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


Solution

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
def pathSum(self, root, sum):
"""
:type root: TreeNode
:type sum: int
:rtype: int
"""
if root is None:
return 0
else:
res = 0
res += self.pathFromRoot(sum, root)
if root.left is not None:
res += self.pathSum(root.left, sum)
if root.right is not None:
res += self.pathSum(root.right, sum)
return res

# Find number of paths from root
def pathFromRoot(self, residual, root):
if root is None:
if residual == 0:
return 1
else:
return 0

else:
if root.left is None and root.right is None:
if residual == root.val:
return 1
else:
return 0
else:
res = 0 if residual != root.val else 1
if root.left is not None:
res += self.pathFromRoot(residual - root.val, root.left)
if root.right is not None:
res += self.pathFromRoot(residual - root.val, root.right)

return res