Please briefly describe the idea of the algorithm and implement it through programming（use java）

The provided pseudo-code snippet suggests a method to compute the reflexive transitive closure (`R*`) of a binary relation `R` over a finite set `A`. The key concept here is adding all pairs `(ai, ai)` (i.e., making the relation reflexive by ensuring every element relates to itself) to `R*`, but this alone only ensures reflexivity. To fully achieve both reflexivity and transitivity, we need to ensure that if there's a path from `ai` to `aj`, then `(ai, aj)` should be in `R*`.

Here's a basic implementation using Java:

import java.util.*;

public class ReflexiveTransitiveClosure {
    public static Set<Pair> computeReflexiveTransitiveClosure(Set<Pair> R, int n) {
        // Initialize R* with the reflexive part.
        Set<Pair> RStar = new HashSet<>();
        for(int i = 1; i <= n; i++) {
            RStar.add(new Pair(i, i));
        }
        
        // Add transitive elements to R* based on existing relations in R.
        boolean changes;
        do {
            changes = false;
            Set<Pair> temp = new HashSet<>(RStar);
            for(Pair p : R) {
                for(Pair q : R) {
                    if(p.y == q.x && !temp.contains(new Pair(p.x, q.y))) { 
                        temp.add(new Pair(p.x, q.y)); // Add new transitive pair.
                        changes = true;
                    }
                }
            }
            RStar = temp;
        } while(changes);

        return RStar;
    }

    public static void main(String[] args) {
        // Example usage:
        int n = 3; // Size of set A
        Set<Pair> R = new HashSet<>(); // Initial binary relation R
        
        // Assume R contains these pairs initially
        R.add(new Pair(1, 2));
        R.add(new Pair(2, 3));

        Set<Pair> RStar = computeReflexiveTransitiveClosure(R, n);
        System.out.println("Computed Reflexive Transitive Closure: " + RStar);
    }

    static class Pair {
        int x, y;

        Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Pair)) return false;
            Pair pair = (Pair) o;
            return x == pair.x && y == pair.y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }

        @Override
        public String toString() {
            return "("+x+", "+y+")";
        }
    }
}

In this code, `computeReflexiveTransitiveClosure` function first adds all reflexive pairs `(ai, ai)` to `R*`. Then it enters a loop where it checks for transitive closures until no more such pairs are found to add. This process continues until `R*` stabilizes, indicating all necessary transitive pairs have been added, thereby completing the reflexive transitive closure computation.