# 437. Path Sum III (Easy)

https://leetcode.com/problems/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
```

## Solutions

``````class Solution {
public int pathSum(TreeNode root, int sum) {

// keep the track of visiting path

return traverse(root, path, sum);
}

private int traverse(TreeNode root, LinkedList<Integer> path, int target) {
int ans = 0;
if (root == null) {
return ans;
}

int sum = 0;
int len = path.size();
for (int i = len - 1; i >= 0; i--) {
sum += path.get(i);
if (sum == target) {
ans++;

// do not break once found, there may contains 0 values that brings in another combination
}
}

ans += traverse(root.left, path, target);
ans += traverse(root.right, path, target);

path.removeLast();

return ans;
}
}
``````