Numbers With a Fixed Digit Step

Medium

You get two integers, length and step. Find every number with exactly length digits in which any two neighboring digits differ by exactly step (in absolute value). Leading zeros are not allowed: something like 07 or 0707 does not count as a number of that length. Return the numbers in any order.

Example 1

length=3, step=8 → [191, 808, 919]

Neighboring digits must differ by 8, which only allows the pairs 0–8 and 1–9. A number like 080 starts with a zero, so 808, 191 and 919 remain.

Example 2

length=2, step=0 → [11, 22, 33, 44, 55, 66, 77, 88, 99]

Both digits are equal: 11, 22, ..., 99. 00 does not count, as it is not a two-digit number.

Constraints

2 ≤ length ≤ 9
0 ≤ step ≤ 9

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Topics

Breadth-First Search Backtracking

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Input

length=3, step=8

Expected

[191, 808, 919]

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