How do you solve Sequential Digits on LeetCode?

Sequential Digits (LeetCode #1291) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Sequential digits can only be formed by starting from 1 to 9 and appending increasing digits.

What is the brute force solution for Sequential Digits?

The brute force approach for Sequential Digits is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible sequential digit numbers and then filtering out those that fall within the specified range. This method is straightforward but inefficient as it checks every number sequentially. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Sequential Digits?

Sequential Digits uses the following concepts: Enumeration. The recommended patterns to study are: Enumeration, Backtracking.

What are the interview tips for Sequential Digits?

Think about how to generate numbers systematically rather than checking each number. Always clarify the range constraints before starting to code. Discuss your thought process and approach with the interviewer to get feedback.

What are common mistakes when solving Sequential Digits?

Not considering the upper limit properly when generating numbers. Confusing the order of digits while appending.

#1291

Sequential Digits

Medium

EnumerationEnumerationBacktracking

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal approach generates sequential digits directly without checking every number. It builds numbers by appending digits in a systematic way, ensuring that only valid sequential numbers are created.

⚙️

Algorithm

5 steps

1Step 1: Initialize an empty list to store results.
2Step 2: Loop through starting digits from 1 to 9.
3Step 3: For each starting digit, build sequential numbers by appending the next digit until the number exceeds high.
4Step 4: If the generated number is within the range [low, high], add it to the results.
5Step 5: Return the sorted results.

solution.py11 lines

1def sequentialDigits(low, high):
2    sequential = []
3    for start in range(1, 10):
4        num = start
5        next_digit = start
6        while num <= high and next_digit < 9:
7            if num >= low:
8                sequential.append(num)
9            next_digit += 1
10            num = num * 10 + next_digit
11    return sorted(sequential)

ℹ

Complexity note: The time complexity is O(n) since we only generate valid sequential numbers directly without unnecessary checks. The space complexity is O(n) due to storing the results in a list.

1Sequential digits can only be formed by starting from 1 to 9 and appending increasing digits.
2The maximum possible sequential digit number is 123456789.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.