第二十四题：在二叉树中找到一个节点的后继节点和前驱节点（Java）

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题目要求：

如标题（Node除了left，right，还有一个指向父节点的指针）

什么前驱和后继节点？ 在二叉树的中序遍历中，一个节点的前一个节点，就是该节点的前驱，一个节点的下一个节点就是该节点的后继。

如何寻找一个节点的前驱？

如果该节点有左子树，那么该节点的前驱就是该节点左子树中最右边的节点；如果该节点没有左子树，从当前节点开始往上寻找，直到当前节点是其父节点的右孩子，那么这个父节点，就是起始节点的前驱。

如果寻找一个节点的后继？

如果该节点有右子树，则该节点的后继是该节点的右子树中最左边的元素；如果该节点没有右子树，从当前节点开始往上寻找，直到当前的节点是其父节点的左孩子，那么这个父节点就是起始节点的后继。

代码实现 ：

package com.isea.brush.tree;

/**
 * 寻找一个节点的后继节点和前驱节点
 */
public class SuccessorNode {
    private static class Node {
        private Integer value;
        private Node left;
        private Node right;
        private Node parent;

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

    /**
     * 传入一个node，返回该node的后继节点
     *
     * @param node
     * @return
     */
    public static Node getSuccessorNode(Node node) {
        if (node == null) {
            return null;
        }
        if (node.right != null) {
            return getMostLeft(node.right);
        } else {
            Node parent = node.parent;
            while (parent != null && node != parent.left) {
                node = parent;
                parent = node.parent;
            }
            return parent;
        }
    }

    /**
     * 返回node为根节点的最左边节点
     *
     * @param node
     * @return
     */
    private static Node getMostLeft(Node node) {
        while (node.left != null) {
            node = node.left;
        }
        return node;
    }

    /**
     * 返回node节点的前驱节点
     *
     * @param node
     * @return
     */
    public static Node getPioneerNode(Node node) {
        if (node == null) {
            return node;
        }
        if (node.left != null) {
            return getMostRight(node.left);
        } else {
            Node parent = node.parent;
            while (parent != null && node != parent.right) {
                node = parent;
                parent = node.parent;
            }
            return parent;
        }
    }

    /**
     * 返回以node为根节点的最右边节点
     *
     * @param node
     * @return
     */
    private static Node getMostRight(Node node) {
        while (node.right != null) {
            node = node.right;
        }
        return node;
    }

    public static void main(String[] args) {
        Node head = new Node(6);
        head.parent = null;
        head.left = new Node(3);
        head.left.parent = head;
        head.left.left = new Node(1);
        head.left.left.parent = head.left;
        head.left.left.right = new Node(2);
        head.left.left.right.parent = head.left.left;
        head.left.right = new Node(4);
        head.left.right.parent = head.left;
        head.left.right.right = new Node(5);
        head.left.right.right.parent = head.left.right;
        head.right = new Node(9);
        head.right.parent = head;
        head.right.left = new Node(8);
        head.right.left.parent = head.right;
        head.right.left.left = new Node(7);
        head.right.left.left.parent = head.right.left;
        head.right.right = new Node(10);
        head.right.right.parent = head.right;

        Node test = head.left.left;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.left.left.right;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.left;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.left.right;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.left.right.right;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.right.left.left;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.right.left;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.right;
        System.out.println(test.value + " next: " + getSuccessorNode(test).value);
        test = head.right.right; // 10's next is null
        System.out.println(test.value + " next: " + getSuccessorNode(test));
    }

}