How do you solve Maximum Star Sum of a Graph on LeetCode?

Maximum Star Sum of a Graph (LeetCode #2497) 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: The star sum can be maximized by focusing on the highest valued neighbors.

What is the brute force solution for Maximum Star Sum of a Graph?

The brute force approach for Maximum Star Sum of a Graph is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every node as a potential center of the star graph and calculating the star sum by considering all its neighbors. This method is straightforward but inefficient for larger graphs. The optimal Optimal Solution approach improves this to O(n log n).

What are the interview tips for Maximum Star Sum of a Graph?

Always clarify the constraints and edge cases before diving into the solution. Explain your thought process clearly as you code, especially when choosing data structures. Consider discussing the trade-offs of different approaches during the interview.

What are common mistakes when solving Maximum Star Sum of a Graph?

Not considering the case where a node has fewer than k neighbors. Failing to handle edge cases like empty edges or negative values.

#2497

Maximum Star Sum of a Graph

Medium

ArrayGreedyGraph TheorySortingHeap (Priority Queue)Hash MapArray

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 leverages a more efficient way to gather neighbors and calculate the star sum. By using a priority queue, we can quickly access the top k neighbors without needing to sort them completely.

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Algorithm

4 steps

1Step 1: Build a graph representation using an adjacency list.
2Step 2: For each node, gather its neighbors and push their values into a max-heap.
3Step 3: Extract the top k values from the heap to calculate the star sum.
4Step 4: Update the maximum star sum encountered.

solution.py21 lines

1# Full working Python code
2import heapq
3from collections import defaultdict
4
5def maxStarSum(vals, edges, k):
6    graph = defaultdict(list)
7    for a, b in edges:
8        graph[a].append(b)
9        graph[b].append(a)
10
11    max_sum = float('-inf')
12    for i in range(len(vals)):
13        star_sum = vals[i]
14        neighbors = [vals[neighbor] for neighbor in graph[i]]
15        if neighbors:
16            largest_neighbors = heapq.nlargest(k, neighbors)
17            star_sum += sum(largest_neighbors)
18        max_sum = max(max_sum, star_sum)
19
20    return max_sum
21

ℹ

Complexity note: The complexity is O(n log n) due to the use of a priority queue for extracting the top k values, which is more efficient than sorting all neighbors.

1The star sum can be maximized by focusing on the highest valued neighbors.
2Using a priority queue allows us to efficiently retrieve the top k neighbor values.

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