How do I create a URL shortener?

I would continue your "convert number to string" approach. However, you will realize that your proposed algorithm fails if your ID is a prime and greater than 52.

Theoretical background

You need a Bijective Function f. This is necessary so that you can find a inverse function g('abc') = 123 for your f(123) = 'abc' function. This means:

• There must be no x1, x2 (with x1 ≠ x2) that will make f(x1) = f(x2),
• and for every y you must be able to find an x so that f(x) = y.

How to convert the ID to a shortened URL

1. Think of an alphabet we want to use. In your case, that's [a-zA-Z0-9]. It contains 62 letters.

2. Take an auto-generated, unique numerical key (the auto-incremented id of a MySQL table for example).

   For this example, I will use 125₁₀ (125 with a base of 10).

3. Now you have to convert 125₁₀ to X₆₂ (base 62).

   125₁₀ = 2×62¹ + 1×62⁰ = [2,1]

   This requires the use of integer division and modulo. A pseudo-code example:

   digits = []
   
   while num > 0
     remainder = modulo(num, 62)
     digits.push(remainder)
     num = divide(num, 62)
   
   digits = digits.reverse
   

   Now map the indices 2 and 1 to your alphabet. This is how your mapping (with an array for example) could look like:

   0  → a
   1  → b
   ...
   25 → z
   ...
   52 → 0
   61 → 9
   

   With 2 → c and 1 → b, you will receive cb₆₂ as the shortened URL.

   http://shor.ty/cb
   

How to resolve a shortened URL to the initial ID

The reverse is even easier. You just do a reverse lookup in your alphabet.

1. e9a₆₂ will be resolved to "4th, 61st, and 0th letter in the alphabet".

   e9a₆₂ = [4,61,0] = 4×62² + 61×62¹ + 0×62⁰ = 19158₁₀

2. Now find your database-record with WHERE id = 19158 and do the redirect.

Example implementations (provided by commenters)

• C++
• Python
• Ruby
• Haskell
• C#
• CoffeeScript
• Perl

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 62 characters, convert the id to a base-40 number and use the characters as the digits.

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.

My approach: Take the Database ID, then Base36 Encode it. I would NOT use both Upper AND Lowercase letters, because that makes transmitting those URLs over the telephone a nightmare, but you could of course easily extend the function to be a base 62 en/decoder.

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");
    })
});

I keep incrementing an integer sequence per domain in the database and use Hashids to encode the integer into a URL path.

static hashids = Hashids(salt = "my app rocks", minSize = 6)

I ran a script to see how long it takes until it exhausts the character length. For six characters it can do 164,916,224 links and then goes up to seven characters. Bitly uses seven characters. Under five characters looks weird to me.

Hashids can decode the URL path back to a integer but a simpler solution is to use the entire short link sho.rt/ka8ds3 as a primary key.

Here is the full concept:

function addDomain(domain) {
    table("domains").insert("domain", domain, "seq", 0)
}

function addURL(domain, longURL) {
    seq = table("domains").where("domain = ?", domain).increment("seq")
    shortURL = domain + "/" + hashids.encode(seq)
    table("links").insert("short", shortURL, "long", longURL)
    return shortURL
}

// GET /:hashcode
function handleRequest(req, res) {
    shortURL = req.host + "/" + req.param("hashcode")
    longURL = table("links").where("short = ?", shortURL).get("long")
    res.redirect(301, longURL)
}

You could hash the entire URL, but if you just want to shorten the id, do as marcel suggested. I wrote this Python implementation:

https://gist.github.com/778542

Take a look at https://hashids.org/ it is open source and in many languages.

Their page outlines some of the pitfalls of other approaches.

If you don't want re-invent the wheel ... http://lilurl.sourceforge.net/

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.

Don't know if anyone will find this useful - it is more of a 'hack n slash' method, yet is simple and works nicely if you want only specific chars.

$dictionary = "abcdfghjklmnpqrstvwxyz23456789";
$dictionary = str_split($dictionary);

// Encode
$str_id = '';
$base = count($dictionary);

while($id > 0) {
    $rem = $id % $base;
    $id = ($id - $rem) / $base;
    $str_id .= $dictionary[$rem];
}


// Decode
$id_ar = str_split($str_id);
$id = 0;

for($i = count($id_ar); $i > 0; $i--) {
    $id += array_search($id_ar[$i-1], $dictionary) * pow($base, $i - 1);
} 

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)
  }

}

Why not just generate a random string and append it to the base URL? This is a very simplified version of doing this in C#.

static string chars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890";
static string baseUrl = "https://google.com/";

private static string RandomString(int length)
{
    char[] s = new char[length];
    Random rnd = new Random();
    for (int x = 0; x < length; x++)
    {
        s[x] = chars[rnd.Next(chars.Length)];
    }
    Thread.Sleep(10);

    return new String(s);
}

Then just add the append the random string to the baseURL:

string tinyURL = baseUrl + RandomString(5);

Remember this is a very simplified version of doing this and it's possible the RandomString method could create duplicate strings. In production you would want to take in account for duplicate strings to ensure you will always have a unique URL. I have some code that takes account for duplicate strings by querying a database table I could share if anyone is interested.

This is my initial thoughts, and more thinking can be done, or some simulation can be made to see if it works well or any improvement is needed:

My answer is to remember the long URL in the database, and use the ID 0 to 9999999999999999 (or however large the number is needed).

But the ID 0 to 9999999999999999 can be an issue, because

1. it can be shorter if we use hexadecimal, or even base62 or base64. (base64 just like YouTube using A-Z a-z 0-9 _ and -)
2. if it increases from 0 to 9999999999999999 uniformly, then hackers can visit them in that order and know what URLs people are sending each other, so it can be a privacy issue

We can do this:

1. have one server allocate 0 to 999 to one server, Server A, so now Server A has 1000 of such IDs. So if there are 20 or 200 servers constantly wanting new IDs, it doesn't have to keep asking for each new ID, but rather asking once for 1000 IDs
2. for the ID 1, for example, reverse the bits. So 000...00000001 becomes 10000...000, so that when converted to base64, it will be non-uniformly increasing IDs each time.
3. use XOR to flip the bits for the final IDs. For example, XOR with 0xD5AA96...2373 (like a secret key), and the some bits will be flipped. (whenever the secret key has the 1 bit on, it will flip the bit of the ID). This will make the IDs even harder to guess and appear more random

Following this scheme, the single server that allocates the IDs can form the IDs, and so can the 20 or 200 servers requesting the allocation of IDs. The allocating server has to use a lock / semaphore to prevent two requesting servers from getting the same batch (or if it is accepting one connection at a time, this already solves the problem). So we don't want the line (queue) to be too long for waiting to get an allocation. So that's why allocating 1000 or 10000 at a time can solve the issue.