What is a sequential digit number?

A number where each digit is exactly one greater than the previous digit, such as 123 or 6789.

How do you efficiently generate sequential digits within a range?

Build numbers by appending consecutive digits based on length and starting digit, then filter by the given low and high values.

Can this approach handle large ranges like up to 10^9?

Yes, because sequential numbers are limited by digit count, generation remains efficient regardless of range size.

Do I need to sort the output after generating numbers?

No, generating numbers from smallest starting digit to largest inherently produces a sorted list.

Which algorithm pattern is most relevant for Sequential Digits?

Enumeration-driven solution strategy is key, focusing on generating valid numbers directly rather than checking each candidate.

#1291

Medium

auto_awesomeEnumeration-driven solution strategy

LeetCode 题解工作台

顺次数

我们定义「顺次数」为：每一位上的数字都比前一位上的数字大 1 的整数。请你返回由 [low, high] 范围内所有顺次数组成的有序列表（从小到大排序）。示例 1：输出： low = 100, high = 300 输出： [123,234] 示例 2：输出： low = 1000, h…

枚举

题目描述

我们定义「顺次数」为：每一位上的数字都比前一位上的数字大 1 的整数。

请你返回由 [low, high] 范围内所有顺次数组成的有序列表（从小到大排序）。

示例 1：

输出：low = 100, high = 300
输出：[123,234]

示例 2：

输出：low = 1000, high = 13000
输出：[1234,2345,3456,4567,5678,6789,12345]

提示：

10 <= low <= high <= 10^9

lightbulb

解题思路

方法一：枚举

我们可以枚举数字的第一位 $i$ ，然后枚举数字的最后一位 $j$ ，那么这个数字就是 $i,i+1,\cdots,j$ 这 $j-i+1$ 个数字组成的。我们可以通过不断地将数字乘以 $10$ 并加上下一个数字 $j+1$ 来得到下一个数字，如果数字在 $[low, high]$ 的范围内，我们就将它加入答案中。

枚举结束后，我们将答案数组排序并返回即可。

时间复杂度近似 $O(1)$ ，空间复杂度 $O(1)$ 。

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class Solution:
    def sequentialDigits(self, low: int, high: int) -> List[int]:
        ans = []
        for i in range(1, 9):
            x = i
            for j in range(i + 1, 10):
                x = x * 10 + j
                if low <= x <= high:
                    ans.append(x)
        return sorted(ans)

speed

复杂度分析

指标	值
时间	complexity is O(1) in practice since the total sequential numbers are limited by digit count (1-9), even with high up to 10^9. Space complexity is O(1) extra beyond the output list, as numbers are generated on the fly and stored only if they fall in range.
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Focuses on generating numbers without testing every integer individually.
question_mark
Expects you to recognize the sequential digit pattern quickly.
question_mark
Checks for efficiency by restricting generation to relevant digit lengths.

warning

常见陷阱

外企场景

error
Attempting to iterate every integer from low to high, which is inefficient.
error
Forgetting to handle different digit lengths separately, leading to missed numbers.
error
Not maintaining ascending order, causing additional unnecessary sorting.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Return sequential digits in descending order instead of ascending.
arrow_right_alt
Count the number of sequential digit numbers within a range instead of listing them.
arrow_right_alt
Find the next sequential digit number greater than a given value.

help

常见问题

外企场景

继续练习

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