There are N students in a class. Some of them are friends, while some are not. Their friendship is transitive in nature. For example, if A is a direct friend of B, and B is a direct friend of C, then A is an indirect friend of C. And we defined a friend circle is a group of students who are direct or indirect friends.
Given a N*N matrix M representing the friend relationship between students in the class. If M[i][j] = 1, then the ithand jth students are direct friends with each other, otherwise not. And you have to output the total number of friend circles among all the students.
Example 1:
Input: [[1,1,0], [1,1,0], [0,0,1]] Output: 2 Explanation:The 0th and 1st students are direct friends, so they are in a friend circle. The 2nd student himself is in a friend circle. So return 2.
Example 2:
Input: [[1,1,0], [1,1,1], [0,1,1]] Output: 1 Explanation:The 0th and 1st students are direct friends, the 1st and 2nd students are direct friends, so the 0th and 2nd students are indirect friends. All of them are in the same friend circle, so return 1.
import java.util.TreeSet;
class Solution {
private interface UF {
int getSize();
boolean isConnected(int p, int q);
void unionElements(int p, int q);
}// 我們的第六版Union-Find
private class UnionFind6 implements UF {// rank[i]表示以i爲根的集合所表示的樹的層數
// 在後續的代碼中, 我們並不會維護rank的語意, 也就是rank的值在路徑壓縮的過程中, 有可能不在是樹的層數值
// 這也是我們的rank不叫height或者depth的原因, 他只是作爲比較的一個標準
private int[] rank;
private int[] parent; // parent[i]表示第i個元素所指向的父節點// 構造函數
public UnionFind6(int size){rank = new int[size];
parent = new int[size];// 初始化, 每一個parent[i]指向自己, 表示每一個元素自己自成一個集合
for( int i = 0 ; i < size ; i ++ ){
parent[i] = i;
rank[i] = 1;
}
}@Override
public int getSize(){
return parent.length;
}// 查找過程, 查找元素p所對應的集合編號
// O(h)複雜度, h爲樹的高度
private int find(int p){
if(p < 0 || p >= parent.length)
throw new IllegalArgumentException("p is out of bound.");// path compression 2, 遞歸算法
if(p != parent[p])
parent[p] = find(parent[p]);
return parent[p];
}// 查看元素p和元素q是否所屬一個集合
// O(h)複雜度, h爲樹的高度
@Override
public boolean isConnected( int p , int q ){
return find(p) == find(q);
}// 合併元素p和元素q所屬的集合
// O(h)複雜度, h爲樹的高度
@Override
public void unionElements(int p, int q){int pRoot = find(p);
int qRoot = find(q);if( pRoot == qRoot )
return;// 根據兩個元素所在樹的rank不同判斷合併方向
// 將rank低的集合合併到rank高的集合上
if( rank[pRoot] < rank[qRoot] )
parent[pRoot] = qRoot;
else if( rank[qRoot] < rank[pRoot])
parent[qRoot] = pRoot;
else{ // rank[pRoot] == rank[qRoot]
parent[pRoot] = qRoot;
rank[qRoot] += 1; // 此時, 我維護rank的值
}
}
}public int findCircleNum(int[][] M) {
int n = M.length;
UnionFind6 uf = new UnionFind6(n);
for(int i = 0 ; i < n ; i ++)
for(int j = 0 ; j < i ; j ++)
if(M[i][j] == 1)
uf.unionElements(i, j);TreeSet<Integer> set = new TreeSet<>();
for(int i = 0 ; i < n ; i ++)
set.add(uf.find(i));
return set.size();
}
}