# Find the longest common prefix using Trie

The problem addressed here is finding the longest common prefix among a set of strings using a Trie data structure. A Trie, also known as a Prefix Tree, is a versatile data structure that is particularly useful for searching strings and efficiently finding common prefixes among them. This article will walk through the process of using a Trie to find the longest common prefix in a collection of strings.

## Problem Description

Given a set of strings, the goal is to find the longest common prefix that exists among all these strings. A common prefix is a sequence of characters that appears at the beginning of two or more strings.

## Idea to Solve

To solve this problem, we can use a Trie data structure. A Trie is a tree-like data structure that is well-suited for dealing with strings. It organizes strings in a way that makes it efficient to search for common prefixes.

## Algorithm

1. Create a `Node` class for the Trie, where each node has a boolean attribute `end` and an array `children` of size `ALPHABETS`, representing the possible characters (26 lowercase English letters).

2. Create a `Trie` class that has a `root` node. Implement an `insert` method in the `Trie` class to insert a string into the Trie.

3. For the longest common prefix, traverse the Trie's structure starting from the root. Find the first node that has multiple non-null children, as this indicates the point where the common prefix diverges.

4. Recursively continue this process, printing the common character and moving to the next level in the Trie, until a point is reached where multiple children exist again.

## Pseudocode

``````class Node:
end = False
children = [None, None, ..., None]  # Size: ALPHABETS

class Trie:
root = Node()

function insert(text):
for each character in text:
index = character - 'a'

Find the first non-null child index, named as 'location'
Iterate over all children:
if child is not null and its index is not 'location':
set status to False
if status is True:
Print character corresponding to 'location'
Call longestPrefix with head.children[location] and same + 1
else if status is False and same is 0:
Print "No Longest Prefix"

matrix = [...]  # The set of strings
obj = Trie()
for each string in matrix:
obj.insert(string)
obj.longestPrefix(obj.root, 0)``````

## Code Solution

``````//C++ program
//Find the Longest Common Prefix using Trie

#include<iostream>

#include<string>

#define ALPHABETS 26
using namespace std;
class Node {
public:
bool end;
Node *children[ALPHABETS];
Node() {
this->end = false;
for (int i = 0; i < ALPHABETS; ++i) {
this->children[i] = NULL;
}
}
};
class Trie {
public:
Node *root;
Trie() {
this->root = new Node();
}
void insert(string text) {
int length = text.size();
int index = 0;
for (int level = 0; level < length; level++) {
index = text[level] - 'a';
}
}
}
}
void longestPrefix(Node *head, int same) {
int location = -1;
bool status = true;
for (int i = 0; i < ALPHABETS && status; i++) {
if (location == -1) {
location = i;
}
if (i != location) {
status = false;
}

}
}
if (status == true) {
cout << ((char)(location + 97));
} else if (status == false && same == 0) {
cout << "No Longest Prefix" << endl;
}

}
}
};
int main() {
Trie obj;
//Insert following data
obj.insert("cool");
obj.insert("coder");
obj.insert("confirm");
obj.insert("cow");

obj.longestPrefix(obj.root, 0);
cout << endl;
}```
```

#### Output

``co``
``````/*
Java program
Find the Longest Common Prefix using Trie
*/

class Node {
//Indicates end of string
public boolean end;

public Node[] children;

public Node(int size) {
end = false;
children = new Node[size];
}
}
public class Trie
{
public int ALPHABETS = 26;
public Node root;

public Trie()
{
root = new Node(ALPHABETS);
}

public void insert(String text)
{
//first get the length of text
int length = text.length();

//This variable are used to task find the index location of character
int index = 0;

//get the root node

for (int level = 0; level < length ; level++ )
{
//Get the index
index = text.charAt(level)-'a';

{
//When need to add new Node
}

}
{
//indicates end of string
}
}
{
int location = -1;
boolean status = true;
for (int i = 0; i < ALPHABETS && status; i++) {
if (location == -1) {
location = i;
}
if (i != location) {
status = false;
}

}
}
if (status == true) {
System.out.print((char)(location+97));
} else if (status == false && same == 0) {

System.out.print("No Longest Prefix");
}

}

}

public static void main(String[] args)
{
//Make object
Trie obj = new Trie();

obj.insert("cool");
obj.insert("coder");
obj.insert("confirm");
obj.insert("cow");

obj.longestPrefix(obj.root,0);
System.out.println();
}
}```
```

#### Output

``co``
``````/*
C# program
Find the Longest Common Prefix using Trie
*/
using System;
public class Node {
//Indicates end of string
public Boolean end;

public Node[] children;

public Node(int size) {
end = false;
children = new Node[size];
}
}
public class Trie
{
public int ALPHABETS = 26;
public Node root;

public Trie()
{
root = new Node(ALPHABETS);
}

public void insert(String text) {
//first get the.Length of text
int size = text.Length;

//This variable are used to task find the index location of character
int index = 0;

//get the root node

for (int level = 0; level < size; level++) {
//Get the index
index = text[level] - 'a';

//When need to add new Node
}

}
//indicates end of string
}
}
{
int location = -1;
Boolean status = true;
for (int i = 0; i < ALPHABETS && status; i++) {
if (location == -1) {
location = i;
}
if (i != location) {
status = false;
}

}
}
if (status == true) {
Console.Write((char)(location+97));
} else if (status == false && same == 0) {

Console.Write("No Longest Prefix");
}

}

}

public static void Main(String[] args)
{
//Make object
Trie obj = new Trie();

obj.insert("cool");
obj.insert("coder");
obj.insert("confirm");
obj.insert("cow");

obj.longestPrefix(obj.root,0);
Console.WriteLine();
}
}```
```

#### Output

``co``
``````# Ruby Program
# Find the Longest Common Prefix using Trie
class Node
attr_accessor :end, :children
def initialize(size)
@end = false
@children = Array.new(size){nil}
end
end

class Trie
attr_accessor :ALPHABETS, :root
def initialize()
@ALPHABETS = 26
@root = Node.new(@ALPHABETS)
end
def insert(text)
length = text.length()
location = 0
level = 0
while (level < length)
location = text[level].ord - 'a'.ord
end
level += 1
end
end
end
location = -1
status = true
i = 0
while (i < @ALPHABETS and status==true)
if (location == -1)
location = i
elsif (i != location)
status = false
end
end
i += 1
end
if (status == true)
print((location + 97).chr)
elsif (status == false and same == 0)
print("No Longest Prefix")
end
end
end
end
def main()
obj = Trie.new()
obj.insert("cool")
obj.insert("coder")
obj.insert("confirm")
obj.insert("cow")
obj.longestPrefix(obj.root,0)
print("\n")
end
main()```
```

#### Output

``co``
``````# Python Program
# Find the Longest Common Prefix using Trie
class Node :

def __init__(self, size) :
self.end = False;
self.children = [None]*size;

class Trie :

def __init__(self) :
self.ALPHABETS = 26;
self.root = Node(self.ALPHABETS);

def insert(self, text) :
length = len(text)
index = 0
level = 0
while (level < length) :
index = ord(text[level]) - ord('a')

level += 1

location = -1;
status = True;
i = 0;
while (i < self.ALPHABETS and status) :
if (location == -1) :
location = i;

if (i != location) :
status = False;

i += 1;

if (status == True) :
print(chr(location + 97),end="")
elif (status == False and same == 0) :
print("No Longest Prefix");

def main() :
obj = Trie();
obj.insert("cool");
obj.insert("coder");
obj.insert("confirm");
obj.insert("cow");
obj.longestPrefix(obj.root,0);
print();

if __name__ == "__main__":
main()```
```

#### Output

``co``
``````/*
Node JS Program
Find the Longest Common Prefix using Trie
*/
class Node {

constructor(size) {
this.end = false;
this.children =  new Array(size).fill(null);
}
}
class Trie {

constructor() {
this.ALPHABETS = 26;
this.root = new Node(this.ALPHABETS);
}
insert(text) {
var length = text.length;
var index = 0;
var level = 0;
while (level < length) {
index = text.charCodeAt(level) - 'a'.charCodeAt(0);;
}
level++;
}
}
}
var location = -1;
var status = true;
var i = 0;
while (i < this.ALPHABETS && status) {
if (location == -1) {
location = i;
}
if (i != location) {
status = false;
}
}
i++;
}
if (status == true) {
process.stdout.write(String.fromCharCode(location + 97));
} else
if (status == false && same == 0) {
process.stdout.write("No Longest Prefix");
}
}
}
}

function main() {
var obj = new Trie();
obj.insert("cool");
obj.insert("coder");
obj.insert("confirm");
obj.insert("cow");
obj.longestPrefix(obj.root,0);
process.stdout.write("\n");
}
main();```
```

#### Output

``co``
``````<?php
/*
Php Program
Find the Longest Common Prefix using Trie
*/
class Node {
public \$end;
public \$children;

function __construct(\$size) {
\$this->end = false;
\$this->children = array_fill(0, \$size, null);
}
}
class Trie {
public \$ALPHABETS = 26;
public \$root;

function __construct() {
\$this->root = new Node(\$this->ALPHABETS);
}
public  function insert(\$text) {
\$length = strlen(\$text);
\$index = 0;
\$level = 0;
while (\$level < \$length) {
\$index = ord(\$text[\$level]) - ord('a');
}
\$level++;
}
}
}
\$location = -1;
\$status = true;
\$i = 0;
while (\$i < \$this->ALPHABETS && \$status) {
if (\$location == -1) {
\$location = \$i;
}
if (\$i != \$location) {
\$status = false;
}
}
\$i++;
}
if (\$status == true) {
echo(chr(\$location + 97));
} else
if (\$status == false && \$same == 0) {
echo("No Longest Prefix");
}
}

}
}
function main() {
\$obj = new Trie();
\$obj->insert("cool");
\$obj->insert("coder");
\$obj->insert("confirm");
\$obj->insert("cow");
\$obj->longestPrefix(\$obj->root,0);
echo ("\n");
}
main();```
```

#### Output

``co``

## Time Complexity

• Inserting each string into the Trie takes O(length), where `length` is the average length of the strings.
• Finding the longest common prefix takes O(n), where `n` is the length of the longest common prefix among the given strings.

## Comment

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