剑指Offer-题54（Java版）：二叉搜索树的第k个结点

参考自：《剑指Offer——名企面试官精讲典型编程题》

题目：二叉搜索树的第k个结点
给定一棵二叉搜索树，按节点值从小到大排列，找出其中的第k（k≥1）个结点。

主要思路：使用中序遍历，每遍历一个节点时，判断k的值，若k等于1，则当前遍历到的节点就是所求节点，否则使k减1。

关键点：中序遍历

时间复杂度：O(n)

public class KthNodeOfTree
{
    private static TreeNode result;
    private static int runK;

    public static void main(String[] args)
    {
//            10
//         /      \
//        6        14
//       /\        /\
//      4  8     12  16
        TreeNode root = TreeNode.generateBinaryTree();
        System.out.println(findKthNode(root, 1).val);  //4
        System.out.println(findKthNode(root, 3).val);  //8
        System.out.println(findKthNode(root, 5).val);  //12
        //System.out.println(findKthNodeByLoop(root, 5).val);  //12
    }

    private static TreeNode findKthNode(TreeNode root, int k)
    {
        if (root == null || k == 0) return null;
        result = null;
        runK = k;
        findKthNode(root);
        return result;
    }

    //递归
    private static void findKthNode(TreeNode root)
    {
        if (root == null || result != null) return;
        //中序遍历，先遍历左节点
        findKthNode(root.left);
        if (result == null)
        {
            if (runK == 1)
            {
                result = root;
                return;
            }
            runK--;
        }
        //遍历右节点
        findKthNode(root.right);
    }

    //循环
    private static TreeNode findKthNodeByLoop(TreeNode root, int k)
    {
        Stack<TreeNode> stack = new Stack<>();
        TreeNode cur = root;
        while (cur != null || !stack.isEmpty())
        {
            while (cur != null)
            {
                stack.push(cur);
                cur = cur.left;
            }
            if (!stack.isEmpty())
            {
                cur = stack.pop();
                if (k == 1)
                {
                    return cur;
                }
                k--;
                cur = cur.right;
            }
        }
        return null;
    }
}

class TreeNode
{
    public  int val;
    public  TreeNode left;
    public  TreeNode right;

    public TreeNode(int x)
    {
        val = x;
    }

//            10
//         /      \
//        6        14
//       /\        /\
//      4  8     12  16
    /**
     * 生成二叉搜索树
     * @return
     */
    public static TreeNode generateBinaryTree()
    {
        TreeNode root = new TreeNode(10);
        TreeNode node6 = new TreeNode(6);
        TreeNode node14 = new TreeNode(14);
        TreeNode node4 = new TreeNode(4);
        TreeNode node8 = new TreeNode(8);
        TreeNode node12 = new TreeNode(12);
        TreeNode node16 = new TreeNode(16);
        connectNode(root, node6, node14);
        connectNode(node6, node4, node8);
        connectNode(node14, node12, node16);
        return root;
    }

    public static void connectNode(TreeNode root, TreeNode left, TreeNode right)
    {
        root.left = left;
        root.right = right;
    }
}