# 437 Path Sum III

### Problem

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
``````

### Solutions

``````/**
* 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) {
HashMap<Integer, Integer> sums = new HashMap<Integer, Integer>();
sums.put(0, 1);
int[] res = new int[1];
process(root, res, 0, sum, sums);
return res[0];
}
private void process(TreeNode node, int[] res, int currSum, int sum, HashMap<Integer, Integer> sums) {
if (node == null) {
return;
}
int newSum = currSum + node.val;
if (sums.containsKey(newSum - sum)) {
res[0] += sums.get(newSum - sum);
}
if (!sums.containsKey(newSum)) {
sums.put(newSum, 0);
}
sums.put(newSum, sums.get(newSum) + 1);
process(node.left, res, newSum, sum, sums);
process(node.right, res, newSum, sum, sums);
sums.put(newSum, sums.get(newSum) - 1);
}
}
``````