437. 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

Solution:

We can recursively check:

1. can we get a path sum to target from current node?
2. can we get a path sum to target from the child of this node?


Code:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int pathSum(TreeNode root, int sum) {
        if (root == null) {
            return 0;
        }
        return helper(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum);
    }
    
    public int helper(TreeNode root, int sum) {
        if (root == null) {
            return 0;
        }
        return (sum == root.val ? 1 : 0) + helper(root.left, sum - root.val) + helper(root.right, sum - root.val);
    }
}