Is Minimum Number of Lines to Cover Points easy or hard?

This problem is rated Medium but feels closer to Hard if you are unfamiliar with subset dynamic programming. The difficulty comes from recognizing that small input size allows bitmask DP and from efficiently precomputing collinear point sets.

Minimum Number of Lines to Cover Points Python/Java solution

Implementations typically compute line masks using nested loops and store them in an array. A DP array of size 2^n tracks the minimum lines required for each subset. The same logic works across Python, Java, C++, and Go because the algorithm relies mainly on bit operations and simple geometry checks.

How to solve Minimum Number of Lines to Cover Points in O(n^2 * 2^n)?

First compute a bitmask for every pair of points representing all points that lie on the same line. Then run dynamic programming over subsets where dp[mask] stores the minimum lines needed to cover that subset. For each state, select an uncovered point and try all lines passing through it to update the DP state.

What is the best approach for Minimum Number of Lines to Cover Points?

The most efficient solution uses bitmask dynamic programming with precomputed collinear point sets. Each subset of points is represented by a bitmask, and DP transitions simulate drawing a line that covers multiple points at once. This reduces the search space significantly compared to brute-force recursion and runs in O(n^2 * 2^n) time.

Is Minimum Number of Lines to Cover Points asked at Google/Amazon/Meta?

Problems combining geometry with bitmask dynamic programming frequently appear in interviews at companies like Google and Meta. They test the ability to model a geometric constraint as a subset DP problem and optimize brute-force search using bitmasks.

What data structure is used in Minimum Number of Lines to Cover Points?

The solution relies on bitmasks to represent subsets of points and a DP array to store results for each subset. Basic geometry calculations are used to test whether three points are collinear. Arrays and bit operations are the core data structures involved.

What is the time complexity of Minimum Number of Lines to Cover Points?

The optimal approach runs in O(n^2 * 2^n) time with O(2^n) space. The algorithm first precomputes which points lie on the same line and stores them as bitmasks. Then dynamic programming iterates over all subsets of points to compute the minimum number of lines required.

Description Hints 4 Solution Video 54:05

2152. Minimum Number of Lines to Cover Points

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You are given an array points where points[i] = [x_i, y_i] represents a point on an X-Y plane.

Straight lines are going to be added to the X-Y plane, such that every point is covered by at least one line.

Return the minimum number of straight lines needed to cover all the points.

Example 1:

Input: points = [[0,1],[2,3],[4,5],[4,3]]
Output: 2
Explanation: The minimum number of straight lines needed is two. One possible solution is to add:
- One line connecting the point at (0, 1) to the point at (4, 5).
- Another line connecting the point at (2, 3) to the point at (4, 3).

Example 2:

Input: points = [[0,2],[-2,-2],[1,4]]
Output: 1
Explanation: The minimum number of straight lines needed is one. The only solution is to add:
- One line connecting the point at (-2, -2) to the point at (1, 4).

Constraints:

1 <= points.length <= 10
points[i].length == 2
-100 <= x_i, y_i <= 100
All the points are unique.

Asked at 1 company

Morgan Stanley

Topics

Hints open one at a time

Hint 1

What is the highest possible answer for a set of n points?

Hint 2

The highest possible answer is n / 2 (rounded up). This is because you can cover at least two points with a line, and if n is odd, you need to add one extra line to cover the last point.

Hint 3

Suppose you have a line covering two points, how can you quickly check if a third point is also covered by that line?

Hint 4

Calculate the slope from the first point to the second point. If the slope from the first point to the third point is the same, then it is also covered by that line.

54:05

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