Sequential digits are numerical sequences where each digit in a number is incremented by one compared to its predecessor. For example, 123, 234, and 345 are sequential digits because each subsequent number follows a pattern of increasing by one. These sequences are not only intriguing but also have practical applications in mathematics, computer science, and puzzle-solving.

Algorithmic Approach:

The provided Java solution utilizes a TreeSet to maintain a sorted collection of unique sequential digits within the given range. Let’s break down the algorithm:

1. Calculate the length of digits in the low and high range numbers.
2. Iterate through each starting digit from 1 to 9.
3. For each starting digit, generate sequential digits of varying lengths from lowDigitLength to highDigitLength.
4. Check if the generated number falls within the specified range.
5. Add valid sequential digits to the TreeSet to ensure uniqueness and sorted order.
6. Convert the TreeSet to an ArrayList for the final result.

class Solution {
    public List<Integer> sequentialDigits(int low, int high) {
        int lowDigitLength = Integer.toString(low).length();
        int highDigitLength = Integer.toString(high).length();
        TreeSet<Integer> list = new TreeSet<Integer>();
        for(int startDigit=1;startDigit<=9;startDigit++) {
            for(int digitLength=lowDigitLength;digitLength<=highDigitLength;digitLength++) {
                int number = getNextNumber(startDigit, digitLength);
                if (number>= low && number <= high) {
                    list.add(number);
                }
            }
        }
        return new ArrayList<Integer>(list);
    }
    private int getNextNumber(int start, int length) {
        if (start + length > 10) {
            return -1;
        }
        StringBuilder sb = new StringBuilder(Integer.toString(start));
        int nextDigit = start;
        for(int i=1;i<length;i++) {
            nextDigit++;
            sb.append(nextDigit);
        }
        return Integer.valueOf(sb.toString());
    }
}

https://leetcode.com/problems/sequential-digits/