Base62 short codes with collision handling.

The URL shortener of Day 1, chapter 4 stores one mapping, short_code → original_url (section 4.1). A 7-character code over the 62 characters a-z A-Z 0-9 gives 62^7, about 3.5 trillion codes (Week 1 capstone, Deep Dive 1). Build the two pieces every design needs, whichever way the number behind a code is produced:

1. Base62. encode(n, length=7) writes a non-negative integer as exactly length characters of ALPHABET (given: a-z, then A-Z, then 0-9, so a is the digit 0 and 9 is 61), most significant digit first and left-padded with a. decode(code) reverses it.

Raise ValueError when n is negative or doesn't fit in length characters, and when decode sees a character outside ALPHABET.

2. A hashing shortener with collision handling. UrlShortener(db, hash_fn, length=7, max_attempts=3):

Candidate i (from 0) is encode(hash_fn(key_i) % 62 ** length, length), where key_0 is the URL itself and key_i is f"{long_url}#{i}" for i ≥ 1. For each candidate:

• db.put_if_absent(code, long_url) returns True: the code is ours. Return it.
• it returns False and db.get(code) is this URL: it was shortened before. Return the same code (no new row).
• it returns False and the code belongs to another URL: a collision. Try the next candidate.

After max_attempts candidates collide, raise TooManyCollisions (given) and store nothing.

Why put_if_absent and not "get, then put if empty": two servers can both see the code free and both write it, and the second write silently replaces the first user's link. A conditional insert, like the UNIQUE constraint on short_code in the capstone's Edge Case 1, lets exactly one of them win. The given FakeDB has no plain put, so the safe version is the only one you can write.

In JavaScript and TypeScript: encode(n, length = 7), decode(code), new UrlShortener(db, hashFn, length = 7, maxAttempts = 3) with shorten(longUrl) and expand(code) (null when unknown), db.putIfAbsent(code, url), and errors are thrown as RangeError (bad number or character) and TooManyCollisions.