<p>Given the <code>root</code> of a binary tree, return <em>the lowest common ancestor of its deepest leaves</em>.</p>

<p>Recall that:</p>

<ul>
	<li>The node of a binary tree is a leaf if and only if it has no children</li>
	<li>The depth of the root of the tree is <code>0</code>. if the depth of a node is <code>d</code>, the depth of each of its children is <code>d + 1</code>.</li>
	<li>The lowest common ancestor of a set <code>S</code> of nodes, is the node <code>A</code> with the largest depth such that every node in <code>S</code> is in the subtree with root <code>A</code>.</li>
</ul>

<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 leaf-nodes of the tree.
Note that nodes 6, 0, and 8 are also leaf nodes, but the depth of them is 2, but the depth of nodes 7 and 4 is 3.</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, and it&#39;s the lca of itself.
</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 leaf node in the tree is 2, the lca of one node is itself.
</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, 1000]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 1000</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 865: <a href="https://leetcode.com/problems/smallest-subtree-with-all-the-deepest-nodes/" target="_blank">https://leetcode.com/problems/smallest-subtree-with-all-the-deepest-nodes/</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:


    struct Node {
        TreeNode * node;
        int depth;
        std::vector<TreeNode *> path;
        inline bool empty() {
            return node==nullptr;
        }
    };

    std::list<Node> deepestNodes(TreeNode * root) {
        

        std::deque<Node> queue;
        Node current{root, 0, {root}};

        int max_depth = 0;
        std::list<Node> nodes;

        while (!current.empty() || !queue.empty()) {

            while (!current.empty()) {
                queue.push_back(current);
                current.node = current.node->left;
                current.path.push_back(current.node);
                current.depth++;                
            }

            auto & node = queue.back();
            // printf("Found %d depth=%d\n",node.node->val, node.depth);
            if ( node.depth > max_depth) {
                max_depth = node.depth;
                nodes.clear();
            }
            if (node.depth == max_depth) {
                nodes.push_back(node);
            }
            current.node = node.node->right;
            current.depth = node.depth + 1;
            current.path = node.path;  
            current.path.push_back(current.node);          

            queue.pop_back();
        }

        return nodes;
    }

    TreeNode* lcaDeepestLeaves(TreeNode* root) {
        // two step
        // find deepest nodes.

        auto deepest = deepestNodes(root);

        if (deepest.size() == 1 ) {
            return deepest.front().node;
        }


        int max_depth = INT_MAX;
        
        for (auto & deep : deepest) {
            // printf("%d %d path=", deep.node->val, deep.depth);
            max_depth = std::min(max_depth, deep.depth);
        
        }


        TreeNode * lca = root;

        //printf("max depth = %d\n", max_depth);
        for (int i=0;i<=max_depth;i++){            
            TreeNode * last = deepest.front().path[i];
            for (auto & deep : deepest) {
                if (last != deep.path[i]){                    
                    return lca;
                }
            }
            lca = last;
        }

        return lca;
    }
};
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