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, e, r, e, r, e, i, h, t,