算法：并查集（四种方式）_并查集的4种-优快云博客

博客介绍了简单并查集、快速并查集、加权快速并查集和路径压缩的加权快速并查集，并对它们的复杂度进行了对比。

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简单并查集

public class UnionFind {
    private int[] id;
    private int count;

    public UnionFind(int N) {
        count = N;
        id = new int[N];
        for(int i = 0; i < N; i++) id[i] = i;
    }

    public int getCount() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public int find(int p) {
        return id[p];
    }

    public void union(int p, int q){
        int pRoot = find(p);
        int qRoot = find(q);

        if(pRoot == qRoot) return;

        for(int i = 0; i < id.length; i++)
            if(id[i] == pRoot)  id[i] = qRoot;
        count--;
    }
}

快速并查集

public class QuickUnion {
    private int[] id;
    private int count;

    public QuickUnion(int N) {
        count = N;
        id = new int[N];
        for(int i = 0; i < N; i++) id[i] = i;
    }

    public int getCount() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public int find(int p) {
        while(p != id[p]) p = id[p];
        return p;
    }

    public void union(int p, int q){
        int pRoot = find(p);
        int qRoot = find(q);

        if(pRoot == qRoot) return;

        id[pRoot] = qRoot;
        count--;
    }
}

加权快速并查集

public class WeightedQuickUnion {
    private int[] id;
    private int count;
    private int[] sz;

    public WeightedQuickUnion(int N) {
        count = N;
        id = new int[N];
        sz = new int[N];
        for(int i = 0; i < N; i++) {
            id[i] = i;
            sz[i] = 1;
        }
    }

    public int getCount() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public int find(int p) {
        while(p != id[p]) p = id[p];
        return p;
    }

    public void union(int p, int q){
        int pRoot = find(p);
        int qRoot = find(q);

        if(pRoot == qRoot) return;

        if(sz[pRoot] < sz[qRoot]) { id[pRoot] = qRoot; sz[qRoot] += sz[pRoot]; }
        else                      { id[qRoot] = pRoot; sz[pRoot] += sz[qRoot]; }
        count--;
    }

路径压缩的加权快速并查集

public class PathCompressionWeightedQuickUnion {
    private int[] id;
    private int count;
    private int[] sz;

    public PathCompressionWeightedQuickUnion(int N) {
        count = N;
        id = new int[N];
        sz = new int[N];
        for(int i = 0; i < N; i++) {
            id[i] = i;
            sz[i] = 1;
        }
    }

    public int getCount() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public int find(int p) {
        if (p != id[p]) id[p] = find(id[p]);
        return id[p];
    }

    public void union(int p, int q){
        int pRoot = find(p);
        int qRoot = find(q);

        if(pRoot == qRoot) return;

        if(sz[pRoot] < sz[qRoot]) { id[pRoot] = qRoot; sz[qRoot] += sz[pRoot]; }
        else                      { id[qRoot] = pRoot; sz[pRoot] += sz[qRoot]; }
        count--;
    }
}

复杂度对比

                                           存在N伙强盗增长数量级(最坏情况)
      算法                           构造函数        union()         find()
	
union-find算法                         O(n)          O(n)            O(1) 
quick-union算法                        O(n)         树的高度         树的高度
加权quick-union算法                     O(n)         O(lgn)          O(lgn)
路径压缩的加权quick-union算法            O(n)         非常接近O(1)     非常接近O(1)
理想情况                                O(n)          O(1)            O(1)