<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 {
    pair<int, vector<int>> GoodLeafPairsInTree(TreeNode* root, int distance) {
        // return int as good pairs within the tree, vector<int> is the depths
        // of the leafs in the tree
        int leftPairs = 0, rightPairs = 0, crossPairs = 0;
        vector<int> leftDepths, rightDepths;
        // Base Case (Leaf)
        if (root->left == NULL && root->right == NULL) {
            return {0, {0}};
        }
        // Divide and Conquer
        if (root->left != NULL) {
            auto pairsDepths = GoodLeafPairsInTree(root->left, distance);
            leftPairs = pairsDepths.first;
            leftDepths = pairsDepths.second;
        }
        if (root->right != NULL) {
            auto pairsDepths = GoodLeafPairsInTree(root->right, distance);
            rightPairs = pairsDepths.first;
            rightDepths = pairsDepths.second;
        }
        // Combine
        vector<int> depths;
        if (!leftDepths.empty()) {
            for (auto leftD : leftDepths) {
                depths.push_back(leftD + 1);
            }
        }
        if (!rightDepths.empty()) {
            for (auto rightD : rightDepths) {
                depths.push_back(rightD + 1);
            }
        }
        if (!leftDepths.empty() && !rightDepths.empty()) {
            for (auto leftD : leftDepths) {
                for (auto rightD : rightDepths) {
                    if (leftD + rightD + 2 <= distance) {
                        crossPairs++;
                    }
                }
            }
        }
        // cout<<"at node "<<root->val<<" pairs= "<<leftPairs + rightPairs + crossPairs<<"depths= ";
        // for(auto d : depths){
        //     cout<<d<<" ";
        // }
        // cout<<endl;
        return {leftPairs + rightPairs + crossPairs, depths};
    }

public:
    int countPairs(TreeNode* root, int distance) {
        pair<int, vector<int>> ans = GoodLeafPairsInTree(root, distance);
        return ans.first;
    }
};
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