Find Length of Longest Self-Sufficient Proper Substring
Reported by candidates from Amazon's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Amazon asked this in December 2024, and it's a dynamic-programming trap designed to catch candidates who don't spot the substring constraint early. You're hunting for the longest proper substring where some self-sufficiency condition holds, which means you can't just scan linearly and hope. The trick is recognizing that 'proper' rules out the whole string, and 'self-sufficient' is the pattern you need to encode into your DP state. StealthCoder will catch you if you blank on the DP transition, but the core insight is yours to own.
Pattern and pitfall
This is a classic DP problem where you build a table tracking whether substrings satisfy the self-sufficiency condition at each boundary. The pitfall: candidates try greedy or two-pointer first and waste 10 minutes realizing it doesn't work. The real move is defining dp[i][j] as whether substring from i to j is self-sufficient, then iterating all pairs or using a rolling window with DP to find the maximum length that's valid and proper (not the entire string). The self-sufficiency check itself is often O(1) or O(n) per substring depending on the condition. Amazon loves testing whether you can translate a vague business rule into a computable DP recurrence. If you hit the wall live, StealthCoder is your safety net for the exact transition logic.
Memorize the pattern. If you can't, run StealthCoder. The proctor sees the IDE. They don't see what's behind it.
You can drill Find Length of Longest Self-Sufficient Proper Substring cold, or you can hedge it. StealthCoder runs invisibly during screen share and surfaces a working solution in under 2 seconds. The proctor sees the IDE. They don't see what's behind it. Made by an engineer who treats the OA as theater. If yours is tonight, you don't have time to grind. You have time to hedge.
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Find Length of Longest Self-Sufficient Proper Substring FAQ
What does 'self-sufficient' mean in this context?+
The problem text isn't fully provided, but 'self-sufficient' typically means the substring satisfies some internal property without needing elements outside it. Common patterns: all characters appear equally, all elements sum to a target, or character frequencies balance. Read the problem statement carefully on test day.
Why can't I just use a greedy approach?+
Greedy doesn't work because the longest self-sufficient substring might not be found by always extending rightward. You could have a shorter valid one at position 2, a longer one at position 5, and extending greedily from 0 misses both. DP forces you to check all boundaries.
Is this O(n^2) or O(n^3)?+
Typically O(n^2) for the DP table iteration plus the cost of checking self-sufficiency per substring. If the check is O(n), you're at O(n^3). Optimize by precomputing checks or using a rolling hash if possible.
How do I handle the 'proper' constraint?+
A proper substring excludes the entire string. After you compute the max length across all valid substrings, make sure it's strictly less than n. This is a one-line guard that catches off-by-one errors.
Can I solve this in 30 minutes cold?+
Unlikely. The DP state design takes 10-15 minutes to articulate correctly. If Amazon is asking this, they expect you to either recognize the pattern or spend 20 minutes building it carefully. Focus on clarity over speed.