<p>There are <code>n</code> cities. Some of them are connected, while some are not. If city <code>a</code> is connected directly with city <code>b</code>, and city <code>b</code> is connected directly with city <code>c</code>, then city <code>a</code> is connected indirectly with city <code>c</code>.</p>

<p>A <strong>province</strong> is a group of directly or indirectly connected cities and no other cities outside of the group.</p>

<p>You are given an <code>n x n</code> matrix <code>isConnected</code> where <code>isConnected[i][j] = 1</code> if the <code>i<sup>th</sup></code> city and the <code>j<sup>th</sup></code> city are directly connected, and <code>isConnected[i][j] = 0</code> otherwise.</p>

<p>Return <em>the total number of <strong>provinces</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/24/graph1.jpg" style="width: 222px; height: 142px;" />
<pre>
<strong>Input:</strong> isConnected = [[1,1,0],[1,1,0],[0,0,1]]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/24/graph2.jpg" style="width: 222px; height: 142px;" />
<pre>
<strong>Input:</strong> isConnected = [[1,0,0],[0,1,0],[0,0,1]]
<strong>Output:</strong> 3
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 200</code></li>
	<li><code>n == isConnected.length</code></li>
	<li><code>n == isConnected[i].length</code></li>
	<li><code>isConnected[i][j]</code> is <code>1</code> or <code>0</code>.</li>
	<li><code>isConnected[i][i] == 1</code></li>
	<li><code>isConnected[i][j] == isConnected[j][i]</code></li>
</ul>

class UF {
public:
    vector<int> rank;
    vector<int> parents;
    int total;
    UF(int n): total(n) {
        for (int i = 0; i < n; i++) {
            rank.push_back(1);
            parents.push_back(i);
        }
    }
    ~UF(){}
    int getTotal() const {
        return total;
    }

    int find(int x) {
        while (parents[x] != x) {
            x = parents[x];
        }
        return parents[x];
    }
    void connect(int x, int y) {
        int rx = find(x);
        int ry = find(y);
        if (rx == ry) {
            return;
        }
        if (rank[rx] > rank[ry]) {
            parents[ry] = rx;
            if (rank[rx] == rank[ry]) {
                rank[rx]++;
            }
        } else {
            parents[rx] = ry;
        }
        total--;
    }
};
class Solution {
public:
    int findCircleNum(vector<vector<int>>& isConnected) {
        int n = isConnected.size();
        if (n == 0) {
            return 0;
        }
        UF uf(n);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++){
                if (isConnected[i][j]) {
                    uf.connect(i, j);
                }
            }
        }
        return uf.getTotal();
    }
};
18200