📚Beginner-Friendly Guide to Solving "Lexicographical Numbers" LeetCode 1061 (C++ | JavaScript | Python)

The LeetCode 386 problem requires generating numbers from 1 to n in lexicographical order. Lexicographical order resembles dictionary order, differing from numerical order. A naive string-based sorting approach is inefficient, costing O(n log n) time. The goal is to achieve O(n) time and O(1) extra space complexity. The solution simulates a Depth-First Search (DFS) traversal of a tree structure where deeper levels are reached by multiplying by 10 and siblings by incrementing by 1. The algorithm starts at 1 and greedily explores deeper by multiplying by 10 until exceeding n, then moves to the next sibling. Backtracking (dividing by 10) occurs when no further sibling can be reached within the constraints of n. The provided C++, JavaScript, and Python code efficiently implement this logic. The solution utilizes a while loop and conditional statements to simulate the DFS traversal. The space complexity is O(1) because only a constant amount of extra memory is used, excluding the output vector.