<p>Given the <code>root</code> of a binary tree, the depth of each node is <strong>the shortest distance to the root</strong>.</p>

<p>Return <em>the smallest subtree</em> such that it contains <strong>all the deepest nodes</strong> in the original tree.</p>

<p>A node is called <strong>the deepest</strong> if it has the largest depth possible among any node in the entire tree.</p>

<p>The <strong>subtree</strong> of a node is a tree consisting of that node, plus the set of all descendants of that node.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/07/01/sketch1.png" style="width: 600px; height: 510px;" />
<pre>
<strong>Input:</strong> root = [3,5,1,6,2,0,8,null,null,7,4]
<strong>Output:</strong> [2,7,4]
<strong>Explanation:</strong> We return the node with value 2, colored in yellow in the diagram.
The nodes coloured in blue are the deepest nodes of the tree.
Notice that nodes 5, 3 and 2 contain the deepest nodes in the tree but node 2 is the smallest subtree among them, so we return it.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> root = [1]
<strong>Output:</strong> [1]
<strong>Explanation:</strong> The root is the deepest node in the tree.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> root = [0,1,3,null,2]
<strong>Output:</strong> [2]
<strong>Explanation:</strong> The deepest node in the tree is 2, the valid subtrees are the subtrees of nodes 2, 1 and 0 but the subtree of node 2 is the smallest.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree will be in the range <code>[1, 500]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 500</code></li>
	<li>The values of the nodes in the tree are <strong>unique</strong>.</li>
</ul>

<p>&nbsp;</p>
<p><strong>Note:</strong> This question is the same as 1123: <a href="https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/" target="_blank">https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/</a></p>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    #define INF 1000000000
    TreeNode* ans = NULL;
    TreeNode* subtreeWithAllDeepest(TreeNode* root) {
        vector<vector<int>> adj(501);
        toAdj(root, adj);
        // use bfs
        vector<int> distance(501, INF);
        distance[root->val] = 0;
        vector<int> pred(501, -1);
        int max_depth = 0;
        queue<int> q;
        q.push(root->val);
        while(q.size()) {
            int u = q.front();
            q.pop();
            for(int i = 0; i < adj[u].size(); i++)
                if(distance[adj[u][i]] == INF) {
                    distance[adj[u][i]] = distance[u]+1;
                    max_depth = max(max_depth, distance[adj[u][i]]);
                    pred[adj[u][i]] = u;
                    q.push(adj[u][i]);
                }
        }
        vector<int> nums;
        for(int i = 1; i <= 500; i++)
            if(distance[i] == max_depth)
                nums.push_back(i);
        if(nums.size() == 1) {
            TreeNode* node = new TreeNode(nums[0]);
            return node;
        }
        while(1) {
            for(int i = 0; i < nums.size(); i++)
                nums[i] = pred[nums[i]];
            bool isFind = true;
            for(int j = 0; j < nums.size()-1; j++)
                if(nums[j] != nums[j+1]) {
                    isFind = false;
                    break;
                }
            if(isFind) {
                findSubtree(root, nums[0]);
                return ans;
                break;
            }
        }
        return ans;
    }
    void toAdj(TreeNode* node, vector<vector<int>>& adj) {
        if(node) {
            if(node->left) {
                adj[node->val].push_back(node->left->val);
                adj[node->left->val].push_back(node->val);
                toAdj(node->left, adj);
            }
            if(node->right) {
                adj[node->val].push_back(node->right->val);
                adj[node->right->val].push_back(node->val);
                toAdj(node->right, adj);
            }
        }
    }
    void findSubtree(TreeNode* node, int target) {
        if(node) {
            if(node->val == target) {
                ans = node;
                return;
            }
            findSubtree(node->left, target);
            findSubtree(node->right, target);
        }
    }
};
16900