Given a sequence of words, print all anagrams together | Set 2

Given an array of words, print all anagrams together. For example, if the given array is {“cat”, “dog”, “tac”, “god”, “act”}, then output may be “cat tac act dog god”.

We have discussed two different methods in the previous post. In this post, a more efficient solution is discussed.
Trie data structure can be used for a more efficient solution. Insert the sorted order of each word in the trie. Since all the anagrams will end at the same leaf node. We can start a linked list at the leaf nodes where each node represents the index of the original array of words. Finally, traverse the Trie. While traversing the Trie, traverse each linked list one line at a time. Following are the detailed steps.
1) Create an empty Trie 
2) One by one take all words of input sequence. Do following for each word 
…a) Copy the word to a buffer. 
…b) Sort the buffer 
…c) Insert the sorted buffer and index of this word to Trie. Each leaf node of Trie is head of a Index list. The Index list stores index of words in original sequence. If sorted buffer is already present, we insert index of this word to the index list. 
3) Traverse Trie. While traversing, if you reach a leaf node, traverse the index list. And print all words using the index obtained from Index list. 

Below is the implementation of the above approach:

C++

// An efficient program to print all anagrams together
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>

#define NO_OF_CHARS 26

// Structure to represent list node for indexes of words in
// the given sequence. The list nodes are used to connect
// anagrams at leaf nodes of Trie
struct IndexNode
{
    int index;
    struct IndexNode* next;
};

// Structure to represent a Trie Node
struct TrieNode
{
    bool isEnd;  // indicates end of word
    struct TrieNode* child[NO_OF_CHARS]; // 26 slots each for 'a' to 'z'
    struct IndexNode* head; // head of the index list
};


// A utility function to create a new Trie node
struct TrieNode* newTrieNode()
{
    struct TrieNode* temp = new TrieNode;
    temp->isEnd = 0;
    temp->head = NULL;
    for (int i = 0; i < NO_OF_CHARS; ++i)
        temp->child[i] = NULL;
    return temp;
}

/* Following function is needed for library function qsort(). Refer
   http://www.cplusplus.com/reference/clibrary/cstdlib/qsort/ */
int compare(const void* a, const void* b)
{  return *(char*)a - *(char*)b; }

/* A utility function to create a new linked list node */
struct IndexNode* newIndexNode(int index)
{
    struct IndexNode* temp = new IndexNode;
    temp->index = index;
    temp->next = NULL;
    return temp;
}

// A utility function to insert a word to Trie
void insert(struct TrieNode** root, char* word, int index)
{
    // Base case
    if (*root == NULL)
        *root = newTrieNode();

    if (*word != '\0')
        insert( &( (*root)->child[tolower(*word) - 'a'] ), word+1, index );
    else  // If end of the word reached
    {
        // Insert index of this word to end of index linked list
        if ((*root)->isEnd)
        {
            IndexNode* pCrawl = (*root)->head;
            while( pCrawl->next )
                pCrawl = pCrawl->next;
            pCrawl->next = newIndexNode(index);
        }
        else  // If Index list is empty
        {
            (*root)->isEnd = 1;
            (*root)->head = newIndexNode(index);
        }
    }
}

// This function traverses the built trie. When a leaf node is reached,
// all words connected at that leaf node are anagrams. So it traverses
// the list at leaf node and uses stored index to print original words
void printAnagramsUtil(struct TrieNode* root, char *wordArr[])
{
    if (root == NULL)
        return;

    // If a lead node is reached, print all anagrams using the indexes
    // stored in index linked list
    if (root->isEnd)
    {
        // traverse the list
        IndexNode* pCrawl = root->head;
        while (pCrawl != NULL)
        {
            printf( "%s ", wordArr[ pCrawl->index ] );
            pCrawl = pCrawl->next;
        }
    }

    for (int i = 0; i < NO_OF_CHARS; ++i)
        printAnagramsUtil(root->child[i], wordArr);
}

// The main function that prints all anagrams together. wordArr[] is input
// sequence of words.
void printAnagramsTogether(char* wordArr[], int size)
{
    // Create an empty Trie
    struct TrieNode* root = NULL;

    // Iterate through all input words
    for (int i = 0; i < size; ++i)
    {
        // Create a buffer for this word and copy the word to buffer
        int len = strlen(wordArr[i]);
        char *buffer = new char[len+1];
        strcpy(buffer, wordArr[i]);

        // Sort the buffer
        qsort( (void*)buffer, strlen(buffer), sizeof(char), compare );

        // Insert the sorted buffer and its original index to Trie
        insert(&root,  buffer, i);
    }

    // Traverse the built Trie and print all anagrams together
    printAnagramsUtil(root, wordArr);
}


// Driver program to test above functions
int main()
{
    char* wordArr[] = {"cat", "dog", "tac", "god", "act", "gdo"};
    int size = sizeof(wordArr) / sizeof(wordArr[0]);
    printAnagramsTogether(wordArr, size);
    return 0;
}

Java

// An efficient program to print all
// anagrams together
import java.util.Arrays;
import java.util.LinkedList;

public class GFG
{
    static final int NO_OF_CHARS = 26;

    // Class to represent a Trie Node
    static class TrieNode
    {
        boolean isEnd;  // indicates end of word

        // 26 slots each for 'a' to 'z'
        TrieNode[] child = new TrieNode[NO_OF_CHARS];

        // head of the index list
        LinkedList<Integer> head;

        // constructor
        public TrieNode()
        {
            isEnd = false;
            head = new LinkedList<>();
            for (int i = 0; i < NO_OF_CHARS; ++i)
                child[i] = null;
        }
    }

    // A utility function to insert a word to Trie
    static TrieNode insert(TrieNode root,String word,
                                int index, int i)
    {
        // Base case
        if (root == null)
        {
            root = new TrieNode();
        }

        if (i < word.length() )
        {
            int index1 = word.charAt(i) - 'a';
            root.child[index1] = insert(root.child[index1],
                                       word, index, i+1 );
        }
        else  // If end of the word reached
        {
            // Insert index of this word to end of
            // index linked list
            if (root.isEnd == true)
            {
                root.head.add(index);
            }
            else // If Index list is empty
            {
                root.isEnd = true;
                root.head.add(index);
            }
        }
        return root;
    }

    // This function traverses the built trie. When a leaf
    // node is reached, all words connected at that leaf
    // node are anagrams. So it traverses the list at leaf
    // node and uses stored index to print original words
    static void printAnagramsUtil(TrieNode root,
                                      String wordArr[])
    {
        if (root == null)
            return;

        // If a lead node is reached, print all anagrams
        // using the indexes stored in index linked list
        if (root.isEnd)
        {
            // traverse the list
            for(Integer pCrawl: root.head)
                System.out.println(wordArr[pCrawl]);
        }

        for (int i = 0; i < NO_OF_CHARS; ++i)
            printAnagramsUtil(root.child[i], wordArr);
    }

    // The main function that prints all anagrams together.
    // wordArr[] is input sequence of words.
    static void printAnagramsTogether(String wordArr[],
                                               int size)
    {
        // Create an empty Trie
        TrieNode root = null;

        // Iterate through all input words
        for (int i = 0; i < size; ++i)
        {
            // Create a buffer for this word and copy the
            // word to buffer
            char[] buffer = wordArr[i].toCharArray();

            // Sort the buffer
            Arrays.sort(buffer);

            // Insert the sorted buffer and its original
            // index to Trie
            root = insert(root, new String(buffer), i, 0);

        }

        // Traverse the built Trie and print all anagrams
        // together
        printAnagramsUtil(root, wordArr);
    }

    // Driver program to test above functions
    public static void main(String args[])
    {
        String wordArr[] = {"cat", "dog", "tac", "god",
                                        "act", "gdo"};
        int size = wordArr.length;
        printAnagramsTogether(wordArr, size);
    }
}
// This code is contributed by Sumit Ghosh

Python3

import string

# An efficient program to print all anagrams together

NO_OF_CHARS = 26

# Structure to represent list node for indexes of words in
# the given sequence. The list nodes are used to connect
# anagrams at leaf nodes of Trie
class IndexNode:
    def __init__(self, index):
        self.index = index
        self.next = None

# Structure to represent a Trie Node
class TrieNode:
    def __init__(self):
        self.isEnd = False
        self.child = [None]*NO_OF_CHARS
        self.head = None

# A utility function to create a new Trie node
def newTrieNode():
    return TrieNode()

# A utility function to insert a word to Trie
def insert(root, word, index):
    # Base case
    if root is None:
        root = newTrieNode()

    if len(word) > 0:
        root.child[string.ascii_lowercase.index(word[0])] = insert(root.child[string.ascii_lowercase.index(word[0])], word[1:], index)
    else:  # If end of the word reached
        # Insert index of this word to end of index linked list
        if root.isEnd:
            pCrawl = root.head
            while pCrawl.next:
                pCrawl = pCrawl.next
            pCrawl.next = IndexNode(index)
        else:  # If Index list is empty
            root.isEnd = True
            root.head = IndexNode(index)
    return root

# This function traverses the built trie. When a leaf node is reached,
# all words connected at that leaf node are anagrams. So it traverses
# the list at leaf node and uses stored index to print original words
def printAnagramsUtil(root, wordArr):
    if root is None:
        return

    # If a lead node is reached, print all anagrams using the indexes
    # stored in index linked list
    if root.isEnd:
        # traverse the list
        pCrawl = root.head
        while pCrawl is not None:
            print(wordArr[pCrawl.index])
            pCrawl = pCrawl.next

    for i in range(NO_OF_CHARS):
        printAnagramsUtil(root.child[i], wordArr)

#The main function that prints all anagrams together. wordArr[] is input sequence of words.
def printAnagramsTogether(wordArr, size):
    # Create an empty Trie
    root = newTrieNode()
    # Iterate through all input words
    for i in range(size):
        # Create a buffer for this word and copy the word to buffer
        word = ''.join(sorted(wordArr[i].lower()))
        insert(root, word, i)

    printAnagramsUtil(root, wordArr)

#Driver program to test above functions
if __name__ == "__main__":
    wordArr = ["cat", "tac", "act", "dog", "god", "gdo"]
    size = len(wordArr)
    printAnagramsTogether(wordArr, size)

C#

// An efficient C# program to print all
// anagrams together
using System;
using System.Collections.Generic;

class GFG
{
    static readonly int NO_OF_CHARS = 26;

    // Class to represent a Trie Node
    public class TrieNode
    {
        // indicates end of word
        public bool isEnd;

        // 26 slots each for 'a' to 'z'
        public TrieNode[] child = new TrieNode[NO_OF_CHARS];

        // head of the index list
        public List<int> head;

        // constructor
        public TrieNode()
        {
            isEnd = false;
            head = new List<int>();
            for (int i = 0; i < NO_OF_CHARS; ++i)
                child[i] = null;
        }
    }

    // A utility function to insert a word to Trie
    static TrieNode insert(TrieNode root,String word,
                                int index, int i)
    {
        // Base case
        if (root == null)
        {
            root = new TrieNode();
        }

        if (i < word.Length )
        {
            int index1 = word[i] - 'a';
            root.child[index1] = insert(root.child[index1],
                                    word, index, i + 1 );
        }

        // If end of the word reached
        else
        {
            // Insert index of this word to end of
            // index linked list
            if (root.isEnd == true)
            {
                root.head.Add(index);
            }

            // If Index list is empty
            else
            {
                root.isEnd = true;
                root.head.Add(index);
            }
        }
        return root;
    }

    // This function traverses the built trie.
    // When a leaf node is reached, all words
    // connected at that leaf node are anagrams.
    // So it traverses the list at leaf node
    // and uses stored index to print original words
    static void printAnagramsUtil(TrieNode root,
                                    String []wordArr)
    {
        if (root == null)
            return;

        // If a lead node is reached,
        // print all anagrams using the
        // indexes stored in index linked list
        if (root.isEnd)
        {
            // traverse the list
            foreach(int pCrawl in root.head)
                Console.WriteLine(wordArr[pCrawl]);
        }

        for (int i = 0; i < NO_OF_CHARS; ++i)
            printAnagramsUtil(root.child[i], wordArr);
    }

    // The main function that prints
    // all anagrams together. wordArr[]
    // is input sequence of words.
    static void printAnagramsTogether(String []wordArr,
                                            int size)
    {
        // Create an empty Trie
        TrieNode root = null;

        // Iterate through all input words
        for (int i = 0; i < size; ++i)
        {
            // Create a buffer for this word
            // and copy the word to buffer
            char[] buffer = wordArr[i].ToCharArray();

            // Sort the buffer
            Array.Sort(buffer);

            // Insert the sorted buffer and
            // its original index to Trie
            root = insert(root, new String(buffer), i, 0);

        }

        // Traverse the built Trie and
        // print all anagrams together
        printAnagramsUtil(root, wordArr);
    }

    // Driver code
    public static void Main(String []args)
    {
        String []wordArr = {"cat", "dog", "tac", "god",
                                        "act", "gdo"};
        int size = wordArr.Length;
        printAnagramsTogether(wordArr, size);
    }
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// An efficient program to print all
// anagrams together
let NO_OF_CHARS = 26;

// Class to represent a Trie Node
class TrieNode
{
    constructor()
    {
        this.isEnd = false;  // indicates end of word

        // 26 slots each for 'a' to 'z'
        this.child = new Array(NO_OF_CHARS);

        for (let i = 0; i < NO_OF_CHARS; ++i)
                this.child[i] = null;

        // head of the index list
        this.head=[];
    }
}

 // A utility function to insert a word to Trie
function insert(root,word,index,i)
{

    // Base case
        if (root == null)
        {
            root = new TrieNode();
        }
        if (i < word.length )
        {
            let index1 = word[i].charCodeAt(0) - 'a'.charCodeAt(0);

            root.child[index1] = insert(root.child[index1],
                                       word, index, i+1 );
        }
        else  // If end of the word reached
        {
            // Insert index of this word to end of
            // index linked list
            if (root.isEnd == true)
            {
                root.head.push(index);
            }
            else // If Index list is empty
            {
                root.isEnd = true;
                root.head.push(index);
            }
        }
        return root;
}

// This function traverses the built trie. When a leaf
    // node is reached, all words connected at that leaf
    // node are anagrams. So it traverses the list at leaf
    // node and uses stored index to print original words
function printAnagramsUtil(root,wordArr)
{
    if (root == null)
            return;

        // If a lead node is reached, print all anagrams
        // using the indexes stored in index linked list
        if (root.isEnd)
        {
            // traverse the list
            for(let pCrawl=0;pCrawl<root.head.length;pCrawl++)
                document.write(wordArr[root.head[pCrawl]]+"<br>");
        }

        for (let i = 0; i < NO_OF_CHARS; ++i)
            printAnagramsUtil(root.child[i], wordArr);
}

// The main function that prints all anagrams together.
    // wordArr[] is input sequence of words.
function printAnagramsTogether(wordArr,size)
{
    // Create an empty Trie
        let root = null;

        // Iterate through all input words
        for (let i = 0; i < size; ++i)
        {
            // Create a buffer for this word and copy the
            // word to buffer
            let buffer = wordArr[i].split("");

            // Sort the buffer
            (buffer).sort();

            // Insert the sorted buffer and its original
            // index to Trie
            root = insert(root, (buffer).join(""), i, 0);

        }

        // Traverse the built Trie and print all anagrams
        // together
        printAnagramsUtil(root, wordArr);
}

// Driver program to test above functions
let wordArr=["cat", "dog", "tac", "god",
                                        "act", "gdo"];

let size = wordArr.length;
printAnagramsTogether(wordArr, size);

// This code is contributed by rag2127
</script>

Output:

cat
tac
act
dog
god
gdo

Time Complexity : O(MN+N*MlogM) time where-

N = Number of strings
M = Length of the largest string

Inserting all the words in the trie takes O(MN) time and sorting the buffer takes O(N*MlogM) time
Auxiliary Space : To store all the strings we need to allocate O(26*M*N) ~ O(MN) space for the Trie.
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