What is the optimal time complexity of solving Min Cost to Connect All Points?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Min Cost to Connect All Points?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Min Cost to Connect All Points?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Min Cost to Connect All Points?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

Back to Practice Dashboard

Top 150 InterviewEasy

Min Cost to Connect All Points

Learn how to solve the 'Min Cost to Connect All Points' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Easy

You are given an array points representing integer coordinates of some points on a 2D-plane, where points[i] = [xi, yi].

Return the minimum cost to make all points connected. All points are connected if there is exactly one simple path between any two points.

Write a function minCostConnectPoints(points: List[List[int]]) -> int.

Constraints

•1 <= len(points) <= 1000
•-10^6 <= xi, yi <= 10^6
•All points are distinct

Examples

Example 1

Input

points = [[0,0],[2,2],[3,10],[5,2],[7,0]]

Output

Explanation

Connect points as: (0,0)-(2,2) cost 4, (2,2)-(5,2) cost 3, (5,2)-(7,0) cost 4, (2,2)-(3,10) cost 9. Total = 20.

Example 2

Input

points = [[3,12],[-2,5],[-4,1]]

Output

Explanation

Connecting points: (-4,1) to (-2,5) with cost 6, (-2,5) to (3,12) with cost 12. Total 18.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor