<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>

class Solution {
public:
    int height(TreeNode* root) {
        if (!root) return 0;
        int left = height(root->left);
        int right = height(root->right);
        return 1 + max(left, right);
    }

    TreeNode* lca(TreeNode* a, TreeNode* b, unordered_map<TreeNode*, TreeNode*>& parent) {
        unordered_set<TreeNode*> ancestors;
        while (a) {
            ancestors.insert(a);
            a = parent[a];
        }
        while (b) {
            if (ancestors.contains(b)) {
                return b;
            }
            b = parent[b];
        }
        return nullptr;
    }

    TreeNode* lcaDeepestLeaves(TreeNode* root) {
        if (!root) return root;

        int maxDepth = height(root);
        unordered_map<TreeNode*, TreeNode*> parent;
        vector<TreeNode*> last;

        parent[root] = nullptr; 
        queue<pair<TreeNode*, int>> q;
        q.push({root, 1});

        while (!q.empty()) {
            auto [node, depth] = q.front();
            q.pop();

            if (depth == maxDepth) {
                last.push_back(node);
            }

            if (node->left) {
                parent[node->left] = node;
                q.push({node->left, depth + 1});
            }
            if (node->right) {
                parent[node->right] = node;
                q.push({node->right, depth + 1});
            }
        }
        if (last.size() == 1) {
            return last[0];
        }
        return lca(last[0], last[last.size()-1], parent);
    }
};

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