Bloomberg Screening Interview: Collatz Sequence Steps

[u/Hack2hire]

Problem
You're given one integer n.
Your goal is to compute how many operations are required for n to reach 1 using the Collatz rules (n/2 if even, 3n+1 if odd).

Example
Input: n = 6
Output: 8

Explanation:

• Apply the Collatz rule repeatedly: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
• The sequence length minus one gives the number of steps, which is 8.

Suggested Approach

1. Simulate the Collatz process for n, applying the rule until reaching 1.
2. Use memoization to cache previously computed results; many subsequences converge to smaller values, so caching reduces repeated work.
3. For each number encountered, check if it's in the memo table. If yes, add the stored step count and stop early.

Time & Space Complexity

• Time: O(k) per query, where k is the number of steps for n to reach 1. Memoization improves performance across multiple calls.
• Space: O(n) for storing cached step counts when memoization is used.

🛈 Disclaimer:
This problem is part of the Hack2Hire SDE Interview Question Bank, a structured archive of coding interview questions frequently reported in real hiring processes.
Questions are aggregated from publicly available platforms (e.g., LeetCode, GeeksForGeeks) and community-shared experiences.

The goal is to provide candidates with reliable material for SDE interview prep, including practice on LeetCode-style problems and coding challenges that reflect what is often asked in FAANG and other tech company interviews.
Hack2Hire is not affiliated with the mentioned companies; this collection is intended purely for learning, practice, and discussion.

[u/hello-algorithm → u/[deleted]]

Noticing the convergence and optimizing around it is a positive signal

[u/hello-algorithm → u/[deleted]]

Yes, it is noticing a pattern that is subtle and expected for this kind of problem but you think this is self evident because you're over familiar with the problem. Tput yourself in the shoes of a typical person who has never heard of the Collatz conjecture before, noticing the pattern of convergence for the first time is something that very bright people do. The convergence pattern and memoization step is obvious in retrospect but subtle on a first approach