Union checking set

And look up the problems solved

1. Merge two sets
2. Ask if two elements are in a collection

Basic principle

Each set is maintained in the form of a tree. The number of the tree root is the number of the whole set. Each node stores its parent node. p[x] represents the parent node of X

Question 1, how to judge the root of tree: if(p[x] == x);
Question 2, how to find the number of X set: while (P [x]! = x) x = P [x];
Question 3: how to merge two sets? P x is the number of X sets, and p y is the number of Y sets. Let p[x]=y.

Problem 2 Optimization: after a node finds the root node, it points the whole path directly to the root node.

Example

AcWing 836 merge set
There are n numbers in total. The numbers are 1-n. at the beginning, each number is in a set.
Now m operations are needed. There are two types of operations:

1. "M a b" merges the sets of two numbers a and b. if the two numbers are already in the same set, this operation is ignored;
2. "Q a b", asking whether the two numbers a and b are in the same set;

import java.util.*;
class UnionSet{
    private final int N = 100010;
    private int[] p = new int[N];
    public UnionSet(){
        for(int i = 0; i < N; i++){
            p[i] = i;
        }
    }
    // Find the root node of this node
    public int find(int val){
        int temp = val;
        while(p[temp] != temp){
            temp = p[temp];
        }
        p[val] = temp;
        return temp;
    }
    public void union(int a,int b){
        int pa = find(a);
        int pb = find(b);
        if(pa != pb) p[pa] = pb;
    }
    public boolean isunion(int a,int b){
        int pa = find(a);
        int pb = find(b);
        if(pa != pb) return false;
        else return true;
    }
}
public class Main{
    public static void main(String[] args){
        Scanner Reader = new Scanner(System.in);
        int n = Reader.nextInt();
        int m = Reader.nextInt();
        UnionSet us = new UnionSet();
        while(m-- != 0){
            String temp = Reader.next();
            if(temp.equals("M")){
                int v1 = Reader.nextInt(),v2 = Reader.nextInt();
                us.union(v1,v2);
            }
            if(temp.equals("Q")){
                if(us.isunion(Reader.nextInt(),Reader.nextInt()))
                    System.out.println("Yes");
                else
                    System.out.println("No");
            }
        }
    }
}

Number of midpoint in AcWing 837 connected block
Given an undirected graph with n points (No. 1~n), there is no edge in the graph at the beginning.
Now, m operations are needed. There are three types of operations:

1. "C a b", connecting a side between point a and point b, a and b may be equal;
2. "Q1 a b", asking whether point a and point b are in the same connected block, a and b may be equal;
3. "Q2 a", the number of the midpoint of the connecting block where query point a is located;

import java.util.*;
class UnionSet{
    private final int N = 100010;
    private int[] p = new int[N];
    private int[] size = new int[N];
    public UnionSet(){
        for(int i = 0; i < N; i++){
            p[i] = i;
            size[i] = 1;
        }
    }
    // Find the root node of this node
    public int find(int val){
        int temp = val;
        while(p[temp] != temp){
            temp = p[temp];
        }
        p[val] = temp;
        return temp;
    }
    public void union(int a,int b){
        int pa = find(a);
        int pb = find(b);
        if(pa != pb) {
            p[pa] = pb;
            size[pb] += size[pa];
        }
    }
    public boolean isunion(int a,int b){
        int pa = find(a);
        int pb = find(b);
        if(pa != pb) return false;
        else return true;
    }
    public int size(int a){
        return size[find(a)];
    }
}
public class Main{
    public static void main(String[] args){
        Scanner Reader = new Scanner(System.in);
        int n = Reader.nextInt();
        int m = Reader.nextInt();
        UnionSet us = new UnionSet();
        while(m-- != 0){
            String temp = Reader.next();
            if(temp.equals("C")){
                int v1 = Reader.nextInt(),v2 = Reader.nextInt();
                us.union(v1,v2);
            }
            if(temp.equals("Q1")){
                if(us.isunion(Reader.nextInt(),Reader.nextInt()))
                    System.out.println("Yes");
                else
                    System.out.println("No");
            }
            if(temp.equals("Q2")){
                System.out.println(us.size(Reader.nextInt()));
            }
        }
    }
}