Introduction

In this blog post, we will explore how to solve the LeetCode problem "2497" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

There is an undirected graph consisting of n nodes numbered from 0 to n - 1. You are given a 0-indexed integer array vals of length n where vals[i] denotes the value of the ith node. You are also given a 2D integer array edges where edges[i] = [ai, bi] denotes that there exists an undirected edge connecting nodes ai and bi. A star graph is a subgraph of the given graph having a center node containing 0 or more neighbors. In other words, it is a subset of edges of the given graph such that there exists a common node for all edges. The image below shows star graphs with 3 and 4 neighbors respectively, centered at the blue node. The star sum is the sum of the values of all the nodes present in the star graph. Given an integer k, return the maximum star sum of a star graph containing at most k edges. Example 1: Input: vals = [1,2,3,4,10,-10,-20], edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[3,6]], k = 2 Output: 16 Explanation: The above diagram represents the input graph. The star graph with the maximum star sum is denoted by blue. It is centered at 3 and includes its neighbors 1 and 4. It can be shown it is not possible to get a star graph with a sum greater than 16. Example 2: Input: vals = [-5], edges = [], k = 0 Output: -5 Explanation: There is only one possible star graph, which is node 0 itself. Hence, we return -5. Constraints: n == vals.length 1 <= n <= 105 -104 <= vals[i] <= 104 0 <= edges.length <= min(n * (n - 1) / 2, 105) edges[i].length == 2 0 <= ai, bi <= n - 1 ai != bi 0 <= k <= n - 1

Explanation

Here's the breakdown of the solution:

• Iterate through each node as a potential center: Consider each node from 0 to n-1 as the center of a potential star graph.
• Find the best k neighbors: For each potential center, identify its neighbors and select the k neighbors with the highest values.

• Calculate the star sum and maximize: Calculate the star sum for each potential center (center's value + sum of top k neighbors) and maintain the maximum star sum encountered so far.

• Runtime Complexity: O(n (degree + k log(degree))), where n is the number of nodes and degree is the maximum degree of any node. In the worst-case, degree can be O(n), so the complexity can approach O(n^2 log(n)). *Storage Complexity: O(n), primarily for storing the graph's adjacency list and neighbor values.

Code

    def maxStarSum(vals, edges, k):
    n = len(vals)
    adj = [[] for _ in range(n)]
    for u, v in edges:
        adj[u].append(v)
        adj[v].append(u)

    max_sum = float('-inf')
    for center in range(n):
        neighbors = []
        for neighbor in adj[center]:
            neighbors.append(vals[neighbor])

        neighbors.sort(reverse=True)

        current_sum = vals[center]
        num_neighbors = min(k, len(neighbors))
        for i in range(num_neighbors):
            current_sum += neighbors[i]

        max_sum = max(max_sum, current_sum)

    return max_sum