Chain Options with and_then()

Write a Rust function that takes a string, parses it as an integer, then doubles the result, using Option::and_then() to chain the parse and double operations. and_then() is a combinator that applies a function returning Option only if the current Option is Some, otherwise propagates None.

Option::and_then() is the monadic bind operation for Option. It allows chaining computations that may fail. If the Option is Some(value), and_then applies the closure which returns a new Option. If the Option is None, and_then returns None without calling the closure. This eliminates nested match statements and creates a clean pipeline.

The and_then() combinator is fundamental to Rust's error handling philosophy. Unlike exceptions, Rust makes failure modes explicit in the type system and provides combinators like and_then(), map(), and unwrap_or() to compose operations. This approach ensures all failure paths are handled at compile time.

Time complexity is O(1) as and_then is a simple enum match. The string parsing (str::parse) is O(n) where n is the string length. Space complexity is O(1). The combinator itself adds no runtime overhead beyond the operations it chains.

Edge cases include empty strings (parse fails, and_then short-circuits), invalid strings with letters (parse returns None), zero (parses correctly, doubling gives zero), negative numbers, and very large numbers that may overflow the i32 type.