Blue bridge: sympodial plant

Problem description
w A plantation on the planet , Is divided into m * n A little lattice （ East west direction m That's ok , North South n Column ）. There's a sympodial plant in each grid .
This plant has a characteristic , Its roots may extend north-south or East-West , So that it can be integrated with another lattice of plants .
If we tell you which cells are rooted , Can you tell me how many sympodial plants there are in this garden ？

Input format
first line , Two integers m,n, Separate with spaces , Represents the number of rows in the grid 、 Number of columns （1<m,n<1000）.
Next line , An integer k, It means that there are more k Row data (0<k<100000)
Next k That's ok , The first 2+k Line two integers a,b, Indicates that the number is a And the number is b My little lattice is rooted .

The number of the grid line by line , From top to bottom , Number from left to right .
such as ：5 * 4 The little lattice of , Number ：
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
17 18 19 20

The sample input
5 4
16
2 3
1 5
5 9
4 8
7 8
9 10
10 11
11 12
10 14
12 16
14 18
17 18
15 19
19 20
9 13
13 17

Sample explanation ： See the figure below for the root combination （ Be careful ：6 It is also a connected subset ）

Sample output
5

  Union checking set

  Code ：

package p1.text;
import java.util.*;
/**
 * @author WitMoy
 * @version V1.8
 * @date : 2022-07-02 18:16
 */
public class Main {
    private static final Scanner sc = new Scanner(System.in);
    private static int place[] = new int[1005];
    private static int rank[] = new int[1005];
    public static void main(String[] args) {
        int m, n, k;
        m = sc.nextInt();
        n = sc.nextInt();
        k = sc.nextInt();
        int ans = 0;
        init(m * n);
        for(int i = 0; i < k; i++){
            int a = sc.nextInt();
            int b = sc.nextInt();
            join(a,b);
        }
        HashSet<Integer> hs = new HashSet<>();
        for(int i = 1; i < n * m; i++){
            hs.add(place[i]);
        }
        System.out.println(hs.size());
    }
    private static void init(int n){
        for(int i = 1; i <= n; i++){
            place[i] = i;
            rank[i] = 1;
        }
    }
    private static int find(int x){
        if(place[x] == x) return x;
        return place[x] = find(place[x]);
    }
    private static void join(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return;
        if(rank[x] > rank[y]){
            place[y] = x;
        }else{
            if(rank[x] == rank[y]) rank[y]++;
            place[x] = y;
        }
    }
}