How do you solve Maximum Sum of Edge Values in a Graph on LeetCode?

Maximum Sum of Edge Values in a Graph (LeetCode #3547) 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: Higher degree nodes should get higher values.

What is the time complexity of Maximum Sum of Edge Values in a Graph?

The optimal solution for Maximum Sum of Edge Values in a Graph runs in O(n log n) time and uses O(n) space. The complexity arises from sorting the nodes based on their degree.

What is the brute force solution for Maximum Sum of Edge Values in a Graph?

The brute force approach for Maximum Sum of Edge Values in a Graph is Brute Force, with O(n!) time complexity and O(n) space complexity. Try all possible assignments of values from 1 to n to the nodes and calculate the score for each configuration. This method is inefficient but guarantees finding the maximum score. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Sum of Edge Values in a Graph?

Maximum Sum of Edge Values in a Graph uses the following concepts: Math, Greedy, Graph Theory. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximum Sum of Edge Values in a Graph?

Explain your thought process clearly. Discuss trade-offs between brute force and optimal approaches. Practice similar problems to build intuition.

What are common mistakes when solving Maximum Sum of Edge Values in a Graph?

Not considering the degree of nodes when assigning values. Overlooking edge cases like minimal graphs.

#3547

Maximum Sum of Edge Values in a Graph

Hard

MathGreedyGraph TheoryGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

Assign higher values to nodes that are connected by edges. This maximizes the product of connected nodes, leading to a higher score.

⚙️

Algorithm

3 steps

1Step 1: Create a list of node degrees from the edges.
2Step 2: Sort nodes by degree in descending order.
3Step 3: Assign values from n down to 1 based on sorted order and calculate the score.

solution.py9 lines

1def maxScoreOptimal(n, edges):
2    from collections import defaultdict
3    degree = defaultdict(int)
4    for a, b in edges:
5        degree[a] += 1
6        degree[b] += 1
7    sorted_nodes = sorted(degree.keys(), key=lambda x: -degree[x])
8    value_assignment = {node: n - i for i, node in enumerate(sorted_nodes)}
9    return sum(value_assignment[a] * value_assignment[b] for a, b in edges)

ℹ

Complexity note: The complexity arises from sorting the nodes based on their degree.

1Higher degree nodes should get higher values.
2The graph structure (path or cycle) influences value assignment.

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