<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:
    // vector<int> solve(TreeNode* root, int& dist, int& cnt) {
    //     if (root == NULL) {
    //         return {};
    //     }
    //     if (root->left == NULL && root->right == NULL) {
    //         return {1};
    //     }

    //     vector<int> leftNodes= solve(root->left, dist, cnt);
    //     vector<int> rightNodes= solve(root->right, dist, cnt);

    //     for (int i: leftNodes) {
    //         for (int j: rightNodes) {
    //             if (i + j <= dist) {
    //                 cnt++;
    //             }
    //         }
    //     }

    //     vector<int> res;
    //     for (int i: leftNodes) {
    //         if (i +1 <= dist) {
    //             res.push_back(i+1);
    //         }
    //     }
    //     for (int i: rightNodes) {
    //         if (i +1 <= dist) {
    //             res.push_back(i+1);
    //         }
    //     }
    //     return res;
    // }


    unordered_map<int, int> solve(TreeNode* root, int distance, int& cnt) {
        if (!root) {
            return {};
        }
        if (!root->left && !root->right) {
            return {{1, 1}};
        }
        
        unordered_map<int, int> leftDistances = solve(root->left, distance, cnt);
        unordered_map<int, int> rightDistances = solve(root->right, distance, cnt);
        
        // Compare pairs of leaf nodes from left and right subtrees
        for (const auto& left : leftDistances) {
            for (const auto& right : rightDistances) {
                if (left.first + right.first <= distance) {
                    cnt += left.second * right.second;
                }
            }
        }
        
        // Increment the distance for all nodes in the left and right subtree
        unordered_map<int, int> result;
        for (const auto& d : leftDistances) {
            if (d.first + 1 <= distance) {
                result[d.first + 1] += d.second;
            }
        }
        for (const auto& d : rightDistances) {
            if (d.first + 1 <= distance) {
                result[d.first + 1] += d.second;
            }
        }
        
        return result;
    }


    int countPairs(TreeNode* root, int distance) {
        int cnt= 0;
        solve(root, distance, cnt);
        return cnt;
    }
};
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