Introduction

In this blog post, we will explore how to solve the LeetCode problem "2843" 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

You are given two positive integers low and high. An integer x consisting of 2 * n digits is symmetric if the sum of the first n digits of x is equal to the sum of the last n digits of x. Numbers with an odd number of digits are never symmetric. Return the number of symmetric integers in the range [low, high]. Example 1: Input: low = 1, high = 100 Output: 9 Explanation: There are 9 symmetric integers between 1 and 100: 11, 22, 33, 44, 55, 66, 77, 88, and 99. Example 2: Input: low = 1200, high = 1230 Output: 4 Explanation: There are 4 symmetric integers between 1200 and 1230: 1203, 1212, 1221, and 1230. Constraints: 1 <= low <= high <= 104

Explanation

Here's a breakdown of the approach, complexity, and Python code for the symmetric integer counting problem:

• High-Level Approach:

  • Determine the number of digits in low and high. Iterate through even lengths within the relevant range.
  • For each even length, generate all symmetric numbers of that length.
  • Count how many of these generated symmetric numbers fall within the inclusive range [low, high].

• Complexity:

  • Runtime: O(log(high)^2 9^ (log(high)/2)), which simplifies to approximately O(n^2 9^(n/2)), where n is the number of digits of high.
  • Storage: O(9^(log(high)/2)), which simplifies to approximately O(9^(n/2)). This is because the number of symmetric integers we generate for a given length is directly proportional to 9^(n/2), and this needs to be stored during the generation and filtering process.

• Python Code:

Code

    def count_symmetric_integers(low: int, high: int) -> int:
    """
    Counts the number of symmetric integers in the range [low, high].
    """

    def generate_symmetric(length: int) -> list[int]:
        """
        Generates a list of all symmetric integers of the given length.
        """

        if length == 0:
            return [0]

        if length == 2:
            return [i * 11 for i in range(1, 10)]

        result = []

        def backtrack(current: str, sum_digits: int):
            if len(current) == length // 2:
                remaining = sum_digits
                right = ""
                for i in reversed(current):
                    right += str(int(i))
                result.append(int(current + right))
                return

            for i in range(10 if len(current) > 0 else 1, 10):
                backtrack(current + str(i), sum_digits + i)

        backtrack("", 0)
        return result

    low_len = len(str(low))
    high_len = len(str(high))
    count = 0

    for length in range(2 if low_len <= 2 else (low_len + 1) // 2 * 2, high_len + 1, 2):
        symmetric_numbers = generate_symmetric(length)
        for num in symmetric_numbers:
            if low <= num <= high:
                count += 1

    return count