How do you solve Minimum Degree of a Connected Trio in a Graph on LeetCode?

Minimum Degree of a Connected Trio in a Graph (LeetCode #1761) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + e) time complexity and O(n) space complexity. Key insight: Understanding the structure of the graph is crucial for identifying connected trios.

What is the brute force solution for Minimum Degree of a Connected Trio in a Graph?

The brute force approach for Minimum Degree of a Connected Trio in a Graph is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every possible trio of nodes in the graph to see if they form a connected trio. If they do, we calculate the degree and keep track of the minimum degree found. The optimal Optimal Solution approach improves this to O(n + e).

What algorithm or data structure is used to solve Minimum Degree of a Connected Trio in a Graph?

Minimum Degree of a Connected Trio in a Graph uses the following concepts: Graph Theory, Enumeration. The recommended patterns to study are: Graph Traversal, Adjacency List, Degree Calculation.

What are the interview tips for Minimum Degree of a Connected Trio in a Graph?

Always clarify the problem requirements and constraints. Think about edge cases, such as disconnected graphs. Explain your thought process clearly while coding.

What are common mistakes when solving Minimum Degree of a Connected Trio in a Graph?

Not checking if the nodes are connected before calculating the degree. Forgetting to handle cases where no trios exist.

#1761

Minimum Degree of a Connected Trio in a Graph

Hard

Graph TheoryEnumerationGraph TraversalAdjacency ListDegree Calculation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n + e)Space O(n)

The optimal solution uses a more structured approach by leveraging the properties of degrees and adjacency to efficiently find connected trios without checking every combination explicitly.

⚙️

Algorithm

5 steps

1Step 1: Create an adjacency list to represent the graph.
2Step 2: For each node, calculate its degree and store it.
3Step 3: For each edge, check if both endpoints have common neighbors to form a trio.
4Step 4: Calculate the degree of the trio using the formula: degree(u) + degree(v) + degree(w) - 6.
5Step 5: Keep track of the minimum degree found.

solution.py17 lines

1def minTrioDegree(n, edges):
2    from collections import defaultdict
3    graph = defaultdict(set)
4    degree = [0] * (n + 1)
5    for u, v in edges:
6        graph[u].add(v)
7        graph[v].add(u)
8        degree[u] += 1
9        degree[v] += 1
10    min_degree = float('inf')
11    for u in range(1, n + 1):
12        for v in graph[u]:
13            for w in graph[u]:
14                if v < w and w in graph[v]:
15                    trio_degree = degree[u] + degree[v] + degree[w] - 6
16                    min_degree = min(min_degree, trio_degree)
17    return min_degree if min_degree != float('inf') else -1

ℹ

Complexity note: The time complexity is O(n + e) where e is the number of edges, as we traverse the edges to build the graph and then check for trios. The space complexity is O(n) due to the adjacency list and degree array.

1Understanding the structure of the graph is crucial for identifying connected trios.
2Using degrees effectively helps in calculating the minimum degree quickly.

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