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# 437 Path Sum III

## 437. Path Sum III

## 1. Question

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
```

## 2. Implementation

(1) DFS

```java
 class Solution {
    public int pathSum(TreeNode root, int sum) {
        if (root == null) {
            return 0;
        }

        return findPathSum(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum);
    }

    public int findPathSum(TreeNode node, int sum) {
        if (node == null) {
            return 0;
        }

        int count = 0;

        if (node.val == sum) {
            ++count;
        }

        count += findPathSum(node.left, sum - node.val);
        count += findPathSum(node.right, sum - node.val);
        return count;
    }
}
```

## 3. Time & Space Complexity

DFS: 时间复杂度:O(n^2) , 空间复杂度: O(n)