day-130.cpp

/*
  Path Sum III


You are given a binary tree in which each node contains an integer value.

Find the number of paths that sum to a given value.

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

The tree has no more than 1,000 nodes and the values are in the range -1,000,000
to 1,000,000.

Example:

root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8

      10
     /  \
    5   -3
   / \    \
  3   2   11
 / \   \
3  -2   1

Return 3. The paths that sum to 8 are:

1.  5 -> 3
2.  5 -> 2 -> 1
3. -3 -> 11
*/

// Simple recursion approach to solve the problem.
// Calling pathSumUtils for each node in the tree
// So we can continue the search for targetSum from each node to bottom of the
// tree
class Solution {
   public:
    int pathSumUtils(TreeNode* root, int sum) {
        if (root == NULL) return 0;
        int result = 0;
        if (sum == root->val) result += 1;
        result += pathSumUtils(root->left, sum - root->val);
        result += pathSumUtils(root->right, sum - root->val);
        return result;
    }

    int pathSum(TreeNode* root, int sum) {
        if (root == NULL) return 0;
        return pathSum(root->left, sum) + pathSumUtils(root, sum) +
               pathSum(root->right, sum);
    }
};