Intuition¶

Approach¶

1.Calculate Degree of Each City:¶

Create a vector degree of size n value 0 to store the degree (number of connected roads) of each city.
Iterate through the roads array and for each road, increment the degree of both cities connected by that road.

2.Sort Degrees:¶

Sort the degree vector. This will help in assigning the highest possible values to cities with the highest degrees.

3.Assign Values to Cities:¶

After sorting, assign values to the cities based on their degrees. The city with the smallest degree gets the value 1, the next gets 2, and so on up to the city with the highest degree which gets the value n.

4.Calculate Total Importance:¶

Iterate through the sorted degree vector and calculate the total importance by multiplying the degree by its corresponding value (from 1 to n) and summing up these products.

Complexity¶

Time complexity: O(NLogN).
Space complexity: O(N).

Code¶

class Solution {
public:
    long long maximumImportance(int n, vector<vector<int>>& roads) {
        vector<long long> degree(n, 0);
        for (auto &a : roads) {
            degree[a[0]]++;
            degree[a[1]]++;
        }
        sort(degree.begin(), degree.end());
        long long total = 0;
        for (long long i=0;i<n;i++) {
            total += ((i+1)*degree[i]);
        }
        return total;
    }
};