<p>Given the <code>root</code> of a binary tree and an integer <code>targetSum</code>, return <em>the number of paths where the sum of the values&nbsp;along the path equals</em>&nbsp;<code>targetSum</code>.</p>

<p>The path does not need to start or end at the root or a leaf, but it must go downwards (i.e., traveling only from parent nodes to child nodes).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/09/pathsum3-1-tree.jpg" style="width: 450px; height: 386px;" />
<pre>
<strong>Input:</strong> root = [10,5,-3,3,2,null,11,3,-2,null,1], targetSum = 8
<strong>Output:</strong> 3
<strong>Explanation:</strong> The paths that sum to 8 are shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> root = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[0, 1000]</code>.</li>
	<li><code>-10<sup>9</sup> &lt;= Node.val &lt;= 10<sup>9</sup></code></li>
	<li><code>-1000 &lt;= targetSum &lt;= 1000</code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     long val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(long x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(long x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    long targetSum;
    long numPaths;
    vector<long> getSums(TreeNode* node){
        if (node == nullptr){
            vector<long> vec(0);
            return vec;
        }
        else{
            vector<long> result;
            vector<long> vec1 = getSums(node->left);
            vector<long> vec2 = getSums(node->right);

            result.reserve(vec1.size() + vec2.size() + 1);
    
    // Move elements from vec1 to result
            result.insert(result.end(), make_move_iterator(vec1.begin()), make_move_iterator(vec1.end()));
    
    // Move elements from vec2 to result
            result.insert(result.end(), make_move_iterator(vec2.begin()), make_move_iterator(vec2.end()));
    
            for (long i=0; i<result.size(); i++){
                result[i] += node->val;
                if (result[i] == this->targetSum) numPaths++;
            }

            if (node->val == this->targetSum) numPaths++;
            result.push_back(node->val);

            return result;

        }
    }
    long pathSum(TreeNode* root, long targetSum) {
        this->targetSum = targetSum;
        this->numPaths = 0;

        this->getSums(root);
        return this->numPaths;

        
    }
};
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