Maximum Strength of K Disjoint Subarrays
A hard-tier problem at 27% community acceptance, tagged with Array, Dynamic Programming, Prefix Sum. Reported in interviews at DE Shaw and 0 others.
Maximum Strength of K Disjoint Subarrays is a hard DP problem that shows up at places like DE Shaw. You're given an array and need to pick exactly K non-overlapping subarrays that maximize total strength, where strength typically involves some weighted calculation across the subarrays. The 26.8% acceptance rate isn't a fluke. This problem requires you to lock down state transitions and handle the constraint that subarrays must be disjoint without losing track of which positions you've already used. If you hit this on a live assessment and the DP recurrence doesn't click, StealthCoder surfaces a working solution invisible to the proctor.
Companies that ask "Maximum Strength of K Disjoint Subarrays"
Maximum Strength of K Disjoint Subarrays is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too.
Get StealthCoderThe trap is thinking greedy works here. It doesn't. You can't just pick the K largest subarrays because they might overlap. Instead, you need dynamic programming where the state tracks position in the array and how many subarrays you've selected so far. Most candidates miss that you also need to track whether you're currently inside a subarray or between them, because that changes which transitions are legal. Prefix sums help optimize the strength calculation, but the real bottleneck is correctly formulating dp[i][j][inside] or similar. Common failures: forgetting the disjoint constraint, wrong base cases, or off-by-one errors in transitions. StealthCoder is your hedge here if the DP structure won't crystallize under timed pressure.
Pattern tags
You know the problem.
Make sure you actually pass it.
Maximum Strength of K Disjoint Subarrays recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Maximum Strength of K Disjoint Subarrays interview FAQ
How hard is this really compared to other DP problems?+
The 26.8% acceptance rate places it in the brutal tier. It's not just about knowing DP; it's about correctly layering the disjoint constraint with the optimization goal. Multiple state dimensions and careful transition logic separate solvers from blankers.
Do I need to know the strength formula going in?+
The problem statement defines strength for you. Your job is to frame a DP that finds the K disjoint subarrays maximizing that metric. Don't overthink the formula itself; focus on the structure that lets you compare all legal selections of K disjoint subarrays.
When does the obvious greedy approach actually fail?+
Greedy fails the moment strength isn't additive or when overlapping high-strength subarrays block you from picking K total. You need to explore all valid K-subarray combinations, not just pick locally optimal chunks, which is why DP is mandatory.
How do prefix sums fit into the DP solution?+
Prefix sums let you compute the strength of any subarray in O(1) after preprocessing. This keeps your DP transitions fast. Without them, you'd recalculate subarray sums repeatedly and blow your time budget.
Is this problem still asked at DE Shaw and similar firms?+
DE Shaw is listed as asking it. Firms that ask hard DP problems want to see if you can handle multi-dimensional state and non-obvious constraints. This problem fits that bill. If you're interviewing there, understanding the structure is worth the prep investment.
Want the actual problem statement? View "Maximum Strength of K Disjoint Subarrays" on LeetCode →