**Problem:**

Please find the problem here.

**Analysis:**

A standard idea is to build a frequency table. Once the table is built, we go through the table to find out who are the winners. In the worst case where the tree has all distinct elements, this will lead to an extra linear space.

**Solution:**

The key idea is that we can do an in-order traversal of the tree to get a sorted order. We build the tree as usual with a single difference - the table only contain two entries. The current best entry, and the last number entry. Suppose an element X doesn't have enough count, and in the in-order traversal we see Y now, X is never going to win, so we can get X out of the table. Now we have a constant

**space algorithm! (Of course, you still need to save all the answers to report them, which, in the worst case, linear)**

*extra***Code：**

#include "stdafx.h" // https://leetcode.com/problems/find-mode-in-binary-search-tree/ #include "LEET_FIND_MODE_IN_BINARY_SEARCH_TREE.h" #include <map> #include <iostream> #include <sstream> #include <vector> #include <string> using namespace std; namespace _LEET_FIND_MODE_IN_BINARY_SEARCH_TREE { struct TreeNode { int val; TreeNode *left; TreeNode *right; TreeNode(int x) : val(x), left(NULL), right(NULL) {} }; class Solution { public: void findMode(TreeNode* root, vector<int>& result, int& max_count, int& last_node, int& last_count) { if (root == nullptr) { return; } if (root->left != nullptr) { findMode(root->left, result, max_count, last_node, last_count); } if (max_count == 0) { // This is possible only for the very first call result.push_back(root->val); max_count = 1; last_node = root->val; last_count = 1; } else { if (root->val == last_node) { last_count++; } else { last_node = root->val; last_count = 1; } if (last_count == max_count) { result.push_back(last_node); } else if (last_count > max_count) { result.clear(); result.push_back(last_node); max_count = last_count; } } if (root->right != nullptr) { findMode(root->right, result, max_count, last_node, last_count); } } vector<int> findMode(TreeNode* root) { vector<int> result; int max_count = 0; int last_node = 0; int last_count = 0; findMode(root, result, max_count, last_node, last_count); return result; } }; }; using namespace _LEET_FIND_MODE_IN_BINARY_SEARCH_TREE; int LEET_FIND_MODE_IN_BINARY_SEARCH_TREE() { Solution solution; TreeNode a(1); TreeNode b(2); TreeNode c(2); a.left = nullptr; a.right = &b; b.left = &c; b.right = nullptr; c.left = nullptr; c.right = nullptr; vector<int> result = solution.findMode(&a); for (int i = 0; i < result.size(); i++) { cout << result[i] << endl; } return 0; }

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