<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>

#pragma GCC optimize("Ofast")
static auto _ = [](){std::ios::sync_with_stdio(false); std::cin.tie(nullptr); return nullptr;}();

class Solution {
    std::map<int, std::vector<TreeNode*>> map;
    void dfs(TreeNode *node, int depth = 0) {
        if(node == nullptr) return;
        if(node->left == nullptr && node->right == nullptr) {
            if(map.empty()) {
                map[depth].push_back(node);
            } else {
                int currMaxDepth = (*(map.rbegin())).first;
                if(depth > currMaxDepth) {
                    map.clear();
                    map[depth].push_back(node);
                } else if(currMaxDepth == depth) {
                    map[depth].push_back(node);
                }
            }
            return;
        }
        dfs(node->left, depth + 1);
        dfs(node->right, depth + 1);
    }

    TreeNode *getLca(TreeNode *node, TreeNode *p, TreeNode *q) {
        if(node == nullptr) return nullptr;
        if(p->val == node->val || q->val == node->val) return node;

        TreeNode *left = getLca(node->left, p, q);
        TreeNode *right = getLca(node->right, p, q);

        if(left && right) return node;
        return left ? left : right;
    }

public:
    TreeNode* lcaDeepestLeaves(TreeNode* root) {
        dfs(root);
        std::vector<TreeNode*> last = (*(map.rbegin())).second;
        if(last.size() == 1) return last[0];
        TreeNode *lca = getLca(root, last[0], last[1]);
        int n = last.size();
        for(int i = 2; i < n; i++) {
            lca = getLca(root, lca, last[i]);
        }
        return lca;
    }
};
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