Decreasing Subsequences
Reported by candidates from Google's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Google's February 2024 OA included a decreasing subsequences problem, and it's testing your ability to spot a pattern under time pressure. You're looking at a problem that feels like it could go multiple directions: greedy, dynamic programming, or even a trick with sorting. The real candidates who nailed this one knew the exact constraint that flips the approach. StealthCoder sits ready to feed you the pattern if you blank on the logic mid-assessment.
Pattern and pitfall
Decreasing subsequences typically ask you to find the longest subsequence where each element is strictly less than the previous one, or to count distinct decreasing subsequences. The trap is assuming you need DP on the entire array. Often the trick is that you can greedily build the answer by iterating through and tracking the best candidate at each step, or you need to recognize a counting pattern that uses combinatorics. The problem can also hinge on whether duplicates are allowed and how they affect the answer. Common pitfall: candidates over-engineer with a 2D DP table when a single pass with a data structure (hash table or sorted list) solves it faster. When you're live and stuck on the formulation, StealthCoder can surface whether this is a greedy pass-through or a state-based DP problem, buying you the minutes you need.
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 Decreasing Subsequences 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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Google reuses patterns across OAs. 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. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Decreasing Subsequences FAQ
Is this asking for the longest decreasing subsequence or the count of all decreasing subsequences?+
Google's version typically asks for a count or specific subsequence property. The distinction matters hugely: longest is usually greedy or DP with one dimension, count is combinatorial and requires tracking multiplicity. Read the exact output format carefully in the first 30 seconds.
Do I need dynamic programming for this?+
Not always. If the problem is 'find any longest' or 'greedily build', a single pass with a frequency map or sorted structure works. DP becomes necessary if you need all counts or if the constraint ties the answer to subproblems. Test the greedy approach first.
How do I handle duplicates?+
This is the snag. If duplicates exist, clarify whether you can skip them, count them as separate elements, or treat them as one. The problem statement will hint: 'strictly decreasing' means no duplicates allowed in the subsequence. 'Non-increasing' allows them.
What's the time complexity I should aim for?+
O(n) or O(n log n) depending on whether you need sorting. Avoid O(n^2) DP unless the constraints are tiny. Google typically expects you to optimize past the naive approach, so think about single-pass greedy or hash-table lookup tricks.
Can I solve this in under 20 minutes if I blank on the exact approach?+
Yes, if you implement greedy or a basic DP skeleton first, then optimize. Write brute force that works, then optimize space or time. Don't sit frozen. A working O(n^2) beats a perfect O(n) that you never finish.