<p>You are given the <code>root</code> of a binary tree and an integer <code>distance</code>. A pair of two different <strong>leaf</strong> nodes of a binary tree is said to be good if the length of <strong>the shortest path</strong> between them is less than or equal to <code>distance</code>.</p>

<p>Return <em>the number of good leaf node pairs</em> in the tree.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/09/e1.jpg" style="width: 250px; height: 250px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,null,4], distance = 3
<strong>Output:</strong> 1
<strong>Explanation:</strong> The leaf nodes of the tree are 3 and 4 and the length of the shortest path between them is 3. This is the only good pair.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/09/e2.jpg" style="width: 250px; height: 182px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,5,6,7], distance = 3
<strong>Output:</strong> 2
<strong>Explanation:</strong> The good pairs are [4,5] and [6,7] with shortest path = 2. The pair [4,6] is not good because the length of ther shortest path between them is 4.
</pre>

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

<pre>
<strong>Input:</strong> root = [7,1,4,6,null,5,3,null,null,null,null,null,2], distance = 3
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only good pair is [2,5].
</pre>

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

<ul>
	<li>The number of nodes in the <code>tree</code> is in the range <code>[1, 2<sup>10</sup>].</code></li>
	<li><code>1 &lt;= Node.val &lt;= 100</code></li>
	<li><code>1 &lt;= distance &lt;= 10</code></li>
</ul>

/**
 * 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:
    int countPairs(TreeNode* root, int distance) {
        // if level(leaf1) == level(leaf2) then distance(leaf1, leaf2) == 2 or level(leaf1) * 2
        // else distance(leaf1, leaf2) == 2 + abs(level(leaf1) - level(leaf2)) or 2 * min(level(leaf1) + level(leaf2)) + abs(level(leaf1) - level(leaf2))
        std::unordered_map<TreeNode*, std::vector<TreeNode*>> nodeMap;
        dfs(root, nodeMap, std::vector<TreeNode*>());
        int count = 0;
        for (auto iter = nodeMap.begin(); iter != nodeMap.end(); ++iter) {
            for (auto iter2 = std::next(iter); iter2 != nodeMap.end(); ++iter2) {
                int i = 0;
                while (i < std::min(iter->second.size(), iter2->second.size()) && iter->second[i] == iter2->second[i]) {
                    ++i;
                }
                int dist = iter->second.size() + iter2->second.size() - i * 2 + 2;
                if (dist <= distance) {
                    ++count;
                }
            }
        }
        return count;
    }

private:
    void dfs(TreeNode* node, std::unordered_map<TreeNode*, std::vector<TreeNode*>>& nodeMap, std::vector<TreeNode*> path) {
        if (!node) {
            return;
        }

        if (leaf(node)) {
            nodeMap[node] = path;
            return;
        }
        path.emplace_back(node);
        dfs(node->left, nodeMap, path);
        dfs(node->right, nodeMap, path);
    }

    bool leaf(TreeNode* node) {
        return node && !node->left && !node->right;
    }

};
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