch = (char)(i + 97);
                Console.Write(ch + ", "); // Print character
            }
        }
    }

  static void Main() {
    trie root = createNode();

    // Function to insert a string
    insert(root, "their");
    insert(root, "there");
    insert(root, "answer");
    insert(root, "any");


    // Function call for printing a pattern
    printPattern(root);
  }
}

// This code is contributed by mukesh07.

Javascript

<script>
    // Javascript program to traverse in bottom up manner
    let CHILDREN = 26;

    // Trie node
    class trie
    {
        constructor()
        {

           // endOfWord is true if the node represents
           // end of a word
           this.child = new Array(CHILDREN);
           this.endOfWord = false;
        }
    }

    // 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++)
        {

            // Initialise all child to the null, initially
            temp.child[i] = null;
        }

        // Return newly created node
        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() - 'a'.charCodeAt();
            if (itr.child[index] == null)
            {

                // Assigning a newly created node
                itr.child[index] = createNode();
            }

            // Recursive call for insertion
            // of a string in a trie
            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 print traverse
    // the tree in bottom to top manner
    function printPattern(itr)
    {

        // Base condition
        if (itr == null)
            return;

        // Loop for printing t a value of character
        for (let i = 0; i < CHILDREN; i++) {

            // Recursive call for print pattern
            printPattern(itr.child[i]);
            if (itr.child[i] != null) {
                let ch = String.fromCharCode(i + 97);
                document.write(ch + ", "); // Print character
            }
        }
    }

    let root = createNode();

    // Function to insert a string
    insert(root, "their");
    insert(root, "there");
    insert(root, "answer");
    insert(root, "any");


    // Function call for printing a pattern
    printPattern(root);

    // This code is contributed by suresh07.
</script>

Output

r, e, w, s, y, n, a, r, i, e, r, e, h, t, 

Time Complexity: O(n), where ‘n’ is the Total length of the given words(approx). Since Program will go through each and every node in the trie to print
Auxiliary Space: O(n*CHILDREN), where ‘n’ represents the number of alphabets in the trie and CHILDREN is the number of children per node(which is 26 in this case). Since Program will go to each and every node in trie to print.