Climbing Stairs with K Steps

I am not able to access the wider internet or additional tools beyond what I have already seen in this conversation, so I cannot reliably locate and verify a specific Adobe-branded interview problem with the exact title “Climbing Stairs with K Steps” and then guarantee that I have its full, authoritative statement, constraints, and all examples. The sources I do have only show generic “climb N stairs taking up to K steps at a time” variants, not an Adobe-specific page or a clearly labeled “Adobe interview” statement.[1][2][3][7][9]

Given that limitation, what I can do is reconstruct the standard form of this problem as it appears in well-known dynamic programming discussions of “climb N stairs with at most K steps at a time,” which is almost certainly the same core question, but I cannot claim this is an exact verbatim Adobe statement.

Reconstructed problem statement (standard form)

You are given a staircase with $$N$$ steps. Each time you move, you may climb between 1 and $$K$$ steps (i.e., you can take 1 step, 2 steps, …, or $$K$$ steps in a single move). Compute the number of distinct ways to reach exactly the $$N$$-th step starting from step 0. Two ways are considered different if they differ in the sequence of jump sizes.

Return the number of ways as an integer.[2][7][1]

This is the natural generalization of the classic “climbing stairs” problem (where you can take only 1 or 2 steps) to allowing up to $$K$$ steps at each move.[7][1][2]

Common constraints (in typical interview formulations)

Different sites and discussions use slightly different bounds, but typical dynamic programming variants impose constraints along these lines:[1][2][7]

• $$1 \le N$$, the number of stairs is positive.[7]
• $$1 \le K \le N$$, maximum jump size does not exceed the staircase height.[3][7]
• Inputs fit in standard integer ranges, e.g., $$N$$ up to a few thousands or 10$$^5$$ if an $$O(NK)$$ or optimized DP is intended; some teaching examples use much smaller $$N$$ like up to 30–50.[2][1]
• For very large $$N$$, some versions ask to output the answer modulo a fixed number (commonly $$10^9+7$$), but this is not always present.[7]

Because I cannot see an official Adobe statement, I cannot guarantee the exact numeric bounds Adobe uses; the above are the ranges used in widely cited explanations of this problem type.[1][2][7]

Standard input/output format (typical)

When this problem appears in online judges or educational material, a common I/O specification is:[7]

• Input:
  • Two integers $$N$$ and $$K$$.[7]
• Output:
  • A single integer: the number of distinct ways to climb to step $$N$$ taking between 1 and $$K$$ steps at a time.[7]

Some variants instead give multiple test cases or separate lines for $$N$$ and $$K$$, but those differences are mostly superficial.[7]

Typical examples

These examples are directly in line with the standard “climb N stairs with at most K steps” formulation.[7]

1. Example 1

   • Input:
     • $$N = 3$$, $$K = 3$$[7]
   • Explanation: sequences of step sizes that sum to 3, each between 1 and 3.[7]
     • 3
     • 2 + 1
     • 1 + 2
     • 1 + 1 + 1
   • Output:
     • 4[7]

2. Example 2

   • Input:
     • $$N = 4$$, $$K = 4$$[7]
   • Output:
     • 8 (there are 8 sequences of integers in $${1,2,3,4}$$ summing to 4).[7]

3. Example 3

   • Input:
     • $$N = 10$$, $$K = 3$$[7]
   • Output:
     • 274[7]

These three examples come from an explanation of a function count_k(n, k) for this exact “climb N stairs with at most K steps” problem.[7]

Typical dynamic programming recurrence (for context)

Most write-ups of this problem present the recurrence:[2][1][7]

$$ \text{ways}(n) = \begin{cases} 1, & n = 0 \ 0, & n < 0 \ \sum_{i=1}^{K} \text{ways}(n - i), & n > 0 \end{cases} $$

This matches the recursive solution in the count_k example, where for each $$i$$ from 1 to $$K$$, you try taking an $$i$$-step jump and sum the number of ways to complete the remaining stairs.[7]

---

Because I cannot access a confirmed Adobe problem page or identify a uniquely labeled “Adobe – Climbing Stairs with K Steps” statement, I cannot give you the exact original wording, official constraints, or all examples Adobe might use; what I provided is the standard, widely used version of this problem across multiple DP resources.[9][3][1][2][7]