# Problem

https://leetcode.com/problems/path-sum-iii/description/

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 1: Recursion

Time complexity: O(n^2)

Space complexity: O(n)

C++

# Solution 2: Running Prefix Sum

Same idea to 花花酱 LeetCode 560. Subarray Sum Equals K

Time complexity: O(n)

Space complexity: O(h)

C++

# Related Problem

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