# Number Of Provinces Problem

## Description

LeetCode Problem 547.

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:

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

Example 2:

 1 2 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]

## Sample C++ Code using Union Find

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 class Solution { public: int _find(int p, vector& num) { while (p != num[p]) p = num[p]; return p; } void _union(int i, int j, vector& num) { int r1 = _find(i, num); int r2 = _find(j, num); num[r1] = r2; } int findCircleNum(vector>& M) { int n = M.size(); vector parent(n); for (int i = 0; i < n; i ++) parent[i] = i; int r1, r2; for (int i = 0; i < n; i ++) { for (int j = 0; j < n; j ++) { if (i == j) continue; if (M[i][j] == 0) continue; _union(i, j, parent); } } unordered_map mp; for (int i = 0; i < n; i ++) mp[_find(i, parent)] = 1; return mp.size(); } };