Java中的AVL树旋转

Question

我想实现 Java AVL 树并左右旋转树。我没有得到这个。

任何人都可以通过查看下面的代码告诉我如何左右旋转树，然后使用修复这两个函数来平衡 AVL 树吗？

我希望这里有人可以指导我。

import java.util.Random;
import java.util.SortedSet;
import java.util.TreeSet;

public class AVLTree<T> extends 
BinarySearchTree<AVLTree.Node<T>, T> implements SSet<T> {

    Random rand;

    public static class Node<T> extends BSTNode<Node<T>,T> {
        int h;  // the height of the node
    }

    public AVLTree() {
        sampleNode = new Node<T>();
        rand = new Random();
        c = new DefaultComparator<T>();
    }

    public int height(Node<T> u) {
        return (u == null) ? 0 : u.h;
    }

    public boolean add(T x) {
        Node<T> u = new Node<T>();
        u.x = x;
        if (super.add(u)) {
            for (Node<T> w = u; w != nil; w = w.parent) {
                // walk back up to the root adjusting heights
                w.h = Math.max(height(w.left), height(w.right)) + 1;
            }
        fixup(u);
        return true;
    }
    return false;
}

public void splice(Node<T> u) {
    Node<T> w = u.parent;
    super.splice(u);
    for (Node<T> z = u; z != nil; z = z.parent)
        z.h = Math.max(height(z.left), height(z.right)) + 1;            
    fixup(w);
}

public void checkHeights(Node<T> u) {
    if (u == nil) return;
    checkHeights(u.left);
    checkHeights(u.right);
    if (height(u) != 1 + Math.max(height(u.left), height(u.right))) 
        throw new RuntimeException("Check heights shows incorrect heights");
    int dif = height(u.left) - height(u.right);
    if (dif < -1 || dif > 1)
        throw new RuntimeException("Check heights found height difference of " + dif);
}

/**
 * TODO: finish writing this method
 * @param u
 */
public void fixup(Node<T> u) {
    while (u != nil) {
        int dif = height(u.left) - height(u.right);
        if (dif > 1) {
            // TODO: add code here to fix AVL condition 
            // on the path from u to the root, if  necessary
        } else if (dif < -1) {
            // TODO: add code here to fix AVL condition
            // on the path from u to the root, if necessary                 
        }
        u = u.parent;
    }
}

public Node rotateLeft() {
    return rotateLeft(u.parent);
}

public void rotateLeft(Node<T> u) {
    // TODO: Recompute height values at u and u.parent
}

public void rotateRight(Node<T> u) {
    // TODO: Recompute height values at u and u.parent
}

public static <T> T find(SortedSet<T> ss, T x) {
    SortedSet<T> ts = ss.tailSet(x);
    if (!ts.isEmpty()) {
        return ts.first(); 
    }
    return null;
}

/**
 * This just does some very basic correctness testing
 * @param args
 */
public static void main(String[] args) {
    AVLTree<Integer> t = new AVLTree<Integer>();
    Random r = new Random(0);
    System.out.print("Running AVL tests...");
    int n = 1000;
    for (int i = 0; i < n; i++) {
        t.add(r.nextInt(2*n));
        t.checkHeights(t.r);
    }
    for (int i = 0; i < n; i++) {
        t.remove(r.nextInt(2*n));
        t.checkHeights(t.r);
    }
    System.out.println("done");

    t.clear();
    System.out.print("Running correctness tests...");
    n = 100000;
    SortedSet<Integer> ss = new TreeSet<Integer>();
    Random rand = new Random();
    for (int i = 0; i < n; i++) {
        Integer x = rand.nextInt(2*n);
        boolean b1 = t.add(x);
        boolean b2 = ss.add(x);
        if (b1 != b2) {
            throw new RuntimeException("Adding " + x + " gives " + b2 
                    + " in SortedSet and " + b1 + " in AVL Tree");
        }
    }
    for (int i = 0; i < n; i++) {
        Integer x = rand.nextInt(2*n);
        Integer x1 = t.find(x);
        Integer x2 = find(ss, x);
        if (x1 != x2) {
            throw new RuntimeException("Searching " + x + " gives " + x2 
                    + " in SortedSet and " + x1 + " in AVL Tree");
        }
        ss.headSet(x);
    }
    for (int i = 0; i < n; i++) {
        Integer x = rand.nextInt(2*n);
        boolean b1 = t.remove(x);
        boolean b2 = ss.remove(x);
        if (b1 != b2) {
            throw new RuntimeException("Error (2): Removing " + x + " gives " + b2 
                    + " in SortedSet and " + b1 + " in AVL Tree");
        }
    }
    for (int i = 0; i < n; i++) {
        Integer x = rand.nextInt(2*n);
        Integer x1 = t.find(x);
        Integer x2 = find(ss, x);
        if (x1 != x2) {
            throw new RuntimeException("Error (3): Searching " + x + " gives " + x2 
                    + " in SortedSet and " + x1 + " in AVL Tree");
        }
        ss.headSet(x);
    }
    System.out.println("done");
 }
}

Answer 1

完整的 AVL 树实现：

public class AVLTree<T> {

    private AVLNode<T> root;

    private static class AVLNode<T> {

        private T t;
        private int height;
        private AVLNode<T> left;
        private AVLNode<T> right;

        private AVLNode(T t) {
            this.t = t;
            height = 1;
        }
    }

    public void insert(T value) {
        root = insert(root, value);
    }

    private AVLNode<T> insert(AVLNode<T> n, T v) {
        if (n == null) {
            n = new AVLNode<T>(v);
            return n;
        } else {
            int k = ((Comparable) n.t).compareTo(v);
            if (k > 0) {
                n.left = insert(n.left, v);
            } else {
                n.right = insert(n.right, v);
            }
            n.height = Math.max(height(n.left), height(n.right)) + 1;
            int heightDiff = heightDiff(n);
            if (heightDiff < -1) {
                if (heightDiff(n.right) > 0) {
                    n.right = rightRotate(n.right);
                    return leftRotate(n);
                } else {
                    return leftRotate(n);
                }
            } else if (heightDiff > 1) {
                if (heightDiff(n.left) < 0) {
                    n.left = leftRotate(n.left);
                    return rightRotate(n);
                } else {
                    return rightRotate(n);
                }
            } else;

        }
        return n;
    }

    private AVLNode<T> leftRotate(AVLNode<T> n) {
        AVLNode<T> r = n.right;
        n.right = r.left;
        r.left = n;
        n.height = Math.max(height(n.left), height(n.right)) + 1;
        r.height = Math.max(height(r.left), height(r.right)) + 1;
        return r;
    }

    private AVLNode<T> rightRotate(AVLNode<T> n) {
        AVLNode<T> r = n.left;
        n.left = r.right;
        r.right = n;
        n.height = Math.max(height(n.left), height(n.right)) + 1;
        r.height = Math.max(height(r.left), height(r.right)) + 1;
        return r;
    }

    private int heightDiff(AVLNode<T> a) {
        if (a == null) {
            return 0;
        }
        return height(a.left) - height(a.right);
    }

    private int height(AVLNode<T> a) {
        if (a == null) {
            return 0;
        }
        return a.height;
    }


}

Answer 2

这里是用 Java 实现的 AVL 树的完整实现

class Node {
    int key;
    Node left;
    Node right;
    int height;

    Node(int value) {
        key = value;
        left = null;
        right = null;
        height = 1;
    }
}

class AVLTree {
    Node root;

    int height(Node root) {
        if (root == null)
            return 0;

        return root.height;
    }

    int findHeight() {
        return height(root);
    }

    int findHeightFrom(int value) {
        Node node = search(root, value);
        if (node == null)
            return -1;

        return node.height;
    }

    Node search(Node root, int value) {
        if (root == null)
            return null;
        else {
            if (value == root.key)
                return root;
            else if (value < root.key)
                return search(root.left, value);
            else
                return search(root.right, value);
        }
    }

    boolean find(int value) {
        Node node = search(root,value);

        if (node == null)
            return false;

        return true;
    }

    int max(int one, int two) {
        return (one > two) ? one : two;
    }

    Node rightRotate(Node root) {
        Node rootLeftChild = root.left;
        root.left = rootLeftChild.right;
        rootLeftChild.right = root;

        root.height = max(height(root.left), height(root.right)) + 1;
        rootLeftChild.height = max(height(rootLeftChild.left), height(rootLeftChild.right)) + 1;

        return rootLeftChild;
    }

    Node leftRotate(Node root) {
        Node rootRightChild = root.right;
        root.right = rootRightChild.left;
        rootRightChild.left = root;

        root.height = max(height(root.left), height(root.right)) + 1;
        rootRightChild.height = max(height(rootRightChild.left), height(rootRightChild.right)) + 1;

        return rootRightChild;
    }

    Node insertNode(Node root, int value) {
        if (root == null)
            root = new Node(value);
        else {
            if (value < root.key)
                root.left = insertNode(root.left, value);
            else
                root.right = insertNode(root.right, value);
        }

        root.height = max(height(root.left), height(root.right)) + 1;

        int balanceFactor = height(root.left) - height(root.right);

        if (balanceFactor > 1) {
            // either left-left case or left-right case
            if (value < root.left.key) {
                // left-left case
                root = rightRotate(root);
            } else {
                // left-right case
                root.left = leftRotate(root.left);
                root = rightRotate(root);
            }
        } else if (balanceFactor < -1) {
            // either right-right case or right-left case
            if (value > root.right.key) {
                // right-right case
                root = leftRotate(root);
            } else {
                // right-left case
                root.right = rightRotate(root.right);
                root = leftRotate(root);
            }
        }

        return root;
    }

    void insert(int value) {
        root = insertNode(root, value);
    }

    void inorder(Node root) {
        if (root != null) {
            inorder(root.left);
            System.out.print(root.key + " ");
            inorder(root.right);
        }
    }

    void inorderTraversal() {
        inorder(root);
        System.out.println();
    }

    void preorder(Node root) {
        if (root != null) {
            System.out.print(root.key + " ");
            preorder(root.left);
            preorder(root.right);
        }
    }

    void preorderTraversal() {
        preorder(root);
        System.out.println();
    }
}

public class AVLTreeExample {
    public static void main(String[] args) {
        AVLTree avl = new AVLTree();
        avl.insert(10);
        avl.insert(20);
        avl.insert(30);
        avl.insert(40);
        avl.insert(50);
        avl.insert(25);

        System.out.print("Inorder Traversal : "); avl.inorderTraversal();
        System.out.print("Preorder Traversal : "); avl.preorderTraversal();
        System.out.println("Searching for 10 : " + avl.find(10));
        System.out.println("Searching for 11 : " + avl.find(11));
        System.out.println("Searching for 20 : " + avl.find(20));
        System.out.println("Height of the tree : " + avl.findHeight());
        System.out.println("Finding height from 10 : " + avl.findHeightFrom(10));
        System.out.println("Finding height from 20 : " + avl.findHeightFrom(20));
        System.out.println("Finding height from 25 : " + avl.findHeightFrom(25));
    }
}

Answer 3

为了向右旋转 您需要首先检查父级是否不是root 那么如果父母是祖父母的权利 如果是这样，将祖父母的权利设置给孩子 否则，将祖父的左边设置为子

否则， 根是孩子