# Easy to understand recursive C++ solution with explanation

• We can find the solution in either of the 3 manners

1. Some path adds up to sum from the root (i.e. root is a member of the path)
2. Root is not a member of the path and solution lies completely in left sub-tree
3. Root is not a member of the path and solution lies completely in right sub- tree

2 & 3 are taken care of by recursion in the function pathSum()

Case 1 is taken care of in pathSumRec() function.
In this the solution can be reached in three steps again.

1. Root == sum
2. Root + some path in left subtree
3. Root + some path in right subtree
``````
/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Solution {
public:

int pathSumRec(TreeNode* root, int sum) {

if(root == NULL)
return 0;

int rootmatch =  (root->val == sum);
int left = pathSumRec(root->left, sum - root->val);
int right = pathSumRec(root->right, sum - root->val);

return rootmatch + left + right;

}

int pathSum(TreeNode* root, int sum) {

if (root == NULL)
return 0;

int rootval =  pathSumRec(root, sum);
int lefttree = pathSum(root->left, sum);
int righttree = pathSum(root->right, sum);
return (rootval + lefttree + righttree);

}
};

``````

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