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Question 1: Counting Creator Communities

Description:

In a social network, there are multiple creators, and each one may be associated with others, forming a network community. Given an association matrix

related, where related[i][j] == '1' indicates that creator i and j are associated (they belong to the same community), and related[i][j] == '0' indicates no association.

Two creators are considered to be in the same community if they are directly or indirectly connected. For instance, if i is connected to j, and j is connected to k, then i, j, and k belong to the same community.

Implement a function to count and return the total number of communities in the social network.

Input:

• related (List[List[str]]): An n x n matrix representing associations, where related[i][j] is either '1' or '0', and related[i][i] is always '1'.

Output:

• Returns an integer, the number of communities in the network.

Code Example:

class UF: def __init__(self, size): self.parent = list(range(size)) def find(self, x): if self.parent[x] != x: self.parent[x] = self.find(self.parent[x]) return self.parent[x] def merge(self, x, y): px, py = self.find(x), self.find(y) self.parent[px] = py def countCreatorCommunities(related): n = len(related) uf = UF(n) for i in range(n): for j in range(i+1, n): if related[i][j] == '1': uf.merge(i, j) ds = set() for i in range(n): ds.add(uf.find(i)) return len(ds)

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Question 2: Counting Good Arrays

Description:

Given an integer array

arr, where some elements are 0, and other elements are positive integers, write a function to compute the number of “good arrays”. An array is considered a “good array” if it meets specific conditions, including:

1. Elements in arr can be consecutive 0s or some non-zero integers.
2. The count of consecutive 0s meeting specific conditions can generate valid subarrays.

The function should consider the position of these 0s and how they interact with neighboring non-zero numbers to fulfill the “good array” definition.

Input:

• arr (List[int]): An array of integers with some elements as 0 and others as positive integers.

Output:

• Returns the number of “good arrays” that meet the criteria, with the result modulo 10^9 + 7.

Code Example:

def countGoodArrays(arr): n = len(arr) dp = [[0] * (n+1) for _ in range(n)] mod = 10**9 + 7 dp[0][0] = 1 for i in range(1, n): dp[i][0] = 2 * dp[i-1][1] + dp[i-1][0] for j in range(1, i + 1): dp[i][j] = dp[i-1][j-1] + dp[i-1][j] + dp[i-1][j+1] dp[i][j] %= mod res = 1 sb = False prev = -1 eb = False c = 0 for i, x in enumerate(arr): if x == 0: c += 1 else: eb = True if not sb or not eb: res *= 3**c res %= mod else: if c > 0 and abs(x - arr[prev]) > c + 1: return 0 res *= (dp[c][abs(x - arr[prev])] + dp[c][abs(abs(x - arr[prev]) - 1)] + dp[c][abs(x - arr[prev]) + 1]) res %= mod sb = True c = 0 prev = i if c > 0: res *= 3**c res %= mod return res

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