# Leetcode: Path Sum III

Path Sum III

Similar Problems:

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
```

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

```// Blog link: https://code.dennyzhang.com/path-sum-iii
// Basic Ideas: Recursive
// Complexity: Time O(n^2), Space O(n)
/**
* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/

func pathSumFrom(root *TreeNode, sum int) int {
if root == nil { return 0 }
res := 0
if root.Val == sum { res++ }
res += pathSumFrom(root.Left, sum-root.Val)
res += pathSumFrom(root.Right, sum-root.Val)
return res
}

func pathSum(root *TreeNode, sum int) int {
if root == nil { return 0 }
return pathSumFrom(root, sum) + pathSum(root.Left, sum) + pathSum(root.Right, sum)
}
```

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