Number of Provinces
Difficulty: Medium
Category: DSA
Topics: Depth-First Search, Breadth-First Search, Union Find, Graph
Asked at: Amazon, Two Sigma, Goldman Sachs, Dropbox, Facebook, Audible
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 `ith` city and the `jth` city are directly connected, and `isConnected[i][j] = 0` otherwise.
Return _the total number of **provinces**_.
**Example 1:**
**Input:** isConnected = [[1,1,0],[1,1,0],[0,0,1]]
**Output:** 2
```
**Example 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]`