Solution: Lexicographical Numbers

Statement

Given an integer value $n$, write a function that returns all the numbers in the range $1$ to $n$ in lexicographical orderLexicographical order, also known as dictionary order or alphabetical order, is a way of ordering sequences (such as strings) based on the order of their elements. .

Constraints:

• $1 \leq n \leq 10^3$

Solution

Lexicographical order arranges words or sequences like in a dictionary. It compares items character by character, so “apple” comes before “banana” because 'a' is before 'b.' It's the same as alphabetical order but can apply to any sequence, not just words. Therefore, in the context of this problem, arranging the numbers in lexicographical order means that the numbers should be sorted as if they were strings, not as numerical values. For example, “10” comes before “2” because “1,” the first digit of “10”, is smaller than “2.”

To generate numbers in this order, we can think of the numbers as forming a tree, specifically a trie. The trie naturally organizes numbers in lexicographical order:

• The root is just an empty string “”.

• The first level after root has nodes against the numbers $1$, $2$, $3$, ..., ...