547. Number of Provinces

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

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]

🧠 Thuật Toán & Kỹ Thuật

Union Find (Tập hợp rời rạc)
⏱️ Thời gian O(n²)
💾 Không gian O(n)

💻 Lời Giải

Python 0547-number-of-provinces.py 
class Solution:
    def findCircleNum(self, isConnected: List[List[int]]) -> int:
        n = len(isConnected)
        parent = list(range(n))
        
        def find(u: int) -> int:
            if u != parent[u]:
                parent[u] = find(parent[u])
            return parent[u]
        
        self.cnt = n
        
        def union(u: int, v: int) -> None:
            u = find(u)
            v = find(v)
            if u == v:
                return
            parent[u] = v
            self.cnt -= 1
        
        for u in range(n):
            for v in range(n):
                if isConnected[u][v]:
                    union(u, v)
        
        return self.cnt