平衡二叉树（AVL）

Posted 2021-03-10 bingbug

平衡二叉树是一棵空树或它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一棵平衡二叉树

平衡二叉树解决了二叉排序树的查询效率问题（连续递增数据创建二叉排序树时）

平衡二叉树的难点在于左右旋转，这里用 new 代表新节点  old 代表旧 ‘根‘ 节点

左旋转：

　　1)new.value = old.value

　　2)new.left = old.left

　　3)new.right = old.right.left

　　4)old.value = old.right.value

　　5)old.right = old.right.right

　　6)old.left = new

右旋转：

　　1)new.value = old.value

　　2)new.left = old.left.right

　　3)new.right = old.right

　　4)old.value = old.left.value

　　5)old.left= old.left.left

　　6)old.right = new

双旋转：先对子树一层层进行高度判断，不符合要求的进行左或右旋转，一层层往上走即可

public class AVLTreeDemo {

    public static void main(String[] args) {
        int[] arr = {4, 3, 6, 5, 7, 8};
        int[] arr2 = {10, 12, 8, 9, 7, 6};
        int[] arr3 = {10, 11, 7, 6, 8, 9};
        AVLTree avlTree = new AVLTree();
        for (int i = 0; i < arr3.length; i++) {
            avlTree.add(new Node(arr3[i]));
        }
        avlTree.infixOrder();
        System.out.println(avlTree.getRoot().height());
        System.out.println(avlTree.getRoot().leftHeight());
        System.out.println(avlTree.getRoot().rightHeight());
    }
}

class AVLTree {
    private Node root;

    public Node getRoot() {
        return root;
    }

    public void setRoot(Node root) {
        this.root = root;
    }

    public void add(Node node) {
        if (root == null) {
            root = node;
        } else {
            root.add(node);
        }
    }

    public void infixOrder() {
        if (root != null) {
            root.infixOrder();
        }
    }

    public Node search(int value) {
        if (root == null) {
            return null;
        } else {
            return root.search(value);
        }
    }

    public Node searchParent(int value) {
        if (root == null) {
            return null;
        } else {
            return root.searchParent(value);
        }
    }

    public int delRightTreeMin(Node node) {
        Node target = node;
        while (target.right != null) {
            target = target.right;
        }
        delete(target.value);
        return target.value;
    }

    public void delete(int value) {
        if (root == null) {
            return;
        } else {
            Node targetNode = search(value);
            if (targetNode == null) {
                return;
            }
            if (root.left == null && root.right == null) {
                root = null;
                return;
            }

            Node parent = searchParent(value);
            if (targetNode.left == null && targetNode.right == null) {
                if (parent.left != null && parent.left == targetNode) {
                    parent.left = null;
                } else if (parent.right != null && parent.right == targetNode) {
                    parent.right = null;
                }
            } else if (targetNode.left != null && targetNode.right != null) {
                int minVal = delRightTreeMin(targetNode.left);
                targetNode.value = minVal;
            } else {
                if (targetNode.left != null) {
                    if (parent != null) {
                        if (parent.left.value == value) {
                            parent.left = targetNode.left;
                        } else {
                            parent.right = targetNode.left;
                        }
                    } else {
                        root = targetNode.left;
                    }
                } else {
                    if (parent != null) {
                        if (parent.left.value == value) {
                            parent.left = targetNode.right;
                        } else {
                            parent.right = targetNode.right;
                        }
                    } else {
                        root = targetNode.right;
                    }
                }
            }
        }
    }
}

class Node {
    int value;
    Node left;
    Node right;

    public Node(int value) {
        this.value = value;
    }

    @Override
    public String toString() {
        return "Node[" +
                "value=" + value +
                ‘]‘;
    }

    public void add(Node node) {
        if (node == null) {
            return;
        }
        if (node.value < this.value) {
            if (this.left == null) {
                this.left = node;
            } else {
                this.left.add(node);
            }
        } else {
            if (this.right == null) {
                this.right = node;
            } else {
                this.right.add(node);
            }
        }
        if (rightHeight() - leftHeight() > 1) {
            if (right != null && right.rightHeight() < right.leftHeight()) {
                right.rightRotate();
                leftRotate();
            } else {
                leftRotate();
            }
            return;//!!!!!
        }
        if (leftHeight() - rightHeight() > 1) {
            if (left != null && left.rightHeight() > left.leftHeight()) {
                left.leftRotate();
                rightRotate();
            } else {
                rightRotate();
            }
        }
    }

    public void infixOrder() {
        if (this.left != null) {
            this.left.infixOrder();
        }
        System.out.println(this);
        if (this.right != null) {
            this.right.infixOrder();
        }
    }

    public Node search(int value) {
        if (value == this.value) {
            return this;
        } else if (value < this.value) {
            if (this.left == null) {
                return null;
            }
            return this.left.search(value);
        } else {
            if (this.right == null) {
                return null;
            }
            return this.right.search(value);
        }
    }

    /**
     * @param value 要找的值
     * @return 要删除节点的父节点 没有返回null
     */
    public Node searchParent(int value) {
        if ((this.left != null && this.left.value == value) ||
                (this.right != null && this.right.value == value)) {
            return this;
        } else {
            if (value < this.value && this.left != null) {
                return this.left.searchParent(value);
            } else if (value >= this.value && this.left != null) {
                return this.right.searchParent(value);
            } else {
                return null;
            }
        }
    }

    public int height() {
        return Math.max(left == null ? 0 : left.height(), right == null ? 0 : right.height()) + 1;
    }

    public int leftHeight() {
        if (left == null) {
            return 0;
        }
        return left.height();
    }

    public int rightHeight() {
        if (right == null) {
            return 0;
        }
        return right.height();
    }

    //左旋转
    private void leftRotate() {
        Node newNode = new Node(value);
        newNode.left = left;
        newNode.right = right.left;
        value = right.value;
        right = right.right;
        left = newNode;
    }

    //右旋转
    private void rightRotate() {
        Node newNode = new Node(value);
        newNode.right = right;
        newNode.left = left.right;
        value = left.value;
        left = left.left;
        right = newNode;
    }
}