← Morgan Stanley Interview Insights
My first instinct was greedy: find the line covering the most uncovered points, mark them, repeat.
First, clarify the problem constraints and edge cases, then reduce it to a graph problem where points are vertices and lines are cliques. Discuss the general NP-hardness and present a practical approach for small n using backtracking with pruning, or a greedy heuristic for larger n.
Pro tip: Acknowledge the NP-hard nature of the general problem and propose a solution that balances optimality and efficiency, such as using bitmask DP for n ≤ 20 or a greedy set cover approximation for larger n, showing awareness of real-world constraints.
Ask about constraints: n's maximum value, whether points are distinct, and if lines must be unique. This determines the appropriate algorithmic approach.
Represent each point as a vertex and each possible line as a clique (set of collinear points). The goal is to cover all vertices with minimum cliques, which is equivalent to minimum clique cover.
Explain that minimum clique cover is NP-hard in general, so exact solutions are feasible only for small n. For larger n, approximation or heuristics are needed.
For small n (≤20), use bitmask DP or backtracking to find the exact minimum. For larger n, use a greedy set cover approach: repeatedly choose the line covering the most uncovered points.
Compare exact vs. approximate methods, highlighting time complexity, optimality, and practical applicability. Mention that the greedy algorithm gives an O(log n) approximation.
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