Longest Common Prefix using Trie

12 Jul, 2019
Given a set of strings, find the longest common prefix.
Input  : {“geeksforgeeks”, “geeks”, “geek”, “geezer”}
Output : "gee"

Input  : {"apple", "ape", "april"}
Output : "ap"

Previous Approaches : Word by Word Matching , Character by Character Matching, Divide and Conquer , Binary Search.
In this article, an approach using Trie date structure is discussed.Steps:
Insert all the words one by one in the trie. After inserting we perform a walk on the trie.
In this walk, go deeper until we find a node having more than 1 children(branching occurs) or 0 children (one of the string gets exhausted).This is because the characters (nodes in trie) which are present in the longest common prefix must be the single child of its parent, i.e- there should not be branching in any of these nodes.
This is because the characters (nodes in trie) which are present in the longest common prefix must be the single child of its parent, i.e- there should not be branching in any of these nodes.
Algorithm Illustration considering strings as – “geeksforgeeks”, “geeks”, “geek”, “geezer”
C++
Java
Python3
C#
// A Program to find the longest common// prefix of the given words  #include<bits/stdc++.h>using namespace std;  // Alphabet size (# of symbols)#define ALPHABET_SIZE (26)  // Converts key current character into index// use only 'a' through 'z' and lower case#define CHAR_TO_INDEX(c) ((int)c - (int)'a')  // Trie nodestruct TrieNode{    struct TrieNode *children[ALPHABET_SIZE];      // isLeaf is true if the node represents    // end of a word    bool isLeaf;};  // Returns new trie node (initialized to NULLs)struct TrieNode *getNode(void){    struct TrieNode *pNode = new TrieNode;      if (pNode)    {        int i;          pNode->isLeaf = false;          for (i = 0; i < ALPHABET_SIZE; i++)            pNode->children[i] = NULL;    }      return pNode;}  // If not present, inserts the key into the trie// If the key is a prefix of trie node, just marks leaf nodevoid insert(struct TrieNode *root, string key){    int length = key.length();    int index;      struct TrieNode *pCrawl = root;      for (int level = 0; level < length; level++)    {        index = CHAR_TO_INDEX(key[level]);        if (!pCrawl->children[index])            pCrawl->children[index] = getNode();          pCrawl = pCrawl->children[index];    }      // mark last node as leaf    pCrawl->isLeaf = true;}  // Counts and returns the number of children of the// current nodeint countChildren(struct TrieNode *node, int *index){    int count = 0;    for (int i=0; i<ALPHABET_SIZE; i++)    {        if (node->children[i] != NULL)        {            count++;            *index = i;        }    }    return (count);}  // Perform a walk on the trie and return the// longest common prefix stringstring walkTrie(struct TrieNode *root){    struct TrieNode *pCrawl = root;    int index;    string prefix;      while (countChildren(pCrawl, &index) == 1 &&            pCrawl->isLeaf == false)    {        pCrawl = pCrawl->children[index];        prefix.push_back('a'+index);    }    return (prefix);}  // A Function to construct trievoid constructTrie(string arr[], int n, struct TrieNode *root){    for (int i = 0; i < n; i++)        insert (root, arr[i]);    return;}  // A Function that returns the longest common prefix// from the array of stringsstring commonPrefix(string arr[], int n){    struct TrieNode *root = getNode();    constructTrie(arr, n, root);      // Perform a walk on the trie    return walkTrie(root);}  // Driver program to test above functionint main(){    string arr[] = {"geeksforgeeks", "geeks",                    "geek", "geezer"};    int n = sizeof (arr) / sizeof (arr[0]);      string ans = commonPrefix(arr, n);      if (ans.length())        cout << "The longest common prefix is "             << ans;    else        cout << "There is no common prefix";    return (0);}
// Java Program to find the longest common// prefix of the given wordspublic class Longest_common_prefix {          // Alphabet size (# of symbols)    static final int ALPHABET_SIZE = 26;           // Trie node    static class TrieNode    {        TrieNode[] children = new TrieNode[ALPHABET_SIZE];               // isLeaf is true if the node represents        // end of a word        boolean isLeaf;                  // constructor        public TrieNode() {            isLeaf = false;            for (int i = 0; i < ALPHABET_SIZE; i++)                children[i] = null;        }    };           static TrieNode root;    static int indexs;           // If not present, inserts the key into the trie    // If the key is a prefix of trie node, just marks    // leaf node    static void insert(String key)    {        int length = key.length();        int index;               TrieNode pCrawl = root;               for (int level = 0; level < length; level++)        {            index = key.charAt(level) - 'a';            if (pCrawl.children[index] == null)                pCrawl.children[index] = new TrieNode();                   pCrawl = pCrawl.children[index];        }               // mark last node as leaf        pCrawl.isLeaf = true;    }           // Counts and returns the number of children of the    // current node    static int countChildren(TrieNode node)    {        int count = 0;        for (int i=0; i<ALPHABET_SIZE; i++)        {            if (node.children[i] != null)            {                count++;                indexs = i;            }        }        return (count);    }           // Perform a walk on the trie and return the    // longest common prefix string    static String walkTrie()    {        TrieNode pCrawl = root;        indexs = 0;        String prefix = "";               while (countChildren(pCrawl) == 1 &&                pCrawl.isLeaf == false)        {            pCrawl = pCrawl.children[indexs];            prefix += (char)('a' + indexs);        }        return prefix;    }           // A Function to construct trie    static void constructTrie(String arr[], int n)    {        for (int i = 0; i < n; i++)            insert (arr[i]);        return;    }           // A Function that returns the longest common prefix    // from the array of strings    static String commonPrefix(String arr[], int n)    {        root = new TrieNode();        constructTrie(arr, n);               // Perform a walk on the trie        return walkTrie();    }           // Driver program to test above function    public static void main(String args[])    {        String arr[] = {"geeksforgeeks", "geeks",                        "geek", "geezer"};        int n = arr.length;               String ans = commonPrefix(arr, n);               if (ans.length() != 0)            System.out.println("The longest common prefix is "+ans);        else            System.out.println("There is no common prefix");    }}// This code is contributed by Sumit Ghosh
# Python 3 program to find the longest common prefixALPHABET_SIZE = 26indexs = 0class TrieNode:    # constructor    def __init__(self):        self.isLeaf = False        self.children = [None]*ALPHABET_SIZE  # Function to facilitate insertion in Trie# If not present, insert the node in the Triedef insert(key, root):    pCrawl = root    for level in range(len(key)):        index = ord(key[level]) - ord('a')        if pCrawl.children[index] == None:            pCrawl.children[index] = TrieNode()        pCrawl = pCrawl.children[index]    pCrawl.isLeaf = True  # Function to construct Triedef constructTrie(arr, n, root):    for i in range(n):        insert(arr[i], root)  # Counts and returns number of children of the nodedef countChildren(node):    count = 0    for i in range(ALPHABET_SIZE):        if node.children[i] != None:            count +=1            # Keeping track of diversion in the trie            global indexs            indexs = i    return count      # Perform walk on trie and return longest common prefix def walkTrie(root):    pCrawl = root    prefix = ""    while(countChildren(pCrawl) == 1 and pCrawl.isLeaf == False):        pCrawl = pCrawl.children[indexs]        prefix += chr(97 + indexs)    return prefix or -1  # Function that returns longest common prefix def commonPrefix(arr, n, root):    constructTrie(arr, n, root)    return walkTrie(root)  # Driver code to test the coden = 4arr = ["geeksforgeeks", "geeks", "geek", "geezer"]root = TrieNode()print(commonPrefix(arr,n, root))  # This code is Contributed by Akshay Jain (DA-IICT)
// C# Program to find the longest common// prefix of the given wordsusing System;      public class Longest_common_prefix {          // Alphabet size (# of symbols)    static readonly int ALPHABET_SIZE = 26;          // Trie node    public class TrieNode    {        public TrieNode[] children = new TrieNode[ALPHABET_SIZE];              // isLeaf is true if the node represents        // end of a word        public bool isLeaf;                  // constructor        public TrieNode()         {            isLeaf = false;            for (int i = 0; i < ALPHABET_SIZE; i++)                children[i] = null;        }    };          static TrieNode root;    static int indexs;          // If not present, inserts the key into the trie    // If the key is a prefix of trie node, just marks    // leaf node    static void insert(String key)    {        int length = key.Length;        int index;              TrieNode pCrawl = root;              for (int level = 0; level < length; level++)        {            index = key[level] - 'a';            if (pCrawl.children[index] == null)                pCrawl.children[index] = new TrieNode();                  pCrawl = pCrawl.children[index];        }              // mark last node as leaf        pCrawl.isLeaf = true;    }          // Counts and returns the number of children of the    // current node    static int countChildren(TrieNode node)    {        int count = 0;        for (int i = 0; i < ALPHABET_SIZE; i++)        {            if (node.children[i] != null)            {                count++;                indexs = i;            }        }        return (count);    }          // Perform a walk on the trie and return the    // longest common prefix string    static String walkTrie()    {        TrieNode pCrawl = root;        indexs = 0;        String prefix = "";              while (countChildren(pCrawl) == 1 &&                pCrawl.isLeaf == false)        {            pCrawl = pCrawl.children[indexs];            prefix += (char)('a' + indexs);        }        return prefix;    }          // A Function to construct trie    static void constructTrie(String []arr, int n)    {        for (int i = 0; i < n; i++)            insert (arr[i]);        return;    }          // A Function that returns the longest common prefix    // from the array of strings    static String commonPrefix(String []arr, int n)    {        root = new TrieNode();        constructTrie(arr, n);              // Perform a walk on the trie        return walkTrie();    }          // Driver program to test above function    public static void Main(String []args)    {        String []arr = {"geeksforgeeks", "geeks",                        "geek", "geezer"};        int n = arr.Length;              String ans = commonPrefix(arr, n);              if (ans.Length != 0)            Console.WriteLine("The longest common prefix is "+ans);        else            Console.WriteLine("There is no common prefix");    }}  // This code contributed by Rajput-Ji
The longest common prefix is gee
Time Complexity : Inserting all the words in the trie takes O(MN) time and performing a walk on the trie takes O(M) time, where-
N = Number of strings
M = Length of the largest string

Auxiliary Space: To store all the strings we need to allocate O(26*M*N) ~ O(MN) space for the Trie.
 This article is contributed by Rachit Belwariar. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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Longest Common Prefix
Trie
VMWare
Advanced Data Structure
Arrays
Strings
VMWare
Arrays
Strings
Trie
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