How do you solve Min Cost to Connect All Points on LeetCode?

Min Cost to Connect All Points (LeetCode #1584) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Understanding the properties of Minimum Spanning Trees is crucial for solving connection problems.

What is the brute force solution for Min Cost to Connect All Points?

The brute force approach for Min Cost to Connect All Points is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach considers all pairs of points and calculates the total cost of connecting them. This method is straightforward but inefficient for larger datasets. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Min Cost to Connect All Points?

Min Cost to Connect All Points uses the following concepts: Array, Union-Find, Graph Theory, Minimum Spanning Tree. The recommended patterns to study are: Graph Theory, Minimum Spanning Tree, Priority Queue.

What are the interview tips for Min Cost to Connect All Points?

Always clarify the problem requirements and constraints before diving into the solution. Discuss your thought process and approach before coding to ensure you’re on the right track. Practice explaining your code and the logic behind it, as communication is key in interviews.

What are common mistakes when solving Min Cost to Connect All Points?

Not considering the need to track visited nodes, leading to cycles in the MST. Failing to sort edges or not using the correct algorithm for MST can lead to incorrect results.

#1584

Min Cost to Connect All Points

Medium

ArrayUnion-FindGraph TheoryMinimum Spanning TreeGraph TheoryMinimum Spanning TreePriority Queue

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

The optimal solution uses a Minimum Spanning Tree (MST) algorithm like Prim's or Kruskal's. This approach efficiently connects all points with the minimum cost by focusing on edges with the lowest weights.

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Algorithm

3 steps

1Step 1: Use a priority queue to store edges based on their Manhattan distance.
2Step 2: Start from an arbitrary point and add its edges to the queue.
3Step 3: Continuously extract the minimum edge from the queue and add the corresponding point to the MST until all points are connected.

solution.py24 lines

1import heapq
2
3class Solution:
4    def minCostConnectPoints(self, points):
5        n = len(points)
6        visited = [False] * n
7        min_heap = [(0, 0)]  # (cost, point index)
8        total_cost = 0
9        edges_used = 0
10
11        while edges_used < n:
12            cost, u = heapq.heappop(min_heap)
13            if visited[u]:
14                continue
15            visited[u] = True
16            total_cost += cost
17            edges_used += 1
18
19            for v in range(n):
20                if not visited[v]:
21                    distance = abs(points[u][0] - points[v][0]) + abs(points[u][1] - points[v][1])
22                    heapq.heappush(min_heap, (distance, v))
23
24        return total_cost

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Complexity note: The time complexity is O(n log n) due to the priority queue operations. The space complexity is O(n) because we store the visited status of each point and the priority queue.

1Understanding the properties of Minimum Spanning Trees is crucial for solving connection problems.
2Using efficient data structures like priority queues can significantly reduce the time complexity.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.