# Learn Algorithms from LeetCode-120 (0547. Number of Provinces)

## Categories: Graph/Union Find, Level: Medium

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**Question:**

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]`

**Analysis/Approach:**

There are n cities, some of which are directly connected to each other, while others are not. If city a is directly connected to city b, and city b is directly connected to city c, then city a is…