C#LeetCode刷题之#501-二叉搜索树中的众数​​​​​​​（Find Mode in Binary Search Tree）

问题

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给定一个有相同值的二叉搜索树（BST），找出 BST 中的所有众数（出现频率最高的元素）。

假定 BST 有如下定义：

结点左子树中所含结点的值小于等于当前结点的值

结点右子树中所含结点的值大于等于当前结点的值

左子树和右子树都是二叉搜索树

给定 BST [1,null,2,2],

1

    \

     2

    /

   2

返回[2].

提示：如果众数超过1个，不需考虑输出顺序

进阶：你可以不使用额外的空间吗？（假设由递归产生的隐式调用栈的开销不被计算在内）

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Given a binary search tree (BST) with duplicates, find all the mode(s) (the most frequently occurred element) in the given BST.

Assume a BST is defined as follows:

The left subtree of a node contains only nodes with keys less than or equal to the node's key.

The right subtree of a node contains only nodes with keys greater than or equal to the node's key.

Both the left and right subtrees must also be binary search trees.

Given BST [1,null,2,2],

1

    \

     2

    /

   2

return [2].

Note: If a tree has more than one mode, you can return them in any order.

Follow up: Could you do that without using any extra space? (Assume that the implicit stack space incurred due to recursion does not count).

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示例

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public class Program {

    public static void Main(string[] args) {
        var root = new TreeNode(1) {
            left = new TreeNode(3) {
                left = new TreeNode(5),
                right = new TreeNode(7)
            },
            right = new TreeNode(9)
        };

        var res = FindMode(root);
        ShowArray(res);

        Console.ReadKey();
    }

    static void ShowArray(int[] array) {
        foreach(var num in array) {
            Console.Write($"{num} ");
        }
        Console.WriteLine();
    }

    public static int[] FindMode(TreeNode root) {
        if(root == null) return new int[0];
        var dic = new Dictionary<int, int>();
        PreOrder(root, ref dic);
        var max = dic.Values.Max();
        return (from r in dic
                where r.Value == max
                select r.Key).ToArray();
    }

    public static void PreOrder(TreeNode root, ref Dictionary<int, int> dic) {
        if(root == null) return;
        if(dic.ContainsKey(root.val)) {
            dic[root.val]++;
        } else {
            dic[root.val] = 1;
        }
        PreOrder(root?.left, ref dic);
        PreOrder(root?.right, ref dic);
    }

    public class TreeNode {
        public int val;
        public TreeNode left;
        public TreeNode right;
        public TreeNode(int x) { val = x; }
    }

}

以上给出1种算法实现，以下是这个案例的输出结果：

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1 3 5 7 9

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分析：

显而易见，以上算法的时间复杂度为：  。