【数据结构】UnionFind 并查集-1

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数据结构源码 - UnionFind1

接口

public interface UnionFind {

    int getSize();

    boolean isConnected(int p, int q);

    void unionElements(int p, int q);
}

实现类

public class UnionFind1 implements UnionFind {

    private int[] id;

    public UnionFind1(int size) {
        id = new int[size];

        for (int i = 0; i < id.length; i++) {
            id[i] = i;
        }
    }

    @Override
    public int getSize() {
        return id.length;
    }

    /**
     * 查找元素p所对应的集合编号
     * @param p
     * @return
     */
    private int find(int p) {
        if (p < 0 && p >= id.length)
            throw new IllegalArgumentException("p is out of bound");
        return id[p];
    }

    /**
     * 查看元素p和元素q是否属于一个集合
     * @param p
     * @param q
     * @return
     */
    @Override
    public boolean isConnected(int p, int q) {
        return find(p) == find(q);
    }

    /**
     * 合并元素p和q所属的集合
     * @param p
     * @param q
     */
    @Override
    public void unionElements(int p, int q) {
        int pID = find(p);
        int qID = find(q);

        if (pID == qID) {
            return;
        }

        for (int i = 0; i < id.length; i++) {
            if (id[i] == pID)
                id[i] = qID;
        }
    }
}

数据结构拆解 - UnionFind1

维护字段和内部类


    private int[] id;

构造函数


    public UnionFind1(int size) {
        id = new int[size];

        for (int i = 0; i < id.length; i++) {
            id[i] = i;
        }
    }

改


    /**
     * 合并元素p和q所属的集合
     * @param p
     * @param q
     */
    @Override
    public void unionElements(int p, int q) {
        int pID = find(p);
        int qID = find(q);

        if (pID == qID) {
            return;
        }

        for (int i = 0; i < id.length; i++) {
            if (id[i] == pID)
                id[i] = qID;
        }
    }

查



    @Override
    public int getSize() {
        return id.length;
    }

    /**
     * 查找元素p所对应的集合编号
     * @param p
     * @return
     */
    private int find(int p) {
        if (p < 0 && p >= id.length)
            throw new IllegalArgumentException("p is out of bound");
        return id[p];
    }


    /**
     * 查看元素p和元素q是否属于一个集合
     * @param p
     * @param q
     * @return
     */
    @Override
    public boolean isConnected(int p, int q) {
        return find(p) == find(q);
    }

数据结构源码 - UnionFind2

接口

public interface UnionFind {

    int getSize();

    boolean isConnected(int p, int q);

    void unionElements(int p, int q);
}

实现类


import java.util.Random;

/**
 * 第二种UnionFind实现
 */
public class UnionFind2 implements UnionFind {

    private int[] parent;

    public UnionFind2(int size) {
        parent = new int[size];

        for (int i = 0; i < size; i++) {
            parent[i] = i;
        }
    }

    @Override
    public int getSize() {
        return parent.length;
    }

    /**
     * 查找过程，查找元素p所对应的集合编号
     * O(h)复杂度，h为树高度
     * @param p
     * @return
     */
    private int find(int p) {
        if (p < 0 && p >= parent.length)
            throw new IllegalArgumentException("p is out of bound");

        while (p != parent[p]) {
            p = parent[p];
        }
        return p;
    }

    /**
     * 查看元素p和元素q是否所属一个集合
     * @param p
     * @param q
     * @return
     */
    @Override
    public boolean isConnected(int p, int q) {
        return find(p) == find(q);
    }

    /**
     * 合并元素p和元素q所属的集合
     * O(h)复杂度，h为树的高度
     * @param p
     * @param q
     */
    @Override
    public void unionElements(int p, int q) {
        int pRoot = find(p);
        int qRoot = find(q);

        if (pRoot == qRoot)
            return;

        parent[pRoot] = qRoot;
    }

    private static double testUF(UnionFind uf, int m) {

        int size = uf.getSize();

        Random random = new Random();

        long startTime = System.nanoTime();

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.unionElements(a, b);
        }

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.isConnected(a, b);
        }

        long endTime = System.nanoTime();

        return (endTime - startTime) / 1000000000.0;
    }


    public static void main(String[] args) {
        int size = 100000;
        int m = 100000;

        UnionFind1 uf1 = new UnionFind1(size);
        System.out.println("UnionFind1 : " + testUF(uf1, m) + " s");

        UnionFind2 uf2 = new UnionFind2(size);
        System.out.println("UnionFind2 : " + testUF(uf2, m) + " s");
    }
}

数据结构拆解 - UnionFind2

维护字段和内部类


    private int[] parent;

构造函数

    public UnionFind2(int size) {
        parent = new int[size];

        for (int i = 0; i < size; i++) {
            parent[i] = i;
        }
    }

改


    /**
     * 合并元素p和元素q所属的集合
     * O(h)复杂度，h为树的高度
     * @param p
     * @param q
     */
    @Override
    public void unionElements(int p, int q) {
        int pRoot = find(p);
        int qRoot = find(q);

        if (pRoot == qRoot)
            return;

        parent[pRoot] = qRoot;
    }

查



    @Override
    public int getSize() {
        return parent.length;
    }

    /**
     * 查找过程，查找元素p所对应的集合编号
     * O(h)复杂度，h为树高度
     * @param p
     * @return
     */
    private int find(int p) {
        if (p < 0 && p >= parent.length)
            throw new IllegalArgumentException("p is out of bound");

        while (p != parent[p]) {
            p = parent[p];
        }
        return p;
    }

    /**
     * 查看元素p和元素q是否所属一个集合
     * @param p
     * @param q
     * @return
     */
    @Override
    public boolean isConnected(int p, int q) {
        return find(p) == find(q);
    }

测试用例 - UnionFind2


    private static double testUF(UnionFind uf, int m) {

        int size = uf.getSize();

        Random random = new Random();

        long startTime = System.nanoTime();

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.unionElements(a, b);
        }

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.isConnected(a, b);
        }

        long endTime = System.nanoTime();

        return (endTime - startTime) / 1000000000.0;
    }


    public static void main(String[] args) {
        int size = 100000;
        int m = 100000;

        UnionFind1 uf1 = new UnionFind1(size);
        System.out.println("UnionFind1 : " + testUF(uf1, m) + " s");

        UnionFind2 uf2 = new UnionFind2(size);
        System.out.println("UnionFind2 : " + testUF(uf2, m) + " s");
    }

数据结构源码 - UnionFind3

接口

public interface UnionFind {

    int getSize();

    boolean isConnected(int p, int q);

    void unionElements(int p, int q);
}

实现类


import java.util.Random;

/**
 * 第二种UnionFind实现
 */
public class UnionFind3 implements UnionFind {

    private int[] parent;

    private int[] sz;  // sz[i]表示以i为根的集合中元素个数

    public UnionFind3(int size) {
        parent = new int[size];
        sz = new int[size];

        for (int i = 0; i < size; i++) {
            parent[i] = i;
            sz[i] = 1;
        }
    }

    @Override
    public int getSize() {
        return parent.length;
    }

    /**
     * 查找过程，查找元素p所对应的集合编号
     * O(h)复杂度，h为树高度
     * @param p
     * @return
     */
    private int find(int p) {
        if (p < 0 && p >= parent.length)
            throw new IllegalArgumentException("p is out of bound");

        while (p != parent[p]) {
            p = parent[p];
        }
        return p;
    }

    /**
     * 查看元素p和元素q是否所属一个集合
     * @param p
     * @param q
     * @return
     */
    @Override
    public boolean isConnected(int p, int q) {
        return find(p) == find(q);
    }

    /**
     * 合并元素p和元素q所属的集合
     * O(h)复杂度，h为树的高度
     * @param p
     * @param q
     */
    @Override
    public void unionElements(int p, int q) {
        int pRoot = find(p);
        int qRoot = find(q);

        if (pRoot == qRoot)
            return;

        // 根据两个元素所在树的元素个数不同判断合并方向
        if (sz[pRoot] < sz[qRoot]) {
            parent[pRoot] = qRoot;
            sz[qRoot] += sz[pRoot];
        }
        else {  // sz[qRoot] <= sz[pRoot]
            parent[qRoot] = pRoot;
            sz[pRoot] += sz[qRoot];
        }
    }

    private static double testUF(UnionFind uf, int m) {

        int size = uf.getSize();

        Random random = new Random();

        long startTime = System.nanoTime();

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.unionElements(a, b);
        }

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.isConnected(a, b);
        }

        long endTime = System.nanoTime();

        return (endTime - startTime) / 1000000000.0;
    }


    public static void main(String[] args) {
        int size = 100000;
        int m = 100000;

        UnionFind1 uf1 = new UnionFind1(size);
        System.out.println("UnionFind1 : " + testUF(uf1, m) + " s");

        UnionFind2 uf2 = new UnionFind2(size);
        System.out.println("UnionFind2 : " + testUF(uf2, m) + " s");

        UnionFind3 uf3 = new UnionFind3(size);
        System.out.println("UnionFind3 : " + testUF(uf3, m) + " s");
    }
}

数据结构拆解 - UnionFind3

维护字段和内部类


    private int[] parent;

    private int[] sz;  // sz[i]表示以i为根的集合中元素个数

构造函数

    public UnionFind3(int size) {
        parent = new int[size];
        sz = new int[size];

        for (int i = 0; i < size; i++) {
            parent[i] = i;
            sz[i] = 1;
        }
    }

改


   /**
     * 合并元素p和元素q所属的集合
     * O(h)复杂度，h为树的高度
     * @param p
     * @param q
     */
    @Override
    public void unionElements(int p, int q) {
        int pRoot = find(p);
        int qRoot = find(q);

        if (pRoot == qRoot)
            return;

        // 根据两个元素所在树的元素个数不同判断合并方向
        if (sz[pRoot] < sz[qRoot]) {
            parent[pRoot] = qRoot;
            sz[qRoot] += sz[pRoot];
        }
        else {  // sz[qRoot] <= sz[pRoot]
            parent[qRoot] = pRoot;
            sz[pRoot] += sz[qRoot];
        }
    }

查



    @Override
    public int getSize() {
        return parent.length;
    }

    /**
     * 查找过程，查找元素p所对应的集合编号
     * O(h)复杂度，h为树高度
     * @param p
     * @return
     */
    private int find(int p) {
        if (p < 0 && p >= parent.length)
            throw new IllegalArgumentException("p is out of bound");

        while (p != parent[p]) {
            p = parent[p];
        }
        return p;
    }

    /**
     * 查看元素p和元素q是否所属一个集合
     * @param p
     * @param q
     * @return
     */
    @Override
    public boolean isConnected(int p, int q) {
        return find(p) == find(q);
    }

测试用例 - UnionFind3


    private static double testUF(UnionFind uf, int m) {

        int size = uf.getSize();

        Random random = new Random();

        long startTime = System.nanoTime();

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.unionElements(a, b);
        }

        for (int i = 0; i < m; i++) {
            int a = random.nextInt(size);
            int b = random.nextInt(size);
            uf.isConnected(a, b);
        }

        long endTime = System.nanoTime();

        return (endTime - startTime) / 1000000000.0;
    }


    public static void main(String[] args) {
        int size = 100000;
        int m = 100000;

        UnionFind1 uf1 = new UnionFind1(size);
        System.out.println("UnionFind1 : " + testUF(uf1, m) + " s");

        UnionFind2 uf2 = new UnionFind2(size);
        System.out.println("UnionFind2 : " + testUF(uf2, m) + " s");

        UnionFind3 uf3 = new UnionFind3(size);
        System.out.println("UnionFind3 : " + testUF(uf3, m) + " s");
    }
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