Number of Provinces

The key idea

A province is exactly a connected component of the friendship graph. Count components: start at an unvisited city, flood-fill (DFS/BFS) every city reachable through direct or indirect connections to mark the whole group, and add one to the answer for each fresh flood-fill you launch. Each launch discovers one entire province.

Problem

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.

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]

Examples

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

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

Complexity

Time: O(n^2) Space: O(n)

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