<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>

class Solution {
private:
    bool isLeaf(TreeNode* node){
        return (!node->left && !node->right);
    }
    void traverse(TreeNode* node, vector <TreeNode*> &leafNodes){
        if (isLeaf(node)){
            leafNodes.push_back(node);
            return;
        }
        if (node->left) traverse(node->left, leafNodes);
        if (node->right) traverse(node->right, leafNodes);
    }
    void markParents(TreeNode* root, map <TreeNode*, TreeNode*> &parentof){
        queue <TreeNode*> q;
        q.push(root);
        while(!q.empty()){
            TreeNode* node = q.front(); q.pop();
            if (node->left){
                parentof[node->left] = node;
                q.push(node->left);
            }
            if (node->right){
                parentof[node->right] = node;
                q.push(node->right);
            }
        }
        return;
    }
    void helper(TreeNode* node, int dist, map <TreeNode*, TreeNode*> &parentof, set<TreeNode*> &pathVis, int &count){
        if (dist<0) return;
        if (isLeaf(node)){
            count++;
        }
        if (node->left && pathVis.find(node->left) == pathVis.end()){
            pathVis.insert(node->left);
            helper(node->left, dist-1, parentof, pathVis, count);
            pathVis.erase(node->left);
        }
        if (node->right && pathVis.find(node->right) == pathVis.end()){
            pathVis.insert(node->right);
            helper(node->right, dist-1, parentof, pathVis, count);
            pathVis.erase(node->right);
        }
        if (parentof.find(node)!=parentof.end() && pathVis.find(parentof[node]) == pathVis.end()){
            pathVis.insert(parentof[node]);
            helper(parentof[node], dist-1, parentof, pathVis, count);
            pathVis.erase(parentof[node]);
        }
        return;
    }
public:
    int countPairs(TreeNode* root, int distance) {
        vector <TreeNode*> leafNodes;
        map <TreeNode*, TreeNode*> parentof;
        markParents(root, parentof);
        // cout<<parentof.size()<<endl;
        int count = 0;
        traverse(root, leafNodes);
        // cout<<leafNodes.size()<<endl;
        for(auto node: leafNodes){
            count--;
            set <TreeNode*> pathVis;
            pathVis.insert(node);
            helper(node, distance, parentof, pathVis, count);
        }
        return count>>1;
    }
};
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