How do you solve Maximal Network Rank on LeetCode?

Maximal Network Rank (LeetCode #1615) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + m) time complexity and O(n) space complexity. Key insight: Understanding how to calculate degrees of nodes is crucial for optimizing graph problems.

What is the brute force solution for Maximal Network Rank?

The brute force approach for Maximal Network Rank is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach calculates the network rank for every possible pair of cities. This means we check each pair and sum their direct connections, which is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n + m).

What algorithm or data structure is used to solve Maximal Network Rank?

Maximal Network Rank uses the following concepts: Graph Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximal Network Rank?

Always start with a brute-force solution to understand the problem better. Discuss your thought process with the interviewer; they may guide you towards optimizations. Practice explaining your code and reasoning clearly, as communication is critical in interviews.

What are common mistakes when solving Maximal Network Rank?

Failing to account for shared roads when calculating the network rank. Not efficiently counting the degree of each city, leading to unnecessary repeated calculations.

#1615

Maximal Network Rank

Medium

Graph TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n + m)Space O(n)

The optimal approach uses a hash map to count the degree of each city and then calculates the network rank in a single pass through the cities. This reduces the time complexity significantly.

⚙️

Algorithm

3 steps

1Step 1: Create an array to count the degree of each city.
2Step 2: Populate the degree array by iterating through the roads.
3Step 3: For each pair of cities, calculate the network rank using the degree array and adjust for shared roads.

solution.py18 lines

1# Full working Python code
2n = 4
3roads = [[0,1],[0,3],[1,2],[1,3]]
4
5def maxNetworkRank(n, roads):
6    degree = [0] * n
7    for a, b in roads:
8        degree[a] += 1
9        degree[b] += 1
10    max_rank = 0
11    for i in range(n):
12        for j in range(i + 1, n):
13            count = (i, j) in roads or (j, i) in roads
14            rank = degree[i] + degree[j] - (1 if count else 0)
15            max_rank = max(max_rank, rank)
16    return max_rank
17
18print(maxNetworkRank(n, roads))

ℹ

Complexity note: The time complexity is O(n + m) where n is the number of cities and m is the number of roads. We traverse the roads once to build the degree array and then check each pair of cities. The space complexity is O(n) for the degree array.

1Understanding how to calculate degrees of nodes is crucial for optimizing graph problems.
2Recognizing that shared connections need to be adjusted in the final rank calculation is key.

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