What is the time complexity of LeetCode 2493. Divide Nodes Into the Maximum Number of Groups?

The Python solution on this page runs in O(n \times (n + m)).

What is the space complexity of LeetCode 2493. Divide Nodes Into the Maximum Number of Groups?

The Python solution on this page uses O(n + m) auxiliary space.

Divide Nodes Into the Maximum Number of Groups — LeetCode 2493 Python Solution

HardDepth-First SearchBreadth-First SearchUnion FindGraph

Problem: #2493
Pattern: Union-Find
Reading time: 5 min
Source: leetcode.com

The problem

You are given a positive integer n representing the number of nodes in an undirected graph. The nodes are labeled from 1 to n.

Example

Input: n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]
Output: 4
Explanation: As shown in the image we:

Python solution

Python

class Solution:
    def magnificentSets(self, n: int, edges: List[List[int]]) -> int:
        g = [[] for _ in range(n)]
        for a, b in edges:
            g[a - 1].append(b - 1)
            g[b - 1].append(a - 1)
        d = defaultdict(int)
        for i in range(n):
            q = deque([i])
            dist = [0] * n
            dist[i] = mx = 1
            root = i
            while q:
                a = q.popleft()
                root = min(root, a)
                for b in g[a]:
                    if dist[b] == 0:
                        dist[b] = dist[a] + 1
                        mx = max(mx, dist[b])
                        q.append(b)
                    elif abs(dist[b] - dist[a]) != 1:
                        return -1
            d[root] = max(d[root], mx)
        return sum(d.values())

Complexity

Measure	Complexity
Time	O(n \times (n + m))
Space	O(n + m) auxiliary

Pattern: Union-Find

Merge groups and ask whether two things are connected, both in near-constant time. LeetCode 2493. Divide Nodes Into the Maximum Number of Groups is filed here because LeetCode tags it Union Find, which is the vocabulary this hub collects.

The union-find guide has the Python template for the pattern and the 83 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 2493. Divide Nodes Into the Maximum Number of Groups?: LeetCode 2493. Divide Nodes Into the Maximum Number of Groups is rated Hard on LeetCode.
What is the time complexity of LeetCode 2493. Divide Nodes Into the Maximum Number of Groups?: The Python solution on this page runs in O(n \times (n + m)).
What is the space complexity of LeetCode 2493. Divide Nodes Into the Maximum Number of Groups?: The Python solution on this page uses O(n + m) auxiliary space.
What topics does LeetCode 2493. Divide Nodes Into the Maximum Number of Groups cover?: LeetCode 2493. Divide Nodes Into the Maximum Number of Groups is tagged Depth-First Search, Breadth-First Search, Union Find and Graph on LeetCode.