数据结构—平衡二叉树（Java）

归子莫

发布于：2020年8月28日

数据结构—平衡二叉树（Java）

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说明

平衡二叉树也叫平衡二叉搜索树（Self-balancing binary search tree）又被称为AVL树，可以保证查询效率较高。
具有以下特点：它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。平衡二叉树的常用实现方法有红黑树、AVL、替罪羊树、Treap、伸展树等。

代码

package cn.guizimo.avl;

public class AVLTree {
    public static void main(String[] args) {
        int[] arr = { 10, 11, 7, 6, 8, 9 };
        AVLTreeDemo avlTree = new AVLTreeDemo();
        for(int i=0; i < arr.length; i++) {
            avlTree.add(new Node(arr[i]));
        }

        System.out.println("中序遍历");
        avlTree.infixOrder();

        System.out.println("平衡");
        System.out.println("树的高度：" + avlTree.getRoot().height()); //3
        System.out.println("左子树高度：" + avlTree.getRoot().leftHeight()); // 2
        System.out.println("右子树高度" + avlTree.getRoot().rightHeight()); // 2
        System.out.println("根节点：" + avlTree.getRoot());//8
    }
}

class AVLTreeDemo{
    private Node root;

    public Node getRoot() {
        return root;
    }

    //查找当前节点
    public Node search(int value) {
        if (root == null) {
            return null;
        } else {
            return root.search(value);
        }
    }

    //找到最小值
    public int delRightTreeMin(Node node) {
        Node target = node;
        while(target.left != null) {
            target = target.left;
        }
        delNode(target.value);
        return target.value;
    }

    //删除节点
    public void delNode(int value) {
        if (root == null) {
            return;
        } else {
            //删除叶子节点
            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.value == value) {
                    parent.left = null;
                } else if (parent.right != null && parent.right.value == value) {
                    parent.right = null;
                }
                //删除两颗子树的节点
            } else if (targetNode.left != null && targetNode.right != null) {
                int i = delRightTreeMin(targetNode.right);
                targetNode.value = i;
                //删除一颗子树的节点
            } else {
                if (targetNode.left != null) {
                    if (parent != null) {
                        if (parent.left.value == value) {
                            parent.left = targetNode.left;
                        } else {
                            parent.right = targetNode.right;
                        }
                    } else {
                        root = targetNode.left;
                    }
                } else {
                    if (parent != null) {
                        if (parent.left.value == value) {
                            parent.left = targetNode.right;
                        } else if (parent.right.value == value) {
                            parent.right = targetNode.right;
                        }
                    } else {
                        root = targetNode.right;
                    }
                }
            }
        }
    }

    //查询当前节点的父节点
    public Node searchParent(int value) {
        if (root == null) {
            return null;
        } else {
            return root.searchParent(value);
        }
    }

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

    //中序遍历
    public void infixOrder() {
        if (root != null) {
            root.infixOrder();
        } else {
            System.out.println("");
        }
    }
}

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

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

    //左子树的高度
    public int leftHeight() {
        if (left == null) {
            return 0;
        }
        return left.height();
    }

    // 右子树的高度
    public int rightHeight() {
        if (right == null) {
            return 0;
        }
        return right.height();
    }

    // 当前节点的高度
    public int height() {
        return Math.max(left == null ? 0 : left.height(), right == null ? 0 : right.height()) + 1;
    }

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

    //查找节点
    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);
        }
    }

    //查询父节点
    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.right != null) {
                return this.right.searchParent(value);
            } else {
                return null;
            }
        }
    }

    //添加节点
    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);
            }
        }

        //左旋转
        if(rightHeight() - leftHeight() > 1) {
            if(right != null && right.leftHeight() > right.rightHeight()) {
                right.rightRotate();
                leftRotate();
            } else {
                leftRotate();
            }
            return ;
        }

        //右旋转
        if(leftHeight() - rightHeight() > 1) {
            if(left != null && left.rightHeight() > left.leftHeight()) {
                left.leftRotate();
                rightRotate();
            } else {
                rightRotate();
            }
        }
    }

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

    //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;
    }

}