547. Number of Provinces

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547. Number of Provinces

Description

There are n cities. Some of them are connected, while some are not. If city a is connected directly with city b, and city b is connected directly with city c, then city a is connected indirectly with city c.

A province is a group of directly or indirectly connected cities and no other cities outside of the group.

You are given an n x n matrix isConnected where isConnected[i][j] = 1 if the i^th city and the j^th city are directly connected, and isConnected[i][j] = 0 otherwise.

Return the total number of provinces .

Example 1:

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Input: isConnected = [[1,1,0],[1,1,0],[0,0,1]]
Output: 2

Example 2:

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Input: isConnected = [[1,0,0],[0,1,0],[0,0,1]]
Output: 3

Constraints:

  • 1 <= n <= 200
  • n == isConnected.length
  • n == isConnected[i].length
  • isConnected[i][j] is 1 or 0.
  • isConnected[i][i] == 1
  • isConnected[i][j] == isConnected[j][i]

Hints/Notes

Solution

Language: C++

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class Solution {
public:
    int findCircleNum(vector<vector<int>>& isConnected) {
        int n = isConnected.size();
        vector<int> roots(n);
        int res = n;
        iota(roots.begin(), roots.end(), 0);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (isConnected[i][j]) {
                    int rootI = findRoot(i, roots), rootJ = findRoot(j, roots);
                    if (rootI != rootJ) {
                        roots[rootI] = rootJ;
                        res--;
                    }
                }
            }
        }
        return res;
    }

    int findRoot(int node, vector<int>& roots) {
        if (node != roots[node]) {
            roots[node] = findRoot(roots[node], roots);
        }
        return roots[node];
    }
};