Minimum Number of Lines to Cover Points
A medium-tier problem at 43% community acceptance, tagged with Array, Hash Table, Math. Reported in interviews at Morgan Stanley and 0 others.
You've got a scatter of points on a 2D plane, and you need to cover all of them with the fewest straight lines possible. Morgan Stanley has asked this one. It's a geometry problem wearing a dynamic programming mask, and the naive greedy approach (draw a line through the two furthest points, repeat) doesn't work. The trick is realizing you're hunting for collinear point sets, then using bitmask DP to explore which subsets can be covered by a single line. If this problem hits your live OA and the geometry intimidates you, StealthCoder surfaces a working solution invisible to the proctor.
Companies that ask "Minimum Number of Lines to Cover Points"
Minimum Number of Lines to Cover Points 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 core insight is that with a small point set (usually n <= 20), you can afford to check all possible lines defined by pairs of points, then use bitmask DP where state represents which points are already covered. For each uncovered point, you branch on all lines that pass through it, greedily taking the line that covers the maximum number of remaining points. The bitmask state tracks which points you've handled, and you recurse on the uncovered subset. Common pitfall: floating-point comparisons when checking collinearity. Use cross products or slope comparisons with integer arithmetic to avoid precision bugs. Most candidates get stuck on the collinearity test or the DP state transition. StealthCoder is your hedge if the geometry logic doesn't click during the assessment.
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Minimum Number of Lines to Cover Points 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. 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.
Minimum Number of Lines to Cover Points interview FAQ
How do I check if three points are collinear without precision errors?+
Use the cross product of vectors: if (p2.y - p1.y) * (p3.x - p1.x) == (p3.y - p1.y) * (p2.x - p1.x), they're collinear. This avoids floating-point division and division-by-zero edge cases that plague slope-based checks.
Why doesn't a greedy 'cover the most points per line' approach work?+
Greedy can get stuck in a suboptimal local choice. A line covering 5 points might force the remaining points to need 3 more lines, while picking a different line covering 4 points leaves remainders solvable in 2 lines. Only exhaustive search (or DP memoization) finds the true minimum.
Is this really asked in interviews, or just competitive programming?+
Morgan Stanley has asked it. It's less common than LeetCode dailies, but it appears in assessments for companies hiring for quant, finance-tech, and algorithmic roles where geometry and optimization matter.
How big can the point set get, and does that change the algorithm?+
Usually n <= 20. At that scale, bitmask DP with O(2^n * n^2) is feasible. If n > 20, you'd need a completely different approach (e.g., approximation or heuristic). Check problem constraints; they define the strategy.
Does the bitmask DP state need memoization?+
Yes. Without it, you'll recompute the same covered-point subsets repeatedly and time out. Store results keyed by the bitmask representing which points are covered. This drops complexity from exponential to manageable.
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