Step 1: Use Cases, Constraints, Assumptions, Back-of-Envelope

Use cases

We'll scope to handle only the core flows that expose the bottlenecks; everything else is deferred.

• User creates a paste / short URL — POST long URL or text, get back https://sho.rt/Ab3x9K (302 redirect for URL, render for paste).
• User reads a paste/short URL — GET /Ab3x9K, cache-hit serves in str: if num == 0: return ALPHABET[0] out = [] while num > 0: num, rem = divmod(num, BASE) out.append(ALPHABET[rem]) return "".join(reversed(out)).rjust(7, "0")

def short_code_for_id(auto_id: int) -> str: # O(k) where k=7, shuffle with Feistel if unpredictable needed return encode_base62(auto_id)

Alternative: hash + collision check for custom aliases

import hashlib def hash_code(url: str) -> str: h = hashlib.md5(url.encode()).hexdigest() num =