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Paradromics·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Interviewed for a software engineer role at Paradromics and got a classic staircase DP problem. Pretty standard coding round, nothing too wild, but the follow-up on optimization is where things got interesting.

Questions Asked (1)

Q1

Write a function that counts the number of distinct ways to climb a staircase of n steps, where you can take either 1 or 2 steps at a time. Then walk through how you'd optimize a naive recursive solution using dynamic programming.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

Started with the recursive approach because I figured they wanted to see my thought process before jumping to the optimized version.

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AI HintsAI Generated

Suggested Approach

Start by defining the problem and presenting a naive recursive solution, then identify overlapping subproblems and optimize using dynamic programming (memoization or tabulation). Finally, discuss space optimization and trade-offs, relating to real-world applications like embedded systems.

Pro tip: Emphasize the importance of optimizing for space, especially in resource-constrained environments like medical devices, and mention how you'd test and validate the solution with edge cases.

1. Understand and Define the Problem

Clarify that the problem is to count distinct ways to climb n steps with 1 or 2 steps at a time, and note that the order of steps matters. Identify the base cases: n=0 (1 way), n=1 (1 way).

2. Naive Recursive Solution

Write a recursive function that returns climb(n-1) + climb(n-2) for n>1, with base cases. Explain that this has exponential time complexity O(2^n) due to repeated computations.

3. Identify Overlapping Subproblems and Optimal Substructure

Show that the recursion tree has many repeated calls (e.g., climb(3) computed multiple times), indicating overlapping subproblems. The optimal solution can be built from optimal solutions of subproblems.

4. Optimize with Dynamic Programming

Introduce memoization (top-down) to cache results, reducing time to O(n) and space to O(n). Then show tabulation (bottom-up) using an array, and finally optimize space to O(1) by keeping only the last two values.

5. Discuss Trade-offs and Applications

Compare time and space complexities of each approach. Mention that the O(1) space solution is ideal for embedded systems. Relate to Paradromics' domain by noting efficiency is critical in medical devices.

Key Points to Mention

  • Time complexity: O(2^n) for naive recursion, O(n) for DP, and O(1) space with iterative optimization.
  • Space complexity: O(n) for memoization and tabulation, O(1) for optimized iterative solution.
  • Overlapping subproblems and optimal substructure as key indicators for DP.
  • Memoization (top-down) vs. tabulation (bottom-up) and when to use each.
  • Edge cases: n=0, n=1, and large n (potential integer overflow).
  • Real-world relevance: efficiency in resource-constrained environments like neural implants.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.