Minimize Connected Groups by Inserting Interval
A medium-tier problem at 50% community acceptance, tagged with Array, Binary Search, Sliding Window. Reported in interviews at DE Shaw and 0 others.
You've got an array of intervals, and you need to insert a new interval to minimize the number of connected groups. It sounds like a merge-sort hybrid, but the trick isn't obvious until you see why the greedy approach fails. DE Shaw asks this one. The acceptance rate hovers around 50%, which means half the people in the assessment room will miss the pattern. If you blank on whether to binary search, slide, or just sort and merge, StealthCoder runs invisible during your screen share and hands you a working solution in seconds. This is the kind of problem that looks simple until you hit the edge case.
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Minimize Connected Groups by Inserting Interval 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. Built by an Amazon engineer who used it to pass JPMorgan's OA and system design loop.
Get StealthCoderThe problem wants you to insert an interval into a list and count how many disjoint groups remain. The trap is thinking you can just insert and count connected components in linear time. The real pattern is recognizing that sorting and binary search work together here. You need to find where the new interval overlaps with existing ones, merge those intervals, then count what's left. Most candidates try a greedy single-pass approach and get burned by overlaps they miss. Sliding window thinking helps once you realize you're looking for contiguous ranges of overlap. The sorting step collapses the problem from messy to clean. If you haven't drilled this exact structure before, hitting it live is rough. StealthCoder is the hedge for the moment you realize you're three minutes in and your logic is leaking edge cases.
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Minimize Connected Groups by Inserting Interval recycles across companies for a reason. It's medium-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. Built by an Amazon engineer who used it to pass JPMorgan's OA and system design loop. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimize Connected Groups by Inserting Interval interview FAQ
What's the actual trick to this problem?+
Sort the intervals first, then binary search to find where your new interval starts overlapping. Once you know the overlap window, merge all touching intervals within that range. Count the resulting disjoint groups. The sorting step is what people skip, thinking they can do it in one pass. They can't.
Why does the greedy single-pass approach fail?+
Because overlaps aren't always obvious when intervals are unsorted. A greedy pass might merge intervals A and B correctly but miss that B actually overlaps with D, not C. Sorting forces you to see the topology of overlaps. Without it, you're flying blind on edge cases.
Is binary search really necessary here?+
Not strictly necessary, but it's the efficient way to locate the start of your overlap window in sorted intervals. If you sort and then linearly scan for the first overlapping interval, you get O(n log n) anyway. Binary search makes the overlap-search step O(log n) instead of O(n), which matters if n is large.
How does sliding window fit into this?+
Once you've binary-searched to the start of overlaps, you slide forward through the sorted intervals, merging each one that touches or overlaps with your accumulated merged interval. It's a window of consecutive overlaps you're collapsing into one. After the window ends, you count the groups.
Will this problem actually come up in a real assessment?+
DE Shaw has asked it. It's not top-frequency, but it's real. Fifty percent acceptance means it's tricky enough to trip up half the candidates who see it. If it shows up and you haven't seen the sort-plus-binary-search pattern, you lose time. If you've drilled it or have StealthCoder, you're fine.
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