[algorithm] How to code a URL shortener?


Answers

Why would you want to use a hash?
You can just use a simple translation of your auto-increment value to an alphanumeric value. You can do that easily by using some base conversion. Say you character space (A-Z,a-z,0-9 etc') has 40 characters, convert the id to a base-40 number and use the characters are the digits.

Question

I want to create a URL shortener service where you can write a long URL into an input field and the service shortens the URL to "http://www.example.org/abcdef".

Edit: Due to the ongoing interest in this topic, I've published an efficient solution to GitHub, with implementations for JavaScript, PHP, Python and Java. Add your solutions if you like :)

Instead of "abcdef" there can be any other string with six characters containing a-z, A-Z and 0-9. That makes 56~57 billion possible strings.

My approach:

I have a database table with three columns:

  1. id, integer, auto-increment
  2. long, string, the long URL the user entered
  3. short, string, the shortened URL (or just the six characters)

I would then insert the long URL into the table. Then I would select the auto-increment value for "id" and build a hash of it. This hash should then be inserted as "short". But what sort of hash should I build? Hash algorithms like MD5 create too long strings. I don't use these algorithms, I think. A self-built algorithm will work, too.

My idea:

For "http://www.google.de/" I get the auto-increment id 239472. Then I do the following steps:

short = '';
if divisible by 2, add "a"+the result to short
if divisible by 3, add "b"+the result to short
... until I have divisors for a-z and A-Z.

That could be repeated until the number isn't divisible any more. Do you think this is a good approach? Do you have a better idea?




A node js and mongodb solution

Since we know the format that mongodb uses to create a new ObjectId with 12 bytes.

  • a 4-byte value representing the seconds since the Unix epoch,
  • a 3-byte machine identifier,
  • a 2-byte process id
  • a 3-byte counter (in your machine), starting with a random value.

Example (I choose a random sequence) a1b2c3d4e5f6g7h8i9j1k2l3

  • a1b2c3d4 represents the seconds since the Unix epoch,
  • 4e5f6g7 represents machine identifier,
  • h8i9 represents process id
  • j1k2l3 represents the counter, starting with a random value.

Since the counter will be unique if we are storing the data in the same machine we can get it with no doubts that it will be duplicate.

So the short URL will be the counter and here is a code snippet assuming that your server is running properly.

const mongoose = require('mongoose');
const Schema = mongoose.Schema;

// create a schema
const shortUrl = new Schema({
    long_url: { type: String, required: true },
    short_url: { type: String, required: true, unique: true },
  });
const ShortUrl = mongoose.model('ShortUrl', shortUrl);

//The user can request to get a short URL by providing a long URL using a form

app.post('/shorten', function(req ,res){
    //create a new shortUrl*/
    //the submit form has an input with longURL as its name attribute. 
    const longUrl = req.body["longURL"];
    const newUrl = ShortUrl({
        long_url : longUrl,
        short_url : "",
    });
    const shortUrl = newUrl._id.toString().slice(-6);
    newUrl.short_url = shortUrl;
    console.log(newUrl);
    newUrl.save(function(err){
        console.log("the new url is added");
    })
});



Here is a decent URL encoding function for PHP...

// From http://snipplr.com/view/22246/base62-encode--decode/
private function base_encode($val, $base=62, $chars='0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ') {
    $str = '';
    do {
        $i = fmod($val, $base);
        $str = $chars[$i] . $str;
        $val = ($val - $i) / $base;
    } while($val > 0);
    return $str;
}



I have a variant of the problem, in that I store web pages from many different authors and need to prevent discovery of pages by guesswork. So my short URLs add a couple of extra digits to the Base-62 string for the page number. These extra digits are generated from information in the page record itself and they ensure that only 1 in 3844 URLs are valid (assuming 2-digit Base-62). You can see an outline description at http://mgscan.com/MBWL.




Here is Node.js implementation that is likely to bit.ly. generate highly random 7 character string. using Node.js crypto to generate highly random 25 charset than random select 7 character.

var crypto = require("crypto");
exports.shortURL = new function () {
    this.getShortURL = function () {
        var sURL = '',
            _rand = crypto.randomBytes(25).toString('hex'),
            _base = _rand.length;
        for (var i = 0; i < 7; i++)
            sURL += _rand.charAt(Math.floor(Math.random() * _rand.length));
        return sURL;
    };
}



Implementation in Scala:

class Encoder(alphabet: String) extends (Long => String) {

  val Base = alphabet.size

  override def apply(number: Long) = {
    def encode(current: Long): List[Int] = {
      if (current == 0) Nil
      else (current % Base).toInt :: encode(current / Base)
    }
    encode(number).reverse
      .map(current => alphabet.charAt(current)).mkString
  }
}

class Decoder(alphabet: String) extends (String => Long) {

  val Base = alphabet.size

  override def apply(string: String) = {
    def decode(current: Long, encodedPart: String): Long = {
      if (encodedPart.size == 0) current
      else decode(current * Base + alphabet.indexOf(encodedPart.head),encodedPart.tail)
    }
    decode(0,string)
  }
}

Test example with Scala test:

import org.scalatest.{FlatSpec, Matchers}

class DecoderAndEncoderTest extends FlatSpec with Matchers {

  val Alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"

  "A number with base 10" should "be correctly encoded into base 62 string" in {
    val encoder = new Encoder(Alphabet)
    encoder(127) should be ("cd")
    encoder(543513414) should be ("KWGPy")
  }

  "A base 62 string" should "be correctly decoded into a number with base 10" in {
    val decoder = new Decoder(Alphabet)
    decoder("cd") should be (127)
    decoder("KWGPy") should be (543513414)
  }

}



alphabet = map(chr, range(97,123)+range(65,91)) + map(str,range(0,10))

def lookup(k, a=alphabet):
    if type(k) == int:
        return a[k]
    elif type(k) == str:
        return a.index(k)


def encode(i, a=alphabet):
    '''Takes an integer and returns it in the given base with mappings for upper/lower case letters and numbers 0-9.'''
    try:
        i = int(i)
    except Exception:
        raise TypeError("Input must be an integer.")

    def incode(i=i, p=1, a=a):
        # Here to protect p.                                                                                                                                                                                                                
        if i <= 61:
            return lookup(i)

        else:
            pval = pow(62,p)
            nval = i/pval
            remainder = i % pval
            if nval <= 61:
                return lookup(nval) + incode(i % pval)
            else:
                return incode(i, p+1)

    return incode()



def decode(s, a=alphabet):
    '''Takes a base 62 string in our alphabet and returns it in base10.'''
    try:
        s = str(s)
    except Exception:
        raise TypeError("Input must be a string.")

    return sum([lookup(i) * pow(62,p) for p,i in enumerate(list(reversed(s)))])a

Here's my version for whomever needs it.




Why not just translate your id to a string? You just need a function that maps a digit between, say, 0 and 61 to a single letter (upper/lower case) or digit. Then apply this to create, say, 4-letter codes, and you've got 14.7 million URLs covered.




Here is my PHP 5 class.

<?php
class Bijective
{
    public $dictionary = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";

    public function __construct()
    {
        $this->dictionary = str_split($this->dictionary);
    }

    public function encode($i)
    {
        if ($i == 0)
        return $this->dictionary[0];

        $result = '';
        $base = count($this->dictionary);

        while ($i > 0)
        {
            $result[] = $this->dictionary[($i % $base)];
            $i = floor($i / $base);
        }

        $result = array_reverse($result);

        return join("", $result);
    }

    public function decode($input)
    {
        $i = 0;
        $base = count($this->dictionary);

        $input = str_split($input);

        foreach($input as $char)
        {
            $pos = array_search($char, $this->dictionary);

            $i = $i * $base + $pos;
        }

        return $i;
    }
}



For a similar project, to get a new key, I make a wrapper function around a random string generator that calls the generator until I get a string that hasn't already been used in my hashtable. This method will slow down once your name space starts to get full, but as you have said, even with only 6 characters, you have plenty of namespace to work with.




/**
 * <p>
 *     Integer to character and vice-versa
 * </p>
 *  
 */
public class TinyUrl {

    private final String characterMap = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
    private final int charBase = characterMap.length();

    public String covertToCharacter(int num){
        StringBuilder sb = new StringBuilder();

        while (num > 0){
            sb.append(characterMap.charAt(num % charBase));
            num /= charBase;
        }

        return sb.reverse().toString();
    }

    public int covertToInteger(String str){
        int num = 0;
        for(int i = 0 ; i< str.length(); i++)
            num += characterMap.indexOf(str.charAt(i)) * Math.pow(charBase , (str.length() - (i + 1)));

        return num;
    }
}

class TinyUrlTest{

    public static void main(String[] args) {
        TinyUrl tinyUrl = new TinyUrl();
        int num = 122312215;
        String url = tinyUrl.covertToCharacter(num);
        System.out.println("Tiny url:  " + url);
        System.out.println("Id: " + tinyUrl.covertToInteger(url));
    }
}



Not an answer to your question, but I wouldn't use case-sensitive shortened URLs. They are hard to remember, usually unreadable (many fonts render 1 and l, 0 and O and other characters very very similar that they are near impossible to tell the difference) and downright error prone. Try to use lower or upper case only.

Also, try to have a format where you mix the numbers and characters in a predefined form. There are studies that show that people tend to remember one form better than others (think phone numbers, where the numbers are grouped in a specific form). Try something like num-char-char-num-char-char. I know this will lower the combinations, especially if you don't have upper and lower case, but it would be more usable and therefore useful.




C# version:

public class UrlShortener 
{
    private static String ALPHABET = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
    private static int    BASE     = 62;

    public static String encode(int num)
    {
        StringBuilder sb = new StringBuilder();

        while ( num > 0 )
        {
            sb.Append( ALPHABET[( num % BASE )] );
            num /= BASE;
        }

        StringBuilder builder = new StringBuilder();
        for (int i = sb.Length - 1; i >= 0; i--)
        {
            builder.Append(sb[i]);
        }
        return builder.ToString(); 
    }

    public static int decode(String str)
    {
        int num = 0;

        for ( int i = 0, len = str.Length; i < len; i++ )
        {
            num = num * BASE + ALPHABET.IndexOf( str[(i)] ); 
        }

        return num;
    }   
}



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