Introduction

In this blog post, we will explore how to solve the LeetCode problem "386" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Given an integer n, return all the numbers in the range [1, n] sorted in lexicographical order. You must write an algorithm that runs in O(n) time and uses O(1) extra space. Example 1: Input: n = 13 Output: [1,10,11,12,13,2,3,4,5,6,7,8,9] Example 2: Input: n = 2 Output: [1,2] Constraints: 1 <= n <= 5 * 104

Explanation

Here's a solution to generate numbers in lexicographical order within the range [1, n] with O(n) time complexity and O(1) extra space (excluding the output array).

• Iterative Deepening: Start with 1, and repeatedly extend the current number by appending 0 to it (multiplying by 10). If the extended number exceeds n, backtrack and try incrementing the current number.
• Backtracking Increment: If extending the number goes beyond n, or if the last digit of the number is 9, backtrack to the last number where incrementing is possible (i.e., the last digit is not 9).
• O(n) time, O(1) space

Code

    def lexicalOrder(n: int) -> list[int]:
    """
    Generates numbers from 1 to n in lexicographical order.

    Args:
        n: The upper bound of the range.

    Returns:
        A list of integers sorted lexicographically.
    """
    result = []
    curr = 1
    for _ in range(n):
        result.append(curr)
        if curr * 10 <= n:
            curr *= 10
        else:
            if curr >= n:
                curr //= 10
            curr += 1
            while curr % 10 == 0:
                curr //= 10
    return result